generation of non linear curves with computer aided ...

Ministry of Higher Education and Scientific Research Iraqi Commission for Computers & Informatics Informatics Institute For Post Graduate Studies

GENERATION OF NON LINEAR CURVES WITH COMPUTER AIDED APPLICATION

A Thesis Submitted to the Informatics Institute for Postgraduate Studies at the Iraqi Commission for Computers and Informatics as a partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science

By FIRAS HUSHAM AL-MUKHTAR

Supervisors Prof. Dr. HILAL M. YOUSIF

Dr. ABDUL-MONEEM S. R.

March - 2003

To My Mother, Father with Love, Respect and Affection To My Wife To the most beautiful creature in the world My Recently born girl “ Lara “

Supervisors Certification

We certify that the preparation of this thesis was made under our supervision in the partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science.

I would like to express my appreciation and thanks to Prof. Dr. Hilal Mohammed Yousif and Dr. Abdul-Moneem Salih for their consistent guidance, thoughtful comments, and support during the development of the project. A very special thanks are due to Prof. Jumaa Al-Wasity and to Dr. Khalil Al-Wasity for the big help and support they provide. I would like to thank the Informatics Institute for Postgraduate Studies for all the help and support they offered, not forgetting professors of the Ph.D. courses who were always a helping hand. And special thanks and gratitude are due to Al-Rafidain University College and the teaching staff for the big support and help, which made this research possible. I would like to express my sincere gratitude to my family for their encouragement and unlimited patience during the project.

Author

The laws are not the unique means for the prevention of forgery, but the technical means are the most effective way to protect the printed documents. Thus, we can define the term printed document security as the unability to reproduce the same product released from the original authority even if the same capabilities are provided for the forging party. The banknote is considered as an important economical aspect and its exchange stability expresses the strength of the country economy. The person’s trust with banknote is influenced with the banknote industry (printing) style that in its turn affects preventing counterfeiting. If any forgery banknote is discovered, this will affect the person’s confidence and thus he will try to use and possess foreign banknotes that have high trust and hence this leads to deteriorate of local banknotes. Therefore, we have tried to make a study, which is concerned with printing banknote documents in a high trusty way. This study is based on technical designs, where banknote documents consist of many curvature designs constructed from a mathematical models that not possible for any one to know because of the control points of these designs that are not visible in the printed designs. A wide variety of simple and complicated models have been established using mathematical and graphical applications, using special interpolation and approximation methods with eight techniques of curve generation, that provide the best conformance applications of curve and control points fitting. We worked in this research on three kinds of coordinates (Cartesian, Parametric and Polar coordinates) to generate non-linear curves drawn in parallel to construct a simple and complicated figures participating in the design process. Many important parts of the banknotes design were implemented in this research; these include (decorative backgrounds, portrait generation, guilloche, frames that surround the document and decorative letters and numbers). These designing elements have an important influence on the security aspects of the banknote document such that these elements are designed according to various mathematical models specially prepared for this purpose. All of the methods developed to protect the curve from regeneration are used in this system to get more secrecy for all of the figures making up banknote document.

Abbreviation Cn CAD CAM CMYK CPn CRT DOVD DPI H/W ID LED LPI MHz Nm PPI S/W SDDS UV V

Meaning nth order parametric Continuity Computer Aided Design Computer Aided Manufacturer Cyan, Magenta, Yellow, Black Convexity Preserving spline of order n Cathode Ray Tube Diffractive Optical Variable Duo tone Dot Per Inch Hardware Identification Light Emitting Diode Line Per Inch Mega Hertz Nano meter = 10-9 meter Pixel Per Inch Software Security Document Design System Ultra Violet Volt

Table No. 2-1 2-2 2-3 2-4 2-5 3-1 3-2 3-3 4-1 4-2 4-3

Page

Liquid Inkjet Advantages and Disadvantages. Solid Inkjet Advantages and Disadvantages. Laser Printer Advantages and Disadvantages. Thermal Wax Advantages and Disadvantages. Sublimation Printer Advantages and Disadvantages. Control Point. The Interpolation Results of the First Four Methods. The Interpolation Results of the Second Four Methods. The Control Points of Simple figure (Letter B). Interpolation of letter B with ∆t=1. Interpolation of the control points with two different intervals of t. 4-4 Interpolation of the Ideal Curvature Figure. 4-5 Interpolation Result of the control points when changing values of t. 4-6 Influence of the Guide Choice on the Produced Curve. 4-7 Polar Curve Interpolation. 4-8 Radius Method. 4-9 Original Raster Data. 4-10 Resulted Raster Data.

29 30 30 31 32 67 67 68 77 77 78 78 79 82 83 86 89 89

Subject

Page no.

Chapter One : Introduction 1.1 Introduction 1.2 Security Printing and Computer Graphics 1.3 The Importance of Computer Graphics 1.4 The Goal of this Research 1.5 Literature Review 1.6 Chapters Preview

1 1 3 4 4 11

Chapter Two : Printing Fundamentals and Banknote Features 2.1 Introduction 2.2 White Light and the Color Spectrum 2.3 Additive and Subtractive Colors 2.4 Pictorial Images 2.5 Halftone Image Formation 2.6 Color Reproduction 2.7 Electronic Color Separation 2.8 Image Size and Resolution 2.9 Printing Techniques 2.10 Digital Printing and Digital Printers 2.11 Ink and Paper 2.12 Importance of Document Security 2.13 Security Features in Banknotes

13 13 14 15 16 17 19 19 23 28 33 38 38

Chapter Three : Theoretical Aspects of Curve Generation 3.1 Introduction 3.2 Curve Fitting and Generation (Interpolation) 3.2.1 Lagrangian Polynomials 3.2.2 Neville's Method 3.2.3 Divided Differences 3.2.4 Least-Squares polynomials 3.2.5 Chebyshev Polynomials

52 53 53 55 55 58 59

3.2.6 Bezier Polynomials 3.2.7 B-Spline Polynomials 3.2.8 Cubic Spline 3.3 Case study 3.4 Coordinate Planes 3.5 Choosing the Suitable Coordinate Systems

61 62 64 66 71 73

Chapter Four : Development of Curve Security Techniques 4.1 Introduction 4.2 Parameterization Method 4.3 Arbitrary Point Control (area parameterisation) 4.4 Interpolation with Polar Coordinate 4.5 Radius Method 4.6 Steganography and Curve Hiding 4.6.1 Image Files 4.6.2 Types of Data Embedding 4.6.3 The Proposed Methods of Information Hiding 4.6.4 Embedding Types and Applications 4.6.4.1 Curve within Image 4.6.4.2 Text within Curve 4.6.4.3 Curve within Curve

75 76 81 83 85 87 87 88 88 89 89 91 91

Chapter Five : Banknote Security and design 5.1 Document Security 5.2 Security features in Banknotes 5.3 The use of security Features in Banknotes 5.4 Banknote Design 5.4.1 Family of Curves 5.4.2 Portrait Reproduction 5.4.2.1 Portrait Implementation Method 5.4.2.2 Contour Lines 5.4.2.3 Pixel Connectivity 5.4.2.4 Parametric Mesh 5.4.2.5 Superimposition of Separate Layers 5.4.3 Background Shadow Effects 5.4.4 Frames 5.4.5 Guilloche 5.4.6 Decorative Alphabets (Text and Type) 5.4.7 Special Anticopy Background Method

92 93 93 93 94 96 98 99 100 102 103 106 109 110 112 118

Chapter Six : Practical Work and Implementation 6.1 Introduction 6.2 System Requirement 6.3 System Implementation and Description 6.3.1 Main Menu 6.3.2 Secondary Menu 6.4 System Hierarchy 6.5 Case Study

121 122 122 123 131 134 136

Chapter Seven : Theoretical Aspects of Curve Generation 7.1 Conclusions 7.2 Recommendations for Future Work

138 139

References

141

Appendices

CHAPTER ONE INTRODUCTION

1.1 Introduction Documents must defend themselves against any forgery trial via their security features even if there is a law that protects certain rights of these documents. These rights, for example, comprise the right to access premises or computer databases (admission tickets, press cards, swipe card, ID card), to cross a border (passport, visa), to use a public telephone system (telephone token), the right to drive a car (driving license), to jobs (diploma’s), to goods (coins, banknotes, credit cards, gift vouchers), and the right to service (stamps, transport tickets, bank forms). These valuable documents must be protected against the misuse of those rights by forgery, counterfeiting and fraudulent impersonation. Document security involves the protection of documents against these infringements of our rights. Documents can be protected by adding security features to the document substrate, to the printing ink, to the printed design, and as postprinted features such as laminating foils, foil print, holograms, optically variable ink and other thin film devices. Printing Design Features are considered as the most important security feature used for increasing document security, and around this built the aesthetics. The importance comes from the privacy of designing features that depends on generating graphical compound and complicated imaginary decorative designing figures used at different stages of printing process, all of which are composed of a group of parallel curves having different shapes and patterns. These curves are distinguished with designing characteristics, which are the thin (finelines) and their approximated color degrees designed to be difficult to counterfeit.

1.2 Security Printing and Computer Graphics Security printing is often considered a specialized field in the graphics arts. Computer graphics is a topic of rapidly growing importance in the computer field. It has always been one of the most visually spectacular branches of computer technology, producing images whose 1

appearance and motion make them quite unlike any other form of computer output [Newman 1981]. Computer graphics is also an extremely effective medium for communication between man and computer; the human eye can absorb the information content of a displayed or perspective view much faster than it can scan a table of numbers [Demel 1984]. Every one must distinguish and have a consensus about what computer graphics and visualization are. The word graphics is associated with charts, graphs, images, pictures and patterns, often in the context of art, design or animation; visualization is the process of converting data into images [Gomes 1997]. In order to understand computer graphics, then, we must study the method for creating and structuring data in the computer as well as methods for turning these data into images. These two steps correspond to the two main areas of research in computer graphics: modeling and visualization [Gomes 1997]. Computer graphics has sought methods to allow the visualization of information stored in computer memory. Since there are practically no limitations on the nature or origins of such data, researchers and professionals use computer graphics today in the most diverse fields of human knowledge. Its use is important whenever it is necessary to have a visual representation of objects, actions, relations, or concepts [Egerton 1998]. Partly because computer graphics has so many applications, there are no sharp boundaries between it and related fields. However, we can take as a working criterion in differentiating among these fields the nature of the input and output of the process in question, as shown in Figure (1-1) [Egerton 1998].

Figure (1-1) Computer graphics and kindred disciplines. 2

In “data processing”, the system takes in data and after processing, returns data of more or less the same nature. In “computer graphics” the input data are (typically) nonvisual, and the output is an image that can be seen through some graphics output device. In “digital image processing” the input is already an image, which, gets processed to yield another image, the output. The goal of “computer vision” given an input image is to obtain information about the physical, geometric, or topological properties of the objects that appear in it. On a computer screen an image is produced using minute subdivisions of the screen called pixels. Each pixel is assigned a shade of gray, or of a color, and the groups of pixels are interpreted as points or lines or surfaces.

1.3 The Importance of Computer Graphics [Asthana 1993] The old Chinese saying “ One picture is worth a thousand words “ can be modified in the computer age into “ one picture is worth many kilobytes of data “ It is natural to expect that graphical communication, which is an older and more popular method of exchanging information than verbal communication, will often be more convenient when computers are utilized for this purpose. This is especially true for a large number of engineering applications where one must describe objects in 2D and 3D spaces. Often it is much easier to display these objects on the screen than to attempt to visualize them from many pages of computer output describing their geometrical shapes. There are two main reasons for the extreme usefulness of computer graphics for many applications:  The first reason is that the computer graphic representation of information may be not only an appropriate but also the only reasonable method of handling information. This fact is tersely expressed by the saying “ A picture is worth a thousands words”.  The second reason is given by the special kind of person–machine interaction that only computer graphics provides.

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1.4 The Goal of This Research The goal of this research is to design the printable banknote features through an interactive graphical editor system that uses a knowledge base keeps track the objects and curves generated by means of curve interpolation methods. The system then apply new created methods of security over the generated curves so as to keep the regeneration process much harder to perform by any counterfeiter, even if the counterfeiter has gained the original formula of curve generation. These security methods are applied to detect any graphical curvature forms, which exists within any document. These printable banknote curvature forms include: engraving portraits that are not an image but a shape composed of many layers of curves. They also include imposing backgrounds built upon a text or a picture. Other forms are the graphical decoration shapes such as boarders or frames surrounding the document, guilloches, decorative letters and numbers). In addition to curve designing and detection, it is important to be able to perform steganography or information hiding for the curves designed or texts, and this is performed with the system according to the new implementations methods and according to the objects used (either curves or texts) such that there is a capability of hiding objects within each other or within the background image of the systems main window.

1.5 Literature Review The design of security features primarily depends on a set of graphical shapes, which consist of a set of curves with many patterns and parameters. There are no literatures or studies concerned with how these security designs are performed, and on which manner or in which application, but a lot of these studies just mention such features in brief. We will try to describe these features in chapter 2. So this section is concerned with studies and literature surveys which focus on curve generation techniques and implementations performed during the previous last years so as to help us understand the nature of these methods or implementations and gives us a simple idea on how to redirect our work to a much more complicated applications, concerns with banknote designing features. These studies are reviewed and sorted according to the year of preparation, these include: 1.5.1 Plass and Stone Study (1983) A study in “Curve-Fitting with Piecewise Parametric Cubics ”, discusses the parametric piecewise-cubic functions that are used throughout the computer graphics industry to represent curved shapes. For many applications, it would be useful to be able to reliably derive this 4

representation from a closely spaced set of points that approximate the desired curve, such as the input from a digitizing tablet or a scanner. This research presents a solution to the problem of automatically generating efficient piecewise parametric cubic polynomial approximations to shapes from sampled data. A developed algorithm that takes a set of sample points, plus optional endpoint and tangent vector specifications, and iteratively derives a single parametric cubic polynomial that lies close to the data points as defined by an error metric based on least-squares. For the data in curve fitting work, the author’s has experimented with hand-tuned digital curves, optically scanned images and simple hand drawn sketches. Most of the work is performed with letter-font shapes. One of the goals of this study is to have a uniform resolution-independent font representation for digital printers. Many of the fonts are currently defined only as bitmaps. Therefore, this study has been motivated to apply methods to convert fonts from bitmaps to curve outlines. (Figure (1-2)) is an example of data derived from such bitmaps.

Figure (1-2 ) An example showing the steps involved in fitting a parametric cubic to a sampled shape.

1.5.2 Parm Study (1989) A research submitted to Monash University, Department of Computer science, presents a method of “Quadratic B-splines for Automatic Curve Fitting”, which passes curves through a given set of points needed to construct a computer aided design. Mathematical curve and surface representation methods allow the designer to modify interactivity curves and surfaces at the display using a small number of 5

guiding points. Quadratic B-spline method can be constructed by dividing the fitting process into two basic steps. Parabolas are firstly generated to fit any three of the given points; a quadratic B-spline is then constructed to fit each piecewise parabola to a prescribed error (Figure (1-3)). The method is based on a digital filter that will be presented as an alternative to a direct method using matrix inversion.

Figure (1-3 ) a piecewise quadratic b-spline that is tangential to the control polygon and ends at the first and last vertices 1.5.3 Barsky and Derose Study (1990) A research with a title “Geometric Continuity of Parametric Curves: Constructions of Geometrically Continuous Splines” describes three equivalent characterizations of geometric continuity that were developed in this article. The issue of continuity is associated with the stitching together of curve segments in a piecewise curve formulation. Geometric continuity arises in the context of the parametric representation. Parametric spline curves are typically constructed so that the first n parametric derivatives agree where the curve segments abut. This type of continuity condition has become known as Cn or nth-order parametric continuity. Geometric continuity of the nth order, denoted Cn, is a relaxed form of parametric continuity. The three equivalent characterizations of geometric continuity are. First, the concept of equivalent parameterizations is used to view geometric continuity as a measure of continuity; that is parameterization independent, a measure that is invariant under reparameterization. The second characterization developed a set of necessary and sufficient conditions, called Beta-constraints that must be satisfied to ensure geometric continuity of curves. Finally, the third characterization showed that two curves meet with Cn continuity if and only if their arc length parameterizations meet with Cn continuity. The author’s describes how Bezier curve segments can be stitched together with C1 or C2 continuity, using geometric constructions. These constructions lead to the development of geometric constructions for 6

quadratic C1 and cubic C2 Beta-splines. Finally, a geometrically continuous subclass of Catmull-Rom splines based on geometric continuity and possessing shape parameters is discussed (Figure (1-4)).

Figure(1-4) (A)The curve has B1 = 1, and is therefore equivalent to the C1 Cat mull-Rom b-spline, (B) the curve has B1 uniformly set to 1/2, (C) the values of B1 forth curve has been computed using a heuristic developed in this research. 1.5.4 Mineur , Lichah, Marie and Giaume Study (1990) A research under the title “A shape controlled fitting method for Bezier curves”, discusses the problem of controlling a shape when fitting a curve to a set of digitized data points by proceeding to a least squares approximation. A nonlinear method of solving this problem dedicated to the abstention of planar curves with a smooth and monotonous variation of curvature is introduced. This method uses particular Bezier curves, called typical curves, whose control polygon is partially constrained in order to provide the desired curve shape. The curve fitting principle is based on variations of the tangent direction at the ends of the curve. These variations are controlled by the displacement of a given curve point. An automatic procedure using this method to get a curve close to a set of data points has been implemented. An application to an airplane body shape design and a comparison with the least squares approximation method is presented and discussed (See Figure (1-5)).

Figure (1-5) Regions for a monotonic curvature variation 7

1.5.5 Piegel Study (1992) A research under the title “Interactive Data Interpolation by rational Bezier Curves”, presents that some interpolation techniques produce curves that the designer considers unsatisfactory. Even when the data points lie on an apparently simple curve, the resulting interpolant may not be the obvious one. L. Piegl produces an algorithm that combines interactive techniques with interpolation methods to allow user intervention. Rational Bezier curves are used as local interpolants, and an approach is discussed for exploiting shape parameters. To do this the algorithm patches together rational bezier conic/cubic segments and applies shape parameters to control the shape of the interpolant locally. The display of the interpolant is therefore not a post-processing step; however, interactive operations are used to modify the curve until it behaves as the draftsman wishes. Moreover, the use of the rational form provides for the application of such special curve segments as circular arcs and straight line segments that can be used, for instance, to round off sharp edges or remove unwanted bumps or wiggles (See Figure (1-6)).

Figure (1-6 ) Piecewise rational cubic interpolants to data obtained from a profile of a human face 1.5.6 Messac and Sivanandan Study (1995) A study in “A new family of convex splines for data interpolation” develops a new family of Convexity-Preserving splines of order n, hereby entitled the CPn-spline that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term. and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. Numerical results that allow for an assessment of the new spline are provided. In particular, a comparative analysis of the CPn-spline, the cubic spline is performed. By varying two parameters, the spline shape can be controlled at the local level, while other conventional means can be used to control the shape at the global level. The CPn-spline has no singularities in the case where inflection 8

points are present. Additionally, a less general form of the CPn-spline that applies to most practical cases can be implemented with extreme ease.

Figure (1-7) Comparison of convex spline (continuous line) and cubic spline (dashed) 1.5.7 Li and Zhang Study (1997) A useful study under the title of “ Basis conversion among Bezier and Tchebyshev ”, where B-spline and Bezier (a special case of B-spline) representations of curves and surfaces are the standard in most CAD/CAM systems. However, polynomial curves and surfaces in Tchebyshev form have found their applications in many geometric operations such as intersecting and offsetting where approximation approaches are involved. Due to the importance of Tchebyshev polynomials in CAD applications, this method concerns with how to convert a curve in Bezier basis into the one in Tchebyshev polynomials form. The author’s suggests a simple, stable and efficient method to convert a Bezier curve first into the power basis, then to the Tchebyshev basis. Since any basis conversion is a linear transformation, the conversion from Bezier to Tchebyshev may be represented as matrices and performed as a matrix multiplication. 9

1.5.8 Kamil Study (2001) A thesis of masters degree under the title “Intelligent system for Fingerprint Experts training“, submitted to the University of Technology, Department of Computer Science, deals with the identification of personal fingerprints. The fingerprints of an individual are unique and do not change throughout one's life, this makes them an ideal "signature" of a person. The basic unit of the fingerprint is a curve, hence the system adopt advanced mathematical approaches to generate curves, in Bezier and in cubic spline forms. The fingerprint is composed of many shapes such as Delta, Core and double core (See Figure (1-8)). Thus the curve forms of Bezier and cubic spline are suited well to design and regenerate the shapes of fingerprint. The system also provides a tool of training the various forms of fingerprint curves and forms to a training person.

Figure (1-8 ) Fingerprint form 1.5.9 Adle Study (2002) A thesis of masters degree under the title “Developing Mathematical Models of Curves for Using in Computer design”, submitted to the Military College of Engineering, Department of Computer Science, describes the simple techniques for increasing documents security by relying on mathematical techniques in controlling the printing of the required documents and by keeping its designing and quality features, whatever it differed in its printing. On that basis, the thesis adopts a mathematical model of curves of Spline functions, as a mathematical basis to generate the designing features of the printed documents as the banknote, passports and stamps. Two curve models are used, these are B-Spline and Cubic Spline are needed to generate the printing features of the portrait's that works in controlling the executive process of the printing die of the portrait by using CNC machine. 10

1.5.10 Idriss Study (2002) A thesis of masters degree under the title “Optimum number of Arabic letter points Curve Fitting “, submitted to the Informatics Institute of Post Graduate Studies of the Iraqi Commission for Computers and Informatics. This thesis deals with Arabic letters and describes the fact that Arabic scripts are cursive, and that Arabic letters that are connected together have many curves. This gives a special feature to the Arabic scripts and makes them different from other language letters. These features have produced technical problems in dealing with the Arabic language. To deal with these technical problems, and for the propose of efficient and fast printing of the Arabic letters, it is necessary to control the Arabic letters technically, through the control of the plots (or points) that represent the individual letter, also reduce the number of points representing each letter as few as possible, keeping the optimal shape of the letter and its peculiar curves. This is done using mathematical models that generate these curves that makeup the full shape of the letter. Using Cubic spline to generate curves because it is a good and efficient method for generate the Arabic letters that are full of curves and artifacts, also the number of points have been controlled to get the least number of points as possible, whether it is a separate or connected letter with their smooth peculiar curves.

1.6 Chapters Preview Chapter 2 “Printing Fundamentals and Banknote Features”, discusses in detail the steps, tools and equipments participating in achieving printing process; These include Ink, paper, digital printers and large printing machines. This chapter also includes a detailed description about the security features used to protect any document (ID card, passport, driving license, banknotes, credit cards, stamps, bank forms, etc.). These security features can be added to the document substrate, to the printing ink, to the printed design, and as post-printed features. Chapter 3 “Theoretical Aspects of Curve Generation”, with this chapter, we have tried to describe in detail, the most common known methods of interpolation and approximation used to generate a smooth curve. A comparison has also been made between the various methods of interpolation according to a set of control points which represents a simple figure showing the 11

strength and the weakness points of each method through a table of interpolated values. An interpolated figure is used for each of the methods to show where the fitting to the control point could happen describing each case in detail. We also proposes in this chapter the suitable coordinate system that could be used with each of the interpolation methods, since each method requires a special environment to work on. Chapter 4 “Developments of Curve Security techniques”, this chapter describes new invented methods that we have explored to protect the curve and to keep the process of its regeneration as secure as possible from any unauthorized person even if he knows the mathematical formulation needed to build the curve form. We also apply a method of steganography to hide a generated curve with other curve or hiding text within generated curve. Chapter 5 “Document Security and Design”, covers in detail the graphical security features we have proposed which are needed to construct a secure document, using a mathematical models combined with methods of interpolations necessary to generate suitable curve forms. These curve forms are used as a basis for any model involved in the design of secure document. These models include the generation of family of curves, portrait regeneration, imposing backgrounds, guilloches, boarders and decorative letters and numbers. Chapter 6 “Practical Work and Implementation” illustrates and discusses the execution of the proposed system in its various fields. This chapter also shows by example the steps required to perform a production design such as a stamp that is composed of many objects performed within this system. Chapter 7 “Conclusions and Recommendations” presents and discusses the results achieved with the proposed applicable system. It also gives recommendations to develop the system performance as a future work with new aspects and new design topics. Appendices A – F, Illustrates figures implemented using the proposed system, with many applicable examples. 12

Chapter Two PRINTING FUNDAMENTALS AND BANKNOTE FEATURES 2.1 Introduction Words and pictures, papers and inks, these are the material of the graphic designer. They are about to meet, go on a journey, and undergo several transformations, before ending up in printed and finished publications that you designed. Something that will communicate ideas and images to large numbers of people. But how do words and pictures get onto the printed page? Printing has always been a mysterious craft. So this chapter is prepared to introduce in detail the essential fundamentals concerning the process of printing, and try to explain the relations that put together components like light and color, images and resolutions, ink and paper, put them all in one template, called the Printing process. This chapter also reviews all the features used with banknote documents so as to provide the ultimate security means, protecting these valuable documents from any forgery attempt. Some of these features are printable, and thus we will try to concentrate of them since they have a big importance in our study research.

2.2 White Light and the Color Spectrum White light that is given off by the sun or a light bulb actually contains all the colors in the rainbow. If you pass white light through an ordinary prism, the light spreads out into a spectrum of colors. These colors generally classed as red, orange, yellow, green, blue, indigo, and violet-make up what is called the visible spectrum of light (Figure(2-1)). These are the frequencies of electromagnetic spectrum (“light”) that we can perceive with naked eye [Corrigan 1994].

Figure (2-1) Colors spectrum through a prism 13

Each part of this visible spectrum has its own unique value, which we call its color. Literally millions of different colors are available to choose from, and the transition from one color to the next is virtually indistinguishable (Figure (2-2)).

Figure (2-2) Visible spectrum range The human eye perceives only a small fraction of the electromagnetic spectrum; within this small range each part of the spectrum is seen as a different color. Most people can detect color in the range of about 400 to 700 nanometers, which is from violet to deep red. When there is no light, we see black. When light from the entire spectrum is present in approximately equal quantities, we see white.

2.3 Additive and Subtractive Colors [Craig 1976] Although the light spectrum contains all possible colors, it can be broken down into three-color regions red (with range from of 780nm – 564nm), green (with range of 563nm – 498nm), blue (with range 497nm – 380nm) each representing a third of the visible spectrum (RGB). As it is possible to break light down into three colors, conversely these same three colors when projected on top of one another create white light. Whereas all three colors overlapping produce white, if one is removed, leaving only two overlapping colors, a totally different color is created: red and green, with the blue removed, produce yellow; red and blue, with the green removed, produce magenta: green and blue, with red removed, produce cyan. The absence of all color is black. Because the red, green, and blue combine to produce white light, they are called ‘additive primaries’. Because the yellow, magenta, and cyan are formed by taking away one of the three additive primaries, they are called ‘subtractive primaries’( See Figure (2-3)). Because all printing inks contain some impurities, the three-color inks Cyan-Magenta-Yellow (CMY) actually produce a muddy brown and must be combined with black (K) ink to produce a true black. Combining these inks to reproduce color is called four-color process printing.

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(A)

(B)

Figure (2-3) (A) additive colors, (B) subtractive colors

2.4 Pictorial Images Images are pictures: a way of recording and presenting information visually. Photography is the imaging technique with which we are most familiar, simply because the information it records is similar to that which we receive using our eyes. Both human vision and photography require a light which interacts with the objects in the scene and some of it reaches the observer, whereupon it is detected by the eyes or by the camera. Information about the objects in the scene is recorded as variation in the intensity and color of detected light [Efford 2000]. Pixels (short for picture elements) represent (hold) these information’s (colors) within the coordinate system in digital imaging world. The image is divided into horizontal lines of adjacent pixels. The number inserted into the digital image at each pixel location reflects the brightness of the image at the corresponding location.

Figure (2-4) Pixel Dimension In the "digital world" of computer images, the term pixel is used for a number of different items: the individual dots on your computer screen, the dots a laser printer produces, and the individual elements of a bitmap graphic. These different elements do not all work the same way, so it can be confusing to refer to all of them as pixels. For clarity, these elements are defined as follows: 15

 Pixels refer to the individual elements within bitmap graphic files (images).  Video pixels refer to the picture elements of your computer screen.  Dots refer to the individual points that laser printers and image setters make.

2.5 Halftone Image Formation [Cambell 1985] When printing by letterpress, lithography or screen (described later), ink is transferred to the surface to be printed in a layer of uniform density. This is fine for areas of solid color, but if gradations of tone are required, such as in a photograph, the original must be broken up into a pattern of dots. Each dot varies in size to give the optical illusion of continuous tone when printed small enough not to be detected when viewed at a normal reading distance.

(A) (B) Figure (2-5) (A) A screen is used to reproduce a halftone image (B) The enlarged halftone dots become clearly visible, the lightest areas are black dots on white, and the shaded Parts are white on a black background. The conversion into dots is made by placing a screen between the original subject and the film negative. The screen itself is a glass cross-line screen which is comprised of two pieces of glass, each one having had parallel grooves etched into its surface, these being filled with opaque pigment. The two pieces are sealed together with the lines intersecting at right angles to create square windows in a lattice pattern of opaque lines. This is placed a few millimeters in front of the photographic film thus allowing incoming light to spread slightly behind the screen. The gap between film and screen is crucial since it is the spread of light dictated by its intensity as reflected from the subject, which determines the final size of the dot. The illusion of different tones of gray in a printed subject is the result of the arrangement of different size dots, their center points being exactly the same distance from each other. 16

The distance at which dot centers occur between each other on a screen is measured in terms of their frequency per inch. Thus a screen with 133 rows of dots (lines) to each inch is referred to as a 133 lpi (line per inch) screen. Screens are available in a variety of sizes ranging from 5 lines per inch to 200 lines per inch. The finer the screen, the finer the detail in a printed subject.

2.6 Color Reproduction The term 'color printing' can be applied to anything, which is printed in more than one color. More often it is used to denote the reproduction of full-color originals. Reproduction is achieved by the use of three 'process' colors - yellow, magenta and cyan, with black also being used to add finer detail and greater density in dark areas (See Figure (26)). Consequently, any original that has been presented in color first has to be separated into pieces of film, each one representing a different color. The easiest way of presenting a fine artwork for color reproduction is to produce a black representation of each respective color on a transparent overlay. If the original is presented in full-color, a separation process must be used. To separate a color original into its process color components, it is necessary to make a negative for each respective color by photographing the original through a color filter, which has been matched to the standard inks and also to the respective parts of the color spectrum. The negative for each of the process colors (subtractive primaries) requires the use of a filter of the respective additive primary color. Thus to make a negative record of the yellow component of the original a blue filter is required, the effect of which will be to absorb all wavelengths of light reflected from the yellow components. The result is that yellow is not recorded on the photographic emulsion whereas the blue reflects light and is recorded. Similarly, a green filter is used to record magenta (in negative), and a red filter for cyan. To separate black, either a combination of all three filters is used, according the color bias of the original, or no filter at all [Cambell 1985].

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Figure (2-6) Color Addition and separation using filters To make color halftone reproductions (image reproduction), each color negative or positive is photographed through the same screen. In order to avoid a screen clash, known as moiré, the screen lines are set at different angles to each other usually about 30° between each, such that the black screen should be placed at an angle of 45 – the least visible angle and the second color screen (magenta) should be at an angle of 75, the third color (yellow) is placed at an angle of 90-this is the most visible angle because yellow is the lightest color. Finally cyan should be placed at an angle of 105 (See Figure (2-7)). This operation produces the desired 'rosette' pattern - imperceptible except under a magnifying glass, giving the appearance of smooth variation in tones when viewed at a normal reading distance. 18

Figure (2-7) Halftone screens with process ink at different screen angles

2.7 Electronic color Separation Although most color separation is still being done photographically, more and more is being done by electronic scanners. The electronic scanner "reads" the colors in the original copy and produces screened or unscreened positive or negative separations. Some scanners not only make separations, but can also strip in background tints at the same time. One of the major advantages of the electronic scanner is that it allows for methods of color correcting to be built right into the system, eliminating much of the handwork involved in conventional color correcting.

2.8 Image Size and Resolution In order to produce high-quality images, it is important to understand how the pixel data of images is measured and displayed. 2.8.1 Pixel dimensions Is the number of pixels along the height and width of a bitmap image. The display size of an image on-screen is determined by the pixel dimensions of the image plus the size and setting of the monitor. For example, a 15-inch monitor typically displays 800 pixels horizontally and 600 vertically. An image with dimensions of 800 pixels by 600 pixels would fill this small screen. On a larger monitor with an 800-by-600-pixel setting, the same image (with 800-by-600-pixel dimensions) would still fill the screen, but each pixel would appear larger. Changing the setting of this larger monitor to 1024-by-768 pixels would display the image at a smaller size, occupying only part of the screen (Figure (2-8)). 19

Figure (2-8) Pixel dimensions 2.8.2 Image Resolution [Fulton 2002] The number of pixels displayed per unit of printed length in an image is usually measured in pixels per inch (ppi). The amount of detail in an image depends on its pixel dimensions; while the image resolution controls how much space the pixels are printed over. For example, you can modify an image's resolution without changing the actual pixel data in the image-all you change is the printed size of the image. However, if you want to maintain the same output dimensions, changing the image's resolution requires a change in the total number of pixels.

A

B

Figure (2-9) (A) 72-ppi and (B) 300-ppi images; inset zoom 200% When printed, an image with a high resolution contains more, and therefore smaller, pixels than an image with a low resolution. For example, a 1-by-1-inch image with a resolution of 72 ppi contains a total of 5184 pixels (72 pixels wide x 72 pixels high = 5184). The same 1-by1-inch image with a resolution of 300 ppi contains a total of 90,000 pixels. Higher-resolution images usually reproduce more detail and subtler color transitions than lower-resolution images. However, increasing the resolution of a low-resolution image only spreads the original pixel information across a greater number of pixels; it rarely improves image quality. 20

2.8.3 Monitor Resolution [Fulton 2002] The number of pixels or dots displayed per unit of length on the monitor is usually measured in dots per inch (dpi). Monitor resolution depends on the size of the monitor plus its pixel setting. A 17-inch monitor screen might measure 12.5 inches horizontally. If it is set to 1024x768 screen size, then the image is obviously 1024 dots / 12.5 inches = 82 dpi resolution in that case. A 15-inch monitor at 800x600 might be 75 dpi. A 14-inch monitor at 640x480 might be about 65 dpi. Most new monitors have a resolution of about 96 dpi. Understanding monitor resolution helps explain why the display size of an image on-screen often differs from its printed size. Image pixels are translated directly into monitor pixels. This means that when the image resolution is higher than the monitor resolution, the image appears larger on-screen than its specified print dimensions. For example, when you display a 1-by-1 inch, 144-ppi images on a 72-dpi monitor, it appears in a 2-by-2 inch area on-screen. Because the monitor can display only 72 pixels per inch, it needs 2 inches to display the 144 pixels that make up one edge of the image. 2.8.4 Printer Resolution Is the number of ink dots per inch (dpi) produced by all type of printers, including imagesetters. Printers resolution vary, some are 300x300, 360x360, 600x600, 720x720, or even 1440x720 at the present days. The printer resolution refers to address ability of the ink dot, and not the resolution of the image. Several print head ink dots are required to make one pixel image dot. The printer's image resolution capability is much less than the advertised dpi numbers [Knoll 2002]. 2.8.5 Screen Frequency[Rogers 1985] The number of printer dots or halftone cells per inch used to print grayscale images or color separations. Is known as screen ruling or line screen, screen frequency is measured in lines per inch (lpi) or lines of cells per inch in a halftone screen. The relationship between image resolution and screen frequency determines the quality of detail in the printed image. Black and white printers do not print shades of gray. They use black ink or black toner, and they can print only black. To simulate gray in graphics, they print halftones. Halftones are arrays of dots arranged in a grid, say 3x3, 6x6 or 8x8 to represent each image pixel as a shade of gray (Figure (2-10)). For dark gray, more grid dots are black. For light gray, more grid dots are white. (More modern methods used for color in magazines vary the size of the dots instead of the ratio of light/dark dots. 21

Figure (2-10) 3x3 cell giving 10 shades of gray The printing graphics software and driver can specify different halftone grid sizes for different effects. For example, a good laser printer might print 600 dpi, or it might print 128 shades of gray. If a larger grid is used, more shades of gray are possible, but less resolution is possible. For example, some grid sizes for a 600 dpi printer are: 1x1 shows 2 shades (black or white, 600 dpi Line art). 6x6 shows 37 gray shades, reducing resolution to 600/6 = 100 lpi. 7x7 shows 50 gray shades, reducing image resolution to 600/7 = 85 lpi. 8x8 shows 65 gray shades, reducing image resolution to 600/8 = 75 lpi. 10x10 shows 101 gray shades of gray, reducing to 600/10 = 60 lpi.

Figure (2-11) A. 65 lpi: Coarse screen typically used to print newsletters and grocery coupons. B. 85 lpi: Average screen typically used to print newspapers. C. 133 lpi: High-quality screen typically used to print four-color magazines. D. 177 lpi: Very fine screen typically used for annual reports and images in art books.

2.9 Printing Techniques Printing may be accomplished in several different ways, such as lithography, letterpress, flexography, gravure, and screen-printing. All of these printing techniques use simple mechanisms for rapidly applying colorants to substrates such as paper or plastic to form multiple reproductions of original images for mass distribution. 22

Process color printing uses four transparent inks-cyan (blue-green), magenta (red), yellow, and black-printed one on top of another in varying amounts. Color photographs and other artwork can be faithfully reproduced by this method. 2.9.1 The Offset Principle[Cambell 1985] In the early part of the 20th century, it was discovered that ink could be transferred from the lithographic surface to an intermediate rubber surface and then to paper. The rubber intermediate, called a blanket, can transfer ink to paper and to a wide variety of materials that cannot be printed directly, including plastics and metals. Because the soft blanket conforms to the texture of the surface to be printed, lithographic image quality is unrivaled. Nowadays, the function of the original stone-printing surface is now served by thin aluminum plates, although other materials, such as stainless steel and plastic, can also be used. The plates are wrapped around the circumference of the printing cylinder and make direct contact with the rubber blanket cylinder. Rubber rollers carry ink and water to the plate surface. The ink is transferred first to the blanket cylinder and then to the paper. Aluminum plate materials have a thin surface coating of lightsensitive material, such as a photopolymer, that undergoes a solubility change when exposed to an intense source of blue and ultraviolet light. Images are transferred to the surface by exposing the plate through a film positive or negative. Some materials can be exposed directly, as in a graphic-arts camera or by a computer-controlled laser beam, thereby eliminating the expense of film and speeding up the plate making process (Figure 2-12).

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Figure (2-12) Offset machine 1-Ink roller. 2-plate cylinder. 3-paper 2.9.2 Lithography[Cambell 1985] By far the most important and versatile printing process today is offset lithography. The underlying principles were established at the end of the 18th century by a German map inspector, Aloys Senefelder, who was experimenting with methods of producing limestone relief printing surfaces using an acid etching process. Senefelder found that a wet limestone surface would repel an oil-based printing ink, and that an image drawn on the surface with a grease pencil would repel water and attract ink. Any drawing on the stone surface could be reproduced by bringing a damp sheet of paper into contact with the freshly inked image. This cycle could be repeated several hundred times before the drawing could no longer be faithfully reproduced. Modern color lithography uses only four inks for a wide range of natural colors. 2.9.3 Gravure[Craig 1976] Gravure, also called rotogravure, is a high-volume printing process employing an ink transfer mechanism that is fundamentally different from that of relief printing. The printing surface is a polished metal cylinder covered with an array of tiny recesses, or cells (as many as 50,000 per sq. inch), that constitute the images to be printed. The cylinder is partially immersed in a reservoir of solvent-based fluid ink. As the cylinder rotates, it is bathed in ink. A steel blade called a doctor blade running the entire length of the cylinder wipes the ink from the polished surface, leaving ink only in the cells. The ink is then transferred immediately to a moving web of paper forced against the cylinder under great pressure (See Figure (2-13)).

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Gravure cylinders are constructed of steel with a thin surface layer of electroplated copper. The copper can be either chemically etched or electronically engraved to form the cells that will transfer ink. Each cell transfers a tiny spot of ink to the paper. The cells can be made to vary in depth from one part of a cylinder to another, causing the darkness of the resulting ink spots to vary also. This enables gravure to print a wide range of gray tones and thus to render excellent reproductions of photographic originals.

Figure (2-13) Gravure Printing machine The expense of manufacturing a set of gravure cylinders has restricted its use to long-run jobs (millions of reproductions). Masscirculation monthly magazines, mail-order catalogs, and packaging are natural markets for the process. Gravure is also used to reproduce a variety of textures and patterns on decorative materials. Most of the simulated wood grains on inexpensive furniture, for example, are printed by gravure. New methods of manufacturing gravure cylinders using computer-controlled electronic engraving machines have reduced the time required to prepare a set of cylinders, but they are still far more expensive than lithographic printing surfaces.

Figure (2-14) Set of Gravure Dies Intaglio printing is a specialized process related to gravure that employs engraved rotary printing surfaces of steel to print currency, bonds, stock certificates, and high-quality business stationery. Ink is 25

transferred from engraved recesses on the printing surface directly to sheets of paper transported through the press. Intaglio printing excels at reproducing artwork that consists of fine lines and small solid areas. It cannot be used to reproduce photographic images or to print large unbroken solids. The use of past ink and deeply recessed printing surfaces gives intaglio printing a distinctive raised texture. (Powdered resins can be heat-fused to freshly printed wet lithographic or letterpress inks to simulate this effect at far less expense. 2.9.4 Screen Printing Originally called silk-screen printing because of its silk-based stencils, screen-printing has become important in the production of a wide array of manufactured items, including decorative panels, printed circuit boards, touch-sensitive switches, plastic containers, and printed garments. Stencils for commercial screen-printing are usually produced by photomechanical means. A fine synthetic fabric or metal mesh is stretched over a rectangular frame, and a photopolymer coating is applied to the entire surface. Exposure of the photopolymer through a film positive causes it to harden in the areas not intended to print. The unexposed material is then washed away to create the open areas of the stencil. In the printing press, this screen is pressed against the surface to be printed, and ink is forced through the open areas of the stencil with a rubber squeegee.

Figure (2-15) Screen-printing technique 2.9.5 Letterpress Printing [Kuna 2001] Originally, letterpress-printing surfaces were prepared by assembling thousands of pieces of metal type on which individual letters or letter combinations were cast in relief to create pages of text called type forms. Ink was applied to the raised areas of the form and then transferred 26

under pressure to paper or vellum. Woodcuts and engravings could be combined with type to produce composite pages containing both text and graphics.

Figure (2-16) Letterpress machine 2.9.6 Flexography Printing The soft plates and highly fluid inks used in flexography make the process ideal for printing on nonporous materials such as foil laminates and polyethylene. Originally, all flexography plates were made of molded rubber, which is still the preferred material when multiple copies of the same image are needed on a single printing cylinder. Rubber plate molds are impressions of original relief surfaces, such as type forms or engravings, and are normally used to make several duplicate rubber plates. The preparation of a printing cylinder using molded rubber plates is a time-consuming process because many rubber plates are mounted on a single cylinder and each plate must be carefully positioned in relation to the others.

Figure (2-17) Flexography machine. 27

Flexography printing presses are simple in design because the fluid ink is easily distributed to the printing surface without an elaborate inking system. Printing is usually done on rolls or webs of substrate rather than on cut sheets, and the printed rolls are then converted into finished products in a separate manufacturing process.

2.10 Digital Printing and Digital Printers This part is concerned with the most currently used technologies of printers today and the methods to reproduce the various gray tones or colors of a digital image. 2.10.1 Liquid Ink-jet [Meylan 2001] The basic principle of ink-jet technology is to throw out small droplets of ink through small tubes, called nozzles that are smaller than the width of human hair. They lay in a row on a print head, moving across the paper. For color printers, the four basic components CMYK (Cyan, Magenta, Yellow, Black) lay side by side on the printing head, so the printing of color document is performed in one single process. Several techniques are used to squirt ink onto the paper sheet. 2.10.1.1 Continuous Ink-jet [Meylan 2001] A pressured ink flow is thrown through the nozzles and separated into droplets by the high frequency vibrations of a piezo-electric crystal (A ceramic component that expands under the influence of voltage. Each jet (or each ink channel) is surrounded by a Piezo crystal). The expansion of each element under voltage generates the necessary pressure to expel the ink from the jet.

Figure (2-18) Continuous ink-jet technology 28

2.10.1.2 Drop on Demand A low pressure is maintained in the ink circuitry, retaining ink in the nozzle. A high pressure is produced each time a droplet is to be thrown away. 2.10.1.3 Bubble Jet [Meylan 2001] Ink is vaporized by an electric resistor within the nozzle, creating a small gas bubble. Under the pressure effect, a small quantity of ink is ejected out (Figure (2-19)).

(A)

(B)

Figure (2-19) Bubble jet technology. (A) Horizontal position, (B) Vertical position. Future developments of liquid ink-jet technology will be the ability to throw two droplets on the same pixel. This will allow producing pixels with two different levels of intensity, resulting in best quality outputs. The drop size has reduced the minimum size to around the limit of human perception on the page, at just three picolitres (One Pico liter corresponds to 10-12 liters = 0,000000000001 liters = 1 billionth of a liter). The result of using such tiny dots is much smoother color graduations and reduced image graininess. The following table lists the advantages and disadvantages of ink-jet printers Table (2-1) Liquid Inkjet advantages and disadvantages Advantages of ink-jet

Disadvantages of ink-jet Needs special paper for optimum quality

1 Cheapest technology Produces nice saturated colors 3 Use of big paper sizes 2

Slow in low-end models

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2.10.2 Solid Ink-jet Solid ink-jet is based on the same principle that liquid ink-jet, except that ink is stored in solid wax sticks, which are melted in a small reservoir. The liquid ink is then squirted to paper, where the colored material resolidifies again. The advantages and disadvantages of solid inkjet is shown in the following table: Table (2-2) Solid Inkjet advantages and disadvantages Advantages of solid ink-jet Disadvantage of solid ink-jet Great for producing 1 Quite slow graphics on standard paper 2.10.3 Laser Printers[Corrigan 1994] Laser technology is the same as for photocopiers, that is to say:  A laser beam is sweeping across a photosensitive cylinder, creating on its surface an electrostatic latent image. The cylinder has the capability of producing electricity under light exposure.  The electrostatic image is then passed in a special powder (toner), whose particles are attracted by electric charges on the cylinder.  The image is transferred onto paper by electric voltage difference between the paper and the cylinder (2,000 V on the paper and 1,000 V on the cylinder).  The image is finally fixed by heating and pressure processes.  The cylinder is cleaned up, in order to get the next image. Color documents are produced by repeating the process for each basic color.

Figure (2-20) Laser technology Table (2-3) Laser printer advantages and Disadvantages Advantages of laser Disadvantages of laser 1 Fast speed 2 Long lasting results 30

2.10.4 LED Printers [Flowers 1994] Led printers are in the same printer family as lasers, but as a still developing technology, their use is far less widespread. Both laser and LED technologies utilize the electro photographic process, having a photosensitized drum that attracts toner and then presses the toner onto the page. LED printers use light-emitting diodes (a special type of semiconductor that illuminates when an electrical charge passes through it) instead of lasers. As you recall, laser printers flash a laser beam that is intercepted by a spinning mirror that, in turn, reflects the light through focusing lenses and onto its appointed spot on the drum. The light from the LED bulbs is special wavelength, near the infrared range, and is invisible to the human eye, although the sensitive material on the drum has no trouble detecting that spectrum of light. From there, the printing process is much the same as that of the black –and –white laser printer. As the bulbs blink off and on, the drum turns, and the bulbs blink the shape of the letters or the graphics onto the drum. 2.10.5 Thermal Wax Transfer[Corrigan 1994] These machines use special colored films (a transfer roll), made of consecutive wax based material that melts locally under the effect of controlled heating resistors. Colored wax is transferred by contact onto paper. For color printings, the process is repeated three times, once for each basic color. Special paper is to be used (Figure (2-21)).

Figure (2-21) Thermal wax transfer technology Table (2-4) Thermal wax advantages and disadvantages Advantages of wax transfer 1 Fast 2 Excellent color quality 3 Precise elementary dots

Disadvantages of wax transfer Needs special expensive paper

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2.10.6 Dye Sublimation[Corrigan 1994] This is the best quality technology used for printing images. The coloring agents are contained in a transfer roll (i. e. a plastic film that contains consecutive layers of cyan, magenta, yellow and black dye). The transfer roll passes across a thermal print head consisting of thousands of heating elements, and once the dyes are hot enough to vaporize, they diffuse to the target paper's surface. The paper is specially designed to absorb the vaporous dye (Figure (2-22)). Each heating element produces 256 different temperatures, and the hotter the temperature; the more dye is transferred onto the paper. So, it is possible to control the intensity of the resulting dot and produce continuous tones images; dye sublimation is the only technology to allow it.

Figure (2-22) Dye sublimation technology Table (2-5) Sublimation Printer advantages and disadvantages Advantages of dye Disadvantages of dye sublimation sublimation High price of the transfer 1 Photographic quality roll and the special paper 2.10.7 Laser Imagesetters [Corrigan 1994] Are similar to laser printers but print to a different medium, which allows for greater resolution than normal laser printers. Imagesetters shine a laser directly onto a piece of photosensitive paper or film, and then process that paper/film in chemicals, just as normal photographic paper/film would be processed. Imagesetters-by eliminating a charged metal plate and powder tones are capable of much higher resolutions typically from 1,800 dpi to more than 3,000 dpi) than normal laser printers (typically from 300 dpi to 1200 dpi). 32

2.10.8 Film Recorders [Pipes 1992] A film recorder is a device dedicated to reproducing an image onto photographic film (either negative or positive film-for making photographic prints or slides). A film recorder consists of a high resolution Cathode Ray Tube (CRT) device, which is much like a computer monitor and an optical camera mounted to photograph the display, the computer hardware and the software to run it all. Film recorders vary in several ways:  The type of film they can record to (35mm film, as in a normal camera; 4x5 film, and even 8x 10 film, commonly used by professional photographers)  The resolution of the CRT display (which can range from 1,000 to more than 8,000 pixels per inch) High quality film recorders look like larger boxes, with larger cameras attached to the outside. Inside the metal box is a CRT display-. The camera can be loaded with ordinary 35mm film to take either negative images (for printing photographs) or slides of the images displayed on the CRT monitor. The real difference in film recorders lies in the quality of the CRT display and of the computer system used to run the equipment. High quality film recorders can display images at resolutions of 4,000 or even 8,000 pixels per inch, with a total pixel amount numbering in the millions. 2.10.9 Vector Plotters [Corrigan 1994] Unlike the previous printing devices, all of which printing use some form of bitmap image; vector plotters actually draw an image on paper, using colored pens (plotters). The most common application of vector plotters is the production of blueprints and technical diagrams-image, which contains hundreds or thousands of vector lines. Vector plotters come in a variety of forms. A plotter may hold a large sheet of paper in a flat tray; while two pulleys move a pen back and forth over the surface of the paper. Vector plotters have the advantage of being able to use very large sheets of paper, allowing them to produce very large output pages. Unfortunately; they are limited to drawing images, which are represented by collections of lines (no bitmaps). This makes plotters a fairly specialized type of printer. 33

2.11 Ink and Paper [Cambell 1985], [Craig 1976] The paper used has a major influence on the quality of the color printed on it. Because process inks are transparent, it is the light reflected from the paper's surface that supplies the light to the ink. For example, let's look at some cyan printed on a sheet of paper. The light passes through the transparent cyan ink as through a glass filter. The cyan absorbs the red color and allows the blue and green color to pass through. These two colors reflect off the paper and back up through the ink. What we see is a blue and green color, or cyan. It is the quality and quantity of the reflected light that dictates the quality of the color. For this reason, the paper must be bright if it is to reflect maximum light. Also, because a rough surface will scatter the light and distort the color, the paper should be smooth so the ink will lie flat and filter properly. White paper reflects all colors, Yellow absorbs blue, reflects red and green. Magenta absorbs green, reflects red and blue, Cyan absorbs red, reflects green and blue. Black absorbs all colors. Rough paper scatters light and distorts color. Smooth paper reflects light evenly. 2.11.1 Basic Ingredients of Ink The specific ingredients used in the manufacture of printing inks are dictated by many factors-the printing process, the ink-drying system, the surface to be printed, etc. However they can be broken down into three categories: pigment, vehicle, and miscellaneous ingredients (mainly driers and compounds).  Pigment, The fine, solid particles that give printing ink its color. Pigments can be mineral, organic, or dyes.  Vehicle, Is the liquid ingredient into which the pigment and other ingredients are mixed. The function of the vehicle is to act as a carrier for the pigment, and as a binder to affix the pigment to the printed surface. It is also mainly responsible for the gloss and hardness of the dried ink film.  Miscellaneous Ingredients, One of the most important ingredients that all oxidizing inks must have is a drier. This is usually made from oil, a metallic salt, or a mineral compound and is added to the ink to help it dry more rapidly. 2.11.2 Ink and the Printing Process Each printing process requires ink with different characteristics. The ink used is also determined by the kind and speed of the press, the surface to be printed, and the end use of the printed piece. Many kinds of inks are used in the printing process, these are: 34

 Letterpress Inks, are designed to print from a raised surface. Letterpress inks must be tacky and viscous enough to hold to the surface of the plate until printed.  Gravure Inks, are designed to print from a depressed surface. Gravure inks must be very fluid to fill the thousands of tiny wells, and at the same time have enough body and adhesion to be pulled from the wells onto the paper. Gravure inks are quick-drying and are usually dried by evaporation.  Offset Lithography Inks, are designed to print from a flat surface. "Litho'' inks are usually longer and more viscous and heavy bodied than letterpress inks. Offset inks must be resistant to the dampening action of the water used in offset printing.  Screen Printing Inks, are designed to be forced through a mesh screen, onto a wide range of surfaces such as, cardboard, metal, ceramic, and glass. Screen printing inks are short and buttery. To ensure good adhesion, the binder must be changed to suit the surface being printed.  Flexography Inks, is another form of letterpress printing which employs rubber plates and aniline inks designed to print on a wide range of surfaces, including paper, cellophane, plastic, and metal foil. Flexography ("flexo") is extremely popular in the packaging industry; the ink colors are bright, strong, opaque and can be made resistant to light and abrasion. Flexography inks are very fluid and fast-drying and can therefore be printed at high speeds.  Letterset Inks, Just as letterset is a combination of letterpress and offset lithography. Letterset inks are a combination of letterpress and offset inks. Letterset inks are transferred from printing plate to blanket to paper on a special offset press that does not require the use of a fountain. 2.11.3 Specialty Inks Specialty inks are the result of the ever-increasing demand for brighter colors, higher speeds, and new printing techniques. The following are some of the more commonly used specialty inks:  Cold Set: Unlike all other inks, cold-set inks are solid at room temperature, but melt at 150° to 200°. The printing plate and the press must first be heated to melt the ink. When printed on the relatively cold paper, the ink immediately reverts to its solid state. 35

Cold-set inks produce sharp printing results, however they require a complicated heating and cooling system.  Fluorescent: Available in a rather limited range of a few reds, yellows, blues, and greens. Fluorescent inks are bright and vibrant, but they require two passes to achieve full color. Fluorescent inks are most widely used for screen-printing signs.  Heat Set: A fast-drying ink that permits large, high-speed, high-quality runs. To use heat-set inks, the press must be equipped with a heating unit, cooling rolls, and an exhaust system. It is used for printing almost any job involving long runs.  High Gloss: It is made possible by the development of a vehicle that permits only a minimal penetration of the paper's surface and ensures a maximum gloss.  Magnetic: These inks are made with special pigments, which can be magnetized after printing. The printed characters can then be recognized by electronic reading equipment. Magnetic inks are used a great deal for such jobs as bank checks and business forms.  Metallic: Metallic powders such as bronze, gold, aluminum, and copper are suspended in the vehicle, which also serves to bind the powders to the surface of the paper. Metallic inks are also available in a metallic paste, which makes far less of a mess. 2.11.4 Choosing the Right Paper Choosing the right paper must satisfy the demands of the printing process as well as meet design and economic requirements. The first thing that must be considered when choosing paper is how the job is to be printed. As letterpress, gravure, and offset lithography are three basically different printing processes, they each require papers with different characteristics:  Letterpress: Letterpress prints by direct impression; that is, the raised metal printing plate comes into direct contact with the paper. The papers used are generally rough and bulky. Letterpress paper must be smooth enough to ensure a uniform ink transfer yet strong enough to accept pressure without tearing.  Gravure: Like letterpress, gravure printing is also a direct impression. However unlike letterpress, the printing plate is relatively smooth and the ink is carried in well-like cells rather than on a raised surface. For these reasons, gravure paper should be 36

smooth and have a certain amount of absorbency: smooth so that the surface will come into close contact with the printing plate; absorbent so they will draw the ink from the cells.  Offset Lithography: Unlike letterpress or gravure, offset is not a direct-impression process; the inked image is first transferred from the printing plate to a rubber blanket and then to the paper. The rubber blanket is compressible, conforming to the surface variations of the paper. This permits offset to print on both smooth and relatively rough surfaces. Offset papers must be properly sized to resist the moisture that is always present in offset printing. 2.11.5 Design Considerations Apart from choosing a paper is to consider its printability. Printability is dictated by a paper's absorbency and smoothness of surface. Good printability is especially crucial when printing color or black and white halftones because the quality of the image will depend entirely on how accurately each dot prints. Not all papers are used for printing; they are also used for wrapping papers, tissue papers, and paper bags, among other things. There are two categories of printable papers: newsprint and book papers. 2.11.5.1 Newsprint Newsprint is one of the lowest grades of printing paper. It is made primarily from ground wood pulp with about 30% chemical wood pulp added for strength and color. Newsprint is a low-cost paper with good bulk and opacity. However, because of impurities in the paper, it has low brightness and a tendency to yellow and become brittle with age. It lacks strength, has limited printing qualities, and tends to discolor. Newsprint is therefore generally used for newspapers, and mass-market paperbacks. 2.11.5.2 Book papers Although called book papers, they are used not only for bookwork, but for practically every thing we read, with the exception of newspapers. Book papers can be divided into two major categories: coated and uncoated:  Coated Papers These papers have a special clay coating which when super calendared gives the paper an extremely glossy finish. The purpose of this coating is to bury the fibers so that the printing ink does not come into contact with them at all.  Uncoated Papers. Uncoated paper is the most basic, least sophisticated type of sheet. It is produced on the papermaking machine without any special coating operations. 37

2.12 Importance of Document security: Crime has a significant negative impact on the sense of security and the overall quality of the world’s citizen’s life. The cost of insurance, security measures to prevent crime, as well as the costs of detection, investigation and prosecution of serious crimes are a burden to national budgets, which can be reduced through the application of state-of-the-art measurement and testing techniques. The threat of counterfeiting is increasing, mainly because of the advancements in reprographic technologies that are currently available, or are in the development stage. Casual crooks are passing poor quality fake documents produced by inkjet printers. The professionals can draw on sophisticated technologies such as color photocopying and graphic scanning that makes it simpler to produce plausible notes. This type of counterfeiting, though small, is growing fast and certainly questions the value of print as a security feature on documents [Renesse 2000].

2.13 Security features in banknotes: Security is a prime requirement of all banknotes. As an anonymous medium of exchange of a valuable negotiable document, it must inherently display exceptional security to gain the confidence and trust of the general public. A wide range of security features available for banknotes are classified into the two main categories: Overt and Covert security features [Gration 2001]. Most importantly, banknotes must possess easily recognizable overt security features for the person in the street. These features must be difficult to counterfeit or simulate, and should be easily recognizable as genuine in the short time available during a normal transaction, ideally without the need for an additional device. Covert security features, generally protected by secrecy and only detectable with the aid of special devices, are often made use of by automatic cash handling machines and high volume cash handling personnel. Modern banknotes contain a range of these features, with an even higher-level security feature reserved exclusively for the issuing authority. Security features are incorporated in four distinct areas of a banknote:  Substrate.  Design.

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 Printing.  Machine-readable features. 2.13.1 Security in substrate: A major advancement in the development of security features for banknotes has been the concept of a self-authenticating banknote. The self-authenticating features currently available in the substrate are: 2.13.1.1 Portrait: This is the first security feature that is difficult to capture by any counterfeiting techniques. A banknote must be designed to be clearly distinguishable from other printed matter, so that it is accepted immediately as a document of value. On choosing motifs for the banknote series it is important to have a good original in the form of a portrait, which is a good likeness. Both men and women are included, either in profile or as full-face portraits. Varying head coverings also contribute to this diversity. The photographs or paintings chosen serve as the original for the printing in intaglio on the banknotes. Some images are engraved by hand into metal plates, whilst others are created using a Computer Aided Design (CAD) system and are drawn onto film by a laser beam. When finished, the images are duplicated many times onto printed plates ready for the presses..

Figure (2-22) shows the details of intaglio portrait Some countries also use this feature of intaglio printing to build up some areas of the note to assist the blind or visually impaired, by placing raised marks on the notes to distinguish which denomination the note is.

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Figure (2-23) shows the engraver work on a portrait The engraved portrait is traditionally made by the engraver transferring an outline of the portrait to a smooth steel plate. The lines are engraved to describe the shape of the face. The depth and closeness of the lines are greatest in the areas which are to be dark, whereas areas, which are to be light, contain only small broken lines, or none at all. Intaglio is a very old printing technique which is still used for banknotes. Its primary function is to provide security, by adding the thick layer of ink and the many details. The print can be felt since the lines are printed from engraved lines, thereby transferring a thick layer of ink to the paper. Once the final design has been determined, the printing plates are made. The face is printed using both intaglio and offset techniques, while only offset is used on the reverse.

Figure (2-24) an example of portraits 2.13.1.2 Water mark: The Italians where the 1st to use watermarks in the manufacture of paper in the 1270's. It is a good security feature because the watermark cannot be photocopied or scanned effectively [Chappell 2000]. A watermark is put onto a special banknote's paper prior to the printing process. The watermark design is usually carved into wax first and then a copper die is made from the wax and the finished design is then stamped into a wire mesh. Then these designs are pressed into the 40

paper during paper manufacture while still moist, by the wire mesh (dandy roll). This causes a thickening or thinning in the paper fibers. When finished the design can be seen by holding the paper up to the light [Image 2000].

Figure (2-25) a small section of a dandy roll used to make a watermark "R" in paper. The watermark is usually a portrait similar to that printed on the note. Watermarks can be single or two toned (varied dark and light). Single tone will be either a watermark that is light (raised watermark) or dark (sunken watermark). The raised areas cause a thinning in the paper fibers and the depressed areas cause fiber buildup causing the light and dark areas. Two toned will be a combination of both.

(B)

(A) Figure (2-26) A- Raised Watermark

B- Sunken Watermark

Two tone watermark ----->>>>>

Single tone Watermark ------>>>>> (Raised watermark)

Figure (2-27) example Belgium - 500 Francs – 1998.

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Figure (2-28) Algeria - 5 Dinars- 1970, Example of a continuous watermark going from one note to the other in almost unbroken line [Bender 2000]. 2.13.1.3 Security thread: The third most common security feature is the security thread. Threads are embedded within the paper fiber and can be completely invisible or have a starburst effect, where the thread appears to weave in and out of the paper when viewed from one side (windowed). The metal security thread consists of a fine metal (aluminum foil) covered with cellophane; the electrical conductivity of the thread was also a test for counterfeiting. This has now evolved from metal into a plastic thread. The embedded security thread can be seen when held up to the light. The "windowed" thread when held up to the light appears as a solid line, and appears as silvery dashes under normal. Many of these threads glows into colors (orange, red, yellow, blue) when held under an ultraviolet light [Kuna 2001]. In some types of these threads, the numerical value of the banknote (micro printing) is printed in negative on the metal security thread in an unbroken series, in such a way as to be turned alternately towards the portrait or towards the central part of the banknote. Some of these security threads incorporating magnetic ink that can be "hidden" under offset inks and that can be read by banknote readable machine [Hari 2000].

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Figure (2-29) plastic readable thread of Thailand banknote, 1000 Baht, 1992.

Windowed Security Thread

Figure (2-30) windowed security thread of English - 10 Pound (1998) The black marks are actually silver under normal lighting conditions, but appear black when photocopied or scanned. When the note is held up to the light and shines through it appears as a solid line [William 1999]. 2.13.1.4 Background: The intricate colorful backgrounds on many notes make them more difficult for would be counterfeiters to duplicate.

Figure (2-31) example of some background figures

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2.13.1.5 Scrambled Indicia : Scrambled Indicia is a unique method of adding security to any kind of printed material such as passports, stamps, banknotes, holograms, trade labels, or any document that needs to be made counterfeit proof. It cannot be copied by digital scanners or any of the conventional coping or reproduction methods that are in current use today. They can also incorporate special ultraviolet inks in the production that can be read by a UV Decoder. Scrambled Indicia is a process that allows one or more images to be encoded within other images rendering them invisible to the naked eye. The encoded images are then only visible after viewing through the appropriate decoder. By using a series of innovative an patented techniques, the pixels of images are scrambled, shifted, bent, flipped, overlapped, twisted or otherwise manipulated to create a hidden image within another image [Alasia 2000].

Figure (2-32) shows the effect of encoding image within another one (Scrambled Indicia).

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2.13.1.6 Microprint : Microprint feature is a type of printing so tiny messages that it can barely be distinguished with the naked eye (usually appear as fine line when viewed by the naked eye). As such, most people don't ever realize it is there. Upon inspection of a crisp un circulated note with a magnifying glass, you will be able to see incredibly small printing designed to foil counterfeiters. There is currently no commonly available machinery or equipment (including computer scanners/printers or copying machines) capable of reproducing microprinting due to the high resolution required.

Figure(2-33) shows microprint around the portrait

Figure (2-34) shows micro printing in Sweden - 20 Kronor - 1994 2.13.1.7 Color Shifting Ink The most recent development in the printing skill are the use of color shifting and metallic inks (also called optical variable ink). The inks change color when held to the light at different angles (i.e. colors turning from metallic green to black). Multi-layered metallic flakes suspended in the ink cause the color change. The metallic inks also help prevent copying, turning black when it is photographed or copied. Because of the

45

special combination elements in the ink, this is very difficult to reproduce.

Figure (2-35) shows color shifting technique an Argentina banknote - 5000 Australia’s – 1989.

Figure (2-36) shows changing in color from bluish-green to purple when viewed from different angles in Japan banknotes 2000 Yen. 2.13.1.8 See through register The precision equipment used to print back notes enables the back and front of the litho portions of the notes to be printed simultaneously. They can also be accurately registered to one another. A feature utilizing this accurate register capability is the see through feature. It comprises of 2 different images, one on the front and the other on the back. When the note is held up to the light a third image is produced by the combination of each image.

Figure (2-37) shows how see through register technique work.

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When the note is held up to the light, the designs become complete. This seems like a small detail, but difficult to due.

Figure (2-38) Shows see through register in Colombia 1000 pesos oro 1992.

2.13.1.9 Latent Images: Latent images are produced by intaglio print and the protection they offer is directly a result of the tactile nature of intaglio print. When viewed straight on, a latent image reveals nothing but lines and that is if you look closely! But viewed at a glancing angle an image appears. These effects are caused by special engraving on the intaglio plates [Hari 2000].

Figure (2-39) shows the latent image

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Figure (2-40) When the banknote is viewed from a certain angle, the number "2000" appears on the bottom left of the front side of Japanese banknote 2000 yen [Zhang 2000]. 2.13.1.10 Fluorescent ink: Another benefit is that the fluorescence resulting from a special type of fluorescent ink can penetrate into the base polymer that can only be seen under UV lighting, thereby creating an indelible specific marking, that can be used for authentication, even if the printing on the banknote is destroyed or deliberately removed. Luminescent compounds can be combined with anything to give it fluorescent properties. It can be combined with the treads, security dots, security strip, and inks. The compounds combined with inks in some notes were probably zinc-orthosilicate or calcium silicate. Zincorthosilicate gives a greenish to yellow appearance and calcium silicate gives a orange to red color

Figure (2-41) Top note fluorescence with UV lighting and the bottom note is with out UV lighting of Sweden banknote, 50 kronor [Niel 1999].

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2.13.1.11 Bar code:- This element consists of some small dark rectangles printed with magnetic ink. This element is useful to process the banknotes with automated equipments. The bar code is either visible or invisible that can be seen under UV lighting [Melody 1999].

Figure (2-42) shows invisible bar code in Scotland banknote , 5 pound 1996. 2.13.1.12 Holograms :- A great example in graphic design of blending the feeling of high security and the ability to mass produce silver hot stamped foil holograms. Optical imaging is where one or more images or designs are etched by laser into a silvery or gold foil. This foil may be imbedded or applied to the surface of the note. Holograms are used in, in medicine, for satellite communications, for protection of valuable documents against duplication, and for high profile product and packaging enhancement and recognition.

Hologram -->>

Figure (2-43) shows holographic in Zaire banknote, 1996.

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2.13.1.13 Screen Angel Modulation (SAM) :- A sophisticated and complex security feature which changes certain visual images by the use of a filter and digitized tone and line images. Whereas the window area on the other new notes is clear, this note has a built-in filter or screener. When the note is folded so that the window within the DOVD is placed over the image of New Zealand on the back of the note, 'Y2K' will become visible. This feature cannot be seen with the naked eye. The DOVD, which can be viewed from both sides of the note, is an aluminum coating in the shape of two silver ferns within the window area. The major characteristics of the DOVD are that the color changes as the viewing angle is varied. The DOVD used in the millennium note is a diffraction grating, so called because light rays are diffracted from the surface of the feature into their various rainbow colors. As the viewing angle changes. different rainbow patterns are produced. This grating contains very small silver fern images as well as some text. Filter

The Island of New Zealand on the back of the note. Seen by the naked eye. The 'Y2K' is not visible.

When the front of the note is folded and the DOVD is placed over the Island of New Zealand on the back of the note, the image of 'Y2K' can be seen

Figure (2-45) DOVD effect

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2.13.2 Security in Design & Printing: Traditionally, banknotes are designed with the aim of creating a document that is secure, and around this is built the aesthetics. The offset of background print has features such, see-through registration, screen traps and multi-colored intricate patterns which are designed to make it difficult to counterfeit, especially by color photocopy reproduction. Intaglio printing has for decades been the recognized printing method and a 'proud' feature of banknotes. A portrait depicting a three dimensional image is an excellent security feature, as well as being an attractive element of the banknote. Besides this, multi-color intaglio printing, micro printing, latent images and embossing are common features used as counterfeit deterrents. Letterpress printing processes the serial number printing and signature printing. This process allows the control of banknote issuing since each note must have different serial numbers Printing inks also contribute to the security of banknotes. Special security inks such as fluorescent inks, phosphorescent inks, infrared absorbing and reflecting inks, optical variable inks are all available to the security printer. Used in appropriate designs these inks can be very effective as banknote security features. A specialist paper manufacturer makes the papers of notes for the Bank. It is manufactured from cotton fiber and linen rag, which makes it tougher and more durable than the more common wood pulp paper. Using copious amounts of water, the cotton is broken down into individual fibers and reformed into reels of paper of the quality required. 2.13.3 Security in machine readable features: The rapidly increasing requirement to authenticate banknotes in processing and vending machines means that machine-readable features are a necessity in banknotes. Much of the machine-readable features are currently used in paper banknotes, these including ink-based features such as phosphorescence, and applied features such as optical variable devices. Two machine readable features commonly used in paper banknotes, security threads and watermarks. The printed security threads incorporating magnetic ink can be "hidden" under offset inks, and the "shadow image" (similar in appearance to a watermark) can be created by varying the depth of the opacifying ink layers. Other features which could be used for machine reading include magnetic (intaglio) ink, infrared absorbing/reflecting (intaglio) ink, invisible fluorescent ink (patch and in serial numbers), offset inks with specific spectral properties and high level authentication system taggants. 51

CHAPTER THREE THEORETICAL ASPECTS OF CURVE GENERATION 3.1 Introduction In chapter one, we have mentioned that the reason for using computer graphic to represent information may not be only an appropriate, but also the only reasonable method of handling information. Any art shapes (lines, circles and curves) produced in graphic techniques are much complicated than pictures taken by a photograph camera, since picture pixels are ink dots spread in an appropriate fashion constructing the forms found in the picture without any intervention on the artist in this operation. Thus the forms produced by graphic systems are much harder to counterfeit, especially when the counterfeiter has no information about how and in which method the design is performed. To introduce the importance of graphics, let us take an example that shows the use of lines or curves compared with a solid area containing a simple text :Action

Lines

Circles

Curves

Pictures

No move Move all interior objects by 5 positions to the right Move only the interior two objects to the left Figure (3-1) The effect of using lines, curves compared with solid pictures 52

From the test above, it is obviously seen that any little change in the position of objects composed of lines or circles or curves is immediately noticed by the human eye. On the other hand, change in solid area draws less attention and cannot be easily recognized. This happens because it is not easy for the human eye to track any change which occurs to small amount of objects found within big space and the reverse is true. Thus it is a suitable way to deal with objects composed of curves (or lines) in the process of generating shapes involved in document security concept. The only way to generate curves for a given set of points ( control points) is by the process of interpolation. This operation is needed to complete the spaces between the control points to form the final curvature construction. Such a subject is described in detail in the following section.

3.2 Curve Fitting and Generation (Interpolation) Interpolation, the computing of values for a tabulated function at points not in the table, is the most important task. Many famous mathematicians have their names associated with procedures for interpolation: Gauss, Newton, Bessel and Stirling. There are three reasons for using interpolation, First, interpolation methods are the basis, for many other procedures like numerical differentiation, integration and solution methods for ordinary and partial-differential equations. Second, these methods demonstrate some important theory about polynomials and the accuracy of numerical methods. Third interpolating with polynomials serves as an excellent introduction to some techniques for drawing smooth curves. This chapter compares several ways of doing interpolation and contrasts these procedures with several ways for fitting imprecise data and for drawing smooth curves (fit a polynomial curve to the points). Several methods for interpolating and approximation can be viewed, some of which are :-

3.2.1 Lagrangian Polynomials [Ralston 1978], [Kuo 1972] The Lagrangian polynomial is the simplest way to exhibit the existence of a polynomial for interpolation with unevenly spaced data. Data where the x-values are not equispaced often occur. If we have four points (xi,fi(x)), i = 0,1,2,3 then Lagrange form can be:-

53

p3(x) 

(x  x1)(x  x2 )(x  x3) (x  x0 )(x  x2 )(x  x3) f0  f1  (x0  x1)(x0  x2 )(x0  x3) (x1  x0 )(x1  x2 )(x1  x3) (x  x0 )(x  x1)(x  x3) (x  x0 )(x  x1)(x  x2 ) ……(3-1) f2  f3 (x2  x0 )(x2  x1)(x2  x3) (x3  x0 )(x3  x1)(x3  x2 )

This equation is made up of four terms. each of which is a cubic in x: hence the sum is a cubic. The pattern of each term is to form the numerator as a product of linear factors of the form (x - xi ), omitting one xi in each term. The omitted value being used to form the denominator by replacing x in each of the numerator factors. In each term, we multiply by the fi corresponding to the xi omitted in the numerator factors. The Lagrangian polynomial for other degrees of interpolating polynomial employs the same pattern of forming a sum of polynomials all of the desired degree: it will have n + 1 terms when the degree is n. An interpolation polynomial does in fact pass through each of the points used in its construction, but may not gives an exactly correct values when used for interpolation. This is because the actual function that generates the xi, fi values is often unknown. We obviously then do not know its (n + 1 )st derivative needed to make the interpolation process. Here is an algorithm for interpolation with a Lagrangian polynomial of degree N. Algorithm: Lagrange Algorithm for Curve interpolation. Input : Given x and a set of N + 1 data pairs (xi, fi ), i = 0, . . . , N. Output: Interpolate the value for f(x), which is in this case the SUM Value. Step 1 : Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Step 9:

Set SUM = 0, I =1. For i= 1 to N SET P = 1. For j = 0 to N IF j#i SET P = P * (x - x(j))/(x(i) - x(j)). Next j. SET SUM =SUM+P*fi Next i. End.

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3.2.2 Neville's Method [Gerald 1997] The trouble with the standard Lagrangian polynomial technique is that we do not know which degree of polynomial to use. If the degree is too low, the interpolating polynomial does not give good estimates of f(x). If the degree is too high, undesirable oscillations in polynomial values can occur. Neville's method can overcome this difficulty. It essentially computes the interpolated value with polynomials of successively higher degree, stopping when the successive values are close together. The successive approximations are actually computed by linear interpolation from the intermediate values. The Lagrange formula for linear interpolation to get f(x) from two data pairs, (x1, f1) and (x2, f2), is

f ( x) 

( x  x2 ) ( x  x1 ) f1  f2 ( x1  x2 ) ( x2  x1 )

…(3-2)

which can be written as

f ( x) 

( x  x2 ) * f1  ( x1  x) * f 2 x1  x2

…(3-3)

Eq. (3.3) will be used in Neville's method. Neville's method begins by arranging the given data pairs, (xi, fi), so the successive values are in order of the closeness of the xi to x. Neville's method begins by renaming the fi as Pi0. We build a table by first interpolating linearly between pairs of values for i = 0, 1, i = 1, 2, i = 2, 3, and so on. These values are written in a column to the right of the first P of each pair. The next column of the table is created by linearly interpolating from the previous column for i = 0, 2, i = 1, 3, i = 2, 4, and so on. The next column after this uses values for i = 0, 3, i = 0, 4, . . . , and continues until we run out of data pairs. The general formula for computing entries into the table is:-

pi , j 

( x  xi ) * pi 1, j 1  ( xi  j  x) * pi , j 1 xi j  xi

…(3-4)

The remaining columns are computed similarly by using Eq. (3-4). 3.2.3 Divided Differences [Gerald 1997] There are two disadvantages to using to Lagrangian polynomial or Neville's method for interpolation. First, it involves more arithmetic operations than does the divided-difference method . Second, and more importantly if we desire to add or subtract a point from the set used to 55

construct the polynomial, we essentially have to start over in the computations. Both the Lagrangian polynomials and Nevill's 's Method also must repeat all of the arithmetic if we must interpolate at a new x-value. The divided-difference method avoids all of this computation. if the nth degree polynomial written in a special way, like : Pn (x) = a0 +(x-x0)a1 + ( x- x0)(x-x1)a2+……+(x-x0)(x-x1)…(x-xn-1)an if we choose the ai so that pn(x) = f(x) at the n +1 known points, (xi,fi), i = 0….n, then pn(x) is an interpolating polynomial. A special standard notation for divided differences is

f [ x0 , x1 ] 

f1  f 0 with f[x0] = f0 = f(x0) x1  x0

called the first divided difference between x0 and x1 The function

f [ x1 , x2 ] 

f 2  f1 x2  x1

is the first divided difference between x1 and x2 . In general,

f [ x s , xt ] 

ft  f s xt  x s

is the first divided difference between xs and xt . Higher-order differences are defined in terms of lower-order differences. For example :-

f [ x0 , x1 ,...xn ] 

f [ x1 , x2 ,....xn ]  f [ x0 , x1 ,...xn1 ] ……. (3-5) xn  x0

writing Eq. (3-5) with x set equal to x0,x1,….xn in succession gives X=x0 : pn(x0)=a0 X=x1: pn(x1)= a0+(x1-x0)a1. X=x2: pn(x2)= a0+(x2-x0)a1 +(x2-x0)(x2-x1)a2 . . X=xn: pn(xn)= a0+(xn-x0)a1 +(xn-x0)(xn-x1)a2+.…+(xn-x0)….(xn-xn-1)an. If Pn(x) is to be an interpolating polynomial, it must match the table for n+1 entries: Pn(xi) = fi

for i = 0,1,2…..n. 56

If the Pn(xi) in each equation is replaced by fi , then getting a triangular system, and each ai can be computed in turn. From Equation (3-5) a0 = f0 = f[x0] makes pn(x0) = f0 if a1 = f[x0,x1], then

pn ( x1 )  f 0  ( x1  x0 )

f1  f 0  f1 x1  x0

if a2 = f[x0,x1,x2], then

p n ( x2 )  f 0  ( x 2  x0 )

f1  f 0  x1  x0

( f 2  f1 ) /( x2  x1 )  ( f1  f 0 ) /( x1  x0 )  f2 x2  x0 It must be shown that each Pn(xi) will equal fi if ai = f[x0,x1,….xi]. Thus if we abbreviate ( x2  x0 )( x2  x1 )

F[xo] = f0[0] F[xo,x1] = f0[1] F[xo,x1,….,xn] = f0[n] Using this abbreviated notation, the interpolating polynomial that fits a divided difference table at x = x0,x1,x2,……, xn is [0]

[1]

[2]

pn (x)  f0  (x  x0 ) f0  (x  x0)(x  x1) f0  [3]

[n]

(x  x0 )(x  x1 )(x  x2 ) f0  .... (x  x0 )(x  x1)....(x  xn1) f0 An algorithm for constructing a divided difference table is :Algorithm : Algorithm for constructing a divided difference table. Input : Given a set of N + 1 data pairs, (xi, fi), i = 0, . . . , N Output: Interpolate the value for f(x). Step 1: Step 2: Step 3:

FOR i = 1 to N FOR j = I to N - I Compute fj[i] = (fj+1[i-1]-fj[i-1])/xj+i – xj) and enter into column i of the table. Step 4: Next j. Step 5: Next i. Step 6: End. 57

3.2.4 Least-Squares Polynomials The usual criterion in this method is to minimize the sum of the squares of the errors so as to determine the best function values f(x) that corresponds to x values. Because polynomials can be readily manipulated, fitting such functions to data that do not plot linearly is common. This method uses n as a degree of the polynomial and N as the number of data pairs and N must be greater than n+1[Ralston 1978]. If the functional relationship is expressed as:y= a0 + a1x + a2x2 + ……..+ an xn with errors defined by ei = Yi – yi = Yi – a0 – a1xi – a2xi2 - … - anxin. Where Yi is the observed or experimental value corresponding to xi with xi free of error, we minimize the sum of squares N

N

2

n

2

S  ei  (Y  a0  a1 xi  a2 xi  ..... an xi )2 i 1

i

i 1

At the minimum, all the partial derivatives S

S

a n

a0

. , S

a1

. ,…..

. vanish. Writing the equations for these gives n + 1 equations: S  a 0

N

0

 i 1 N

S   a1

0

 i 1

2(Y i  a 0  a1 xi  a 2 xi 2  .....  a n xi n ) ( 1).

2 (Y i  a 0  a1 x i  a 2 x i 2  .....  a n x i n ) (  x i ).

. .

N

S  a n

0

 i 1

2(Y i  a 0  a1 x i  a 2 x i 2  .....  a n x i n ) (  x i n ).

Divide each by -2 and rearranging gives the n+1 normal equations to be solved simultaneously n

2

a0 N  a1  xi  a 2  xi  ......  a n  xi   Yi . 2

3

a0  xi  a1  xi  a 2  xi  ......  an  xi 2

3

n

n 1

4

n 1

a0  xi  a1  xi  a2  xi  ......  a n  xi

  xiYi .

n 2

2   xi Yi . …..(3-6)

 a0  xi  a1  xi

 a 2  xi

n 2

 ......  an  xi

58

2n

n

  xi Yi .

Putting these equations in matrix form shows an interesting pattern in the coefficient matrix [Kuo 1972].

 N    xi   xi 2  n  xi

x x x x

i 2

i

3

i n 1

i

x x x x

2

i 3 i 4

i n2

i

..... ..... ..... ......

n

   Yi     i  a    xiYi  ….(3-7) 2 n2   xi Yi  i   n 2n   xi Yi  i 

x x x x

i n 1

All the summations in Eqs. (3-6) and (3-7) run from 1 to N.

3.2.5 Chebyshev Polynomials [Gerald 1997],[Ralston 1978] This method represents a function with minimum error. It develops the theory of a class of orthogonal polynomials that are the basis for fitting nonalgebraic functions with polynomials of maximum efficiency . Chebyshev polynomials can be expressed as functions of polynomials like:T0(x) = 1, T1 (x) = x, T2(x) = 2x2 - 1, T3(x) = 4x3 - 3x T4(x) = 8x4 - 8x2 + 1, ..…..(3-8) 5 3 T5(x) = 16x - 20x + 5x, T6(x) = 32x6 - 48x4 + 18x2 - 1, T7(x) = 64x7 - 112x5 + 56x3 - 7x, T8(x) = 128x8 - 256x6 + 160x4 - 32x2 + 1, T9(x) = 256x9 - 576x7 + 432x5 - 120x3 + 9x, T10(x) = 512x10 - 1280x8 + 1120x6 - 400x4 + 50x2 - 1. The members of this series of polynomials can be generated from the two-term recursion formula Tn+1(x) = 2xTn(x) - Tn-1(x), T0(x) = 1, T1(x) = x

…....(3-9)

Figure (3.1) represents the first four polynomials of the above equations.

59

Figure (3.1) Chebyshev Polynomials The Chebyshev polynomials are also terms of Fourier series, since Tn (x) = cos nθ, ……..(3-10) where θ = arccos x. and that cos 0 = 1, cos θ = cos (arccos x) = x. Eq. (3-10) is likely similar to Eqs. (3-8) and (3-9), thus we recall some trigonometric identities, such as: cos 2θ = 2 cost2 θ - 1, T2(x) = 2x2 - 1; cos 3θ = 4 cos3 θ - 3 cos θ, T3(x) = 4x3 - 3x; cos (n + 1) θ + cos (n - 1) θ = 2 cos θ cos nθ, Tn+1(x) + Tn-1(x) = 2xTn(x). Because of the relation Tn(x) = cos nθ, it is apparent that the Chebyshev polynomials have a succession of maximums and minimums of alternating signs, each of magnitude one. By arranging the Chebyshev polynomials, we can express powers of x in terms of them: 1=T0. x=T1, x2=1/2(T0+T2) x3=1/4(3T1+T3), x4=1/8(3T0+4T2+T4), x5=1/6(10T1+5T3+T5), x6=1/32(10T0+15T2+6T4+T6), x7=1/64(35T1+21T3+7T5+T7), x8=1/128(35T0+56T2+28T4+8T6+T8), x9=1/256(126T1+84T3+36T5+9T7+T9). By substituting these identities into an infinite Taylor series and collecting terms in Ti(x), we create Chebyshev series.

60

3.2.6 Bezier Polynomials The rapid development of new manufacturing technologies has generated ever stronger demand for effective methods of geometric description. Product and tool engineering have seen many new methods, based primarily on polynomial splines and their numerous generalization. These methods, possess good approximation and computational properties [Mineur 1998],[Ligun 1998]. Among the most widely known methods for description of smooth contours in geometric design are Bezier function: R= r(u) = (1-u)3 ro + 3u (1-u)2 r1 + 3u2(1-u) r2 + u3 r3

……(3-11)

where 0 ≤ u ≤ 1 for any given segment, ro = first control point , r1 = second control point , r2 =third control point , r3 =last control point. Thus the curve described by Bezier form passes through the points r0 and r3 and has a tangent at r0 in the direction from r0 to r1, and at r3 has a tangent in the direction from r2 to r3. The significance of these tangents vector is that the direction and length of each vector determine the curvature of Bezier curve, Changing the direction of a vector changes the direction in which the curve curves. While changing the length of a vector changes the amount of area affected by that vector [Faux 1979].

Figure (3-2) Examples of Bezier curves From Eq. (3-11) it's useful to specify the value of r and ř(u) (ř(u)= dr/du), at both ends of the segment, the derivatives ř(0) and ř(1) is proportional to the tangent vectors T(0) and T(1) at the ends. Thus its possible to write : ř(0)= α0 T(0) ; ř(1)= α1T(1);

……..(3-12) 61

The significance of the tangent vector magnitude α0 and α1 is as follows: increasing α0 and α1 simultaneously gives more fullness to the curve .(See Figure (3-3)(a )). Conversly increasing only α0 causes the curve to remain close to the direction of T(0) for a greater part of its length before turning into the direction of T(1). (See Figure(3-3)(b)) . For large values of α0 and α1 kinks and loop occur.

(A)

(B)

Figure (3-3) Tangent vectors with different directions Algorithm : algorithm for drawing a piece of a Bezier curve. Input : Given four points;(xi, yi), i =0,...,3 Output: Interpolate the get new values for each of x and y to draw. Step 1 : For u = 0 to 1 step 0.01 Step 2 : Let X = (1-u)3 x0 + 3(1-u)2 u x1 + 3(1-u) u2 x2 + u3 x3 Step 3 : Let Y = (1-u)3 y0 + 3(1-u)2 u y1 + 3(1 -u) u2 y2+ u3 y3 Step 4 : Plot (X,Y). Step 5 : Next u Step 6: End. To continue the curve ,repeat this process for the next set of four points, beginning with the third point. 3.2.7 B-Spline Polynomials B-splines have proved popular due to the predictable results that they give to the designer and high speed with which they can be computed [Burger 1989]. The B-spline function generates curve section which has continuous slopes so that they fit together smoothly [Harrington 1987]. A B-spline of order k=3 consisting of n-k+2 segments is defined by a linear combination of basis functions ci using n+1 control points vi ci (u)=b-1 (u) vi-1 +b0 (u)vi +b1(u)vi+1 +b2 (u) vi+2

………(3-13)

where the base functions are defined by [Pham 1988]: 62

b-1(u)=1/6(-u3+3u2-3u+2) b0(u) =1/6 (3u3 – 6u2 + 4) b1(u) =1/6 (-3u3+3u2+3u+ 1) b2(u) = 1/6 t3

Figure (3-4) B-Spline curves segment. The fact is that each curve segment shares control points as shown in figure (3-5) that shows the effect of changing control points P1 .This pulls the segments of curve in the appropriate direction and also affects, to a lesser extent parts of the curve, and thus demonstrates the important locality property of B-spline [Watt 2000].

Figure (3-5) The effect of changing the position of control point P1. Algorithm : algorithm for drawing a b-Spline curve. Input : Given n+1 points vi =(xi , yi ), i=0,...,n Output : Interpolate the get new values for each of x and y to draw. Step 1 : Set v-1 = v-2 = v0, and Set vn+1 = vn+2 = vn Step 2: For i = 0 to n-1 Step 3: For u = 0 to 1 step 0.01 Step 4: X=(1-u)3/6 xi-1+(3u3–bu2+4)/6xi+(-3u3+3u2+3u+1)/6xi+1 +u3 /6xi+2 Step 5: Y=(1-u)3/6yi-1+(3u3–bu2+4)/6yi+(-3u3 +3u2+3u+1)/ 6yi+1+u3 /6yi+2 Step 6: plot (X,Y). Step 7: Next u. Step 8: Next i. Step 9: End. 63

3.2.8 Cubic Spline Cubic Spline is one of the more popular Spline functions . It is often formed either, by prescribing the slope at each point , or by requiring continuity of the second derivative over the entire domain. The equations for cubic polynomial in the i th interval gi (xi) are between the points (xi ,yi) and (xi+1 , yi+1), since they fit at the two endpoints of the interval where :gi = ai(x – xi)3 +bi(x-xi)2 + ci(x-xi) +di …..(3-14) such that gi(xi) = yi for i= 0,1,2,……,n-1 thus yi = ai(x – xi)3 +bi(x-xi)2 + ci(x-xi) +di = di When x= xi and yi+1= ai(x – xi+1)3 +bi(x-xi+1)2 + ci(x-xi+1) +yi = aihi3 +bihi2 + cihi +yi When x= xi+1 To perform the slope and curvature of joining spline we differentiate Eq.(3-14) g’(x) = 3ai+hi2+2bihi+ci, g’’(x) = 6aihi + 2bi assuming si = gi’’(xi) we get si= 6ai(xi – xi) +2bi = 2bi , si+1= 6ai(xi+1 – xi) +2bi = 6aihi +2bi After a number of steps we get equation (3-15) [Gerald 1997],[Burden 1997] y  y i y i  y i 1 hi 1 si 1  (2hi 1  2 hi ) s i  hi s i 1  6( i 1  ) ……(3-15) hi hi 1 Equation (3-15) applies at each interval point from i=2 to i=n-1 ,n being the total points, this gives n-2 equations. For each of S2 , S3 ,..., Sn-1, equation (3-15) can be constructed as a matrix form such that h2 h1 2(h1  h2 )  h2 2(h2  h3 )   h3   

 Y3  Y2 Y2  Y1   S1     S  h2 h1   2    Y4  Y3 Y3 Y2      S3  h3   h3 h2   .    *    6 * .  2(h3  h4 ) h4 .......   .    . ...   hn2 2(hn2  hn1 ) hn1   .    .    S Yn Yn1 Yn1  Yn2   n1      Sn  hn2   hn1 64

two additional equations involve S1, and Sn introduced when specifying the conditions pertaining to the end intervals of the whole curve .To some extent these end conditions are arbitrary, three alternative condition are often used, [Gerald 1997]: Condition 1:- Take S1 =0 , Sn =0 , this is equivalent to assuming that the end cubics approach linearity at their extremities (See Figure (3-6)). This condition is called a natural spline. This technique is used very frequently. Then, the coefficient matrices become       

2(h1  h2 )

h2

h2

2(h2  h3 ) h3

h3 2(h3  h4 ) h4 ....... ... hn2 2(hn2  hn1)

      

Condition 2 :- If S1 = S2 , Sn, = Sn-1, , this is equivalent to assuming that the end cubics approach parabolas at their extremities (See Figure (3-6)). Then the coefficient matrices become

      

3(h1  h2 )

h2

h2

2(h2  h3 ) h3

h3 2(h3  h4 ) h4 ....... ... hn2 2(hn2  3hn1)

      

Condition 3 :- Take S1 as a linear extrapolation from S2 and S3, and Sn as a linear extrapolation from Sn-1 and Sn-2. With this assumption, for a set of data that are fit by a single cubic equation, their cubic splines will be this same for all values (See Figure (3-6)). The relations for end condition 3 are: At the left end:

S 2  S1 S 3  S 2  h1 h2 At the right end: S n  S n1 S n 1  S n 2  , hn1 hn 2

, S1 

(h1  h2 ) S 2  h1S3 h2

Sn 

(hn  2  hn 1 ) S n 1  hn 1S n  2 hn  2

65

then the coefficient matrices become         

(h1  h2 )(h1  2h2 ) (h22  h12 ) h2 h2 h2 2(h2  h3 )

h3

h3

2(h3  h4 ) h4 ....... 2

... (hn2  hn12 ) (hn1  hn2 )(hn1  2hn2 ) hn2 hn2

        

After the Si values are calculated, we can get the values of ai , bi , ci , di for each interval to interpolate for new values of the Equation(3-14) . ai = (Si+1-Si) / 6hi; bi =Si /2 ; bi = (Yi+1- Yi) / hi – (2hiSi+hiSi+1) / 6 ; di = Yi ;

Figure (3-6) cubic Splines curves through three conditions.

3.3 Case study In this section, we will give an example with real data control points (table(3-1)), such that these control points are interpolated with the eight methods mentioned earlier each one in turn. Each of the eight methods gives a set of interpolated data which differs from the others, as illustrated with tables (3-2) and (3-3). Figure (3-7)(A-H), showing for each case a clear estimation of the data and showing where and how each method could be used, especially after tracking the variation of values that might be a good or bad feature which helps in providing more secure property when dealing with curve security described in chapter four of this thesis. 66

Table(3-1) control points. Control points I X Y

1 100 300

2 125 200

3 150 200

4 175 250

5 200 300

6 225 280

7 250 250

8 275 260

9 300 220

10 325 300

Table (3-2) shows the interpolation values of the first four methods Lagrange X Y X Y

Divided difference X Y X Y

100 101 103 105 107 109 111 113 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 194 195 197 199 200 203

100 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 178 179 181 183 185 187 189 197 199 203 205 206 207

300 294 282 272 262 252 243 236 224 218 212 206 202 198 194 192 190 188 187 188 188 189 191 194 197 200 200 204 209 213 215 220 224 228 232 236 240 243 248 252 255 260 264 268 272 276 280 289 290 293 298 300 298

205 207 209 211 213 215 219 223 227 229 234 236 238 240 242 244 246 248 252 255 257 259 261 263 265 267 269 271 273 275 277 279 281 283 285 287 289 291 293 295 297 299 300 301 303 305 310 315 316 318 322 324 325

297 296 293 292 291 289 286 282 278 276 270 268 266 263 261 258 255 253 253 256 258 260 260 262 262 262 262 261 261 260 259 256 255 252 250 247 243 240 236 232 228 222 220 225 235 243 263 279 282 286 294 298 300

300 290 273 259 247 237 228 221 216 211 207 204 202 200 198 197 196 195 194 194 194 194 195 196 197 199 201 203 205 208 212 216 220 224 229 234 239 244 250 255 258 260 265 271 275 280 284 297 299 301 301 301 301

209 211 213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 245 247 251 253 255 257 261 263 265 267 269 271 273 275 277 279 281 283 285 287 289 291 293 295 297 299 301 303 305 313 315 319 321 323 325

Neville’s method X Y X Y

300 299 297 295 292 289 286 283 280 276 272 269 266 263 260 257 255 253 251 250 249 250 250 251 253 254 255 257 258 259 259 260 259 258 257 255 253 249 246 241 237 232 227 222 217 213 210 214 221 243 258 277 300

100 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 200 204 206 208 210

67

300 291 274 260 247 237 229 222 216 211 208 205 202 200 198 197 196 195 195 195 195 195 196 196 198 199 201 203 206 209 212 216 220 225 229 234 239 245 250 255 261 266 271 276 280 285 289 292 301 302 301 301 299

216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 318 320 322

293 290 287 283 280 276 273 269 266 263 260 258 255 253 252 251 250 250 250 250 251 252 253 255 256 257 258 259 260 260 260 259 258 256 253 250 246 242 237 232 227 222 218 214 211 209 209 211 215 243 259 278

325 300

Least square X Y X Y 100 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 181 183 185 187 189 191 193 195 205 207 209 211

300 289 270 254 242 232 224 218 213 209 206 203 202 200 199 198 197 196 196 195 195 195 196 197 198 199 201 203 206 209 212 216 220 224 229 234 239 245 250 255 261 266 271 276 281 285 289 292 295 302 301 301 299

213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 245 247 249 251 253 255 257 259 261 263 265 267 269 271 273 275 277 279 281 283 285 287 289 291 293 295 297 299 301 303 305 307 309 313 321 323

297 295 293 290 287 283 280 276 273 270 266 263 260 258 255 253 252 251 250 250 250 250 251 252 253 255 256 257 258 259 260 260 260 259 258 256 253 250 246 242 237 232 227 222 218 214 211 209 208 214 258 278

325 300

Table (3-2) shows the interpolation values of the last four methods Chebyshev method X Y X Y

B-spline method X Y X Y

Bezier method X Y X Y

Cubic spline X Y X Y

100 100 102 104 106 108 109 112 114 116 118 120 121 124 126 129 130 133 135 138 141 144 147 150 153 156 157 160 162 165 166 169 171 174 175 178 180 181 184 186 188 192 194 198 199 202 205 210 213 216 217 220 225 228 231 234 237 240 243

100 104 105 106 107 108 109 111 113 116 119 122 123 126 127 131 133 136 137 140 143 144 147 149 150 153 158 160 161 164 164 167 168 172 173 175 176 180 182 185 186 190 191 195 199 200 203 204 208 208 211 215 220 224 230 231 233 235 238

100 102 104 108 109 112 114 116 118 120 123 126 129 132 135 136 138 141 144 147 148 150 153 156 159 162 165 168 171 174 176 178 180 182 186 188 192 194 198 201 204 207 210 213 216 219 222 225 228 231 234 237 240 243 246 249 253 256 258

100 101 103 105 107 109 111 113 115 117 119 121 123 125 125 127 129 131 133 135 137 139 141 143 145 147 149 150 151 153 155 157 159 161 163 165 167 169 171 173 175 175 177 179 181 183 185 187 189 191 193 195 197 199 200 201 203 205 207

300 297 291 280 275 271 266 257 253 246 243 240 237 232 230 226 224 221 220 218 217 217 218 219 220 223 224 227 229 233 235 240 243 249 250 257 259 262 266 268 271 274 276 278 279 280 280 280 280 279 278 277 274 272 270 267 264 261 258

244 246 247 249 250 250 252 253 254 256 258 259 260 262 264 265 266 268 270 271 272 274 276 277 278 280 282 283 285 286 288 289 291 292 294 295 297 298 300 301 303 304 306 307 309 310 312 313 315 316 318 319 321 322 324 325

256 254 253 251 250 250 251 251 251 252 252 252 252 252 251 251 251 251 251 250 250 250 249 249 249 249 249 249 249 249 249 249 249 250 250 251 252 253 254 255 257 258 260 262 264 266 269 272 275 278 281 285 289 293 298 300

300 283 281 278 272 269 266 256 249 240 232 223 221 214 213 207 206 203 203 203 203 204 205 207 208 212 219 223 223 228 229 234 235 244 245 250 251 259 265 269 270 277 278 283 288 288 290 290 290 290 289 287 283 280 273 272 270 268 265

239 242 254 260 266 271 280 282 286 289 293 293 297 300 303 306 306 307 308 310 314 317 320 321 321 322 322 323 323 324 324 325

265 262 256 255 255 254 247 247 243 240 239 238 238 240 243 247 248 250 250 254 263 270 276 285 288 290 292 295 297 297 299 300

68

300 294 283 273 268 259 255 248 245 241 236 231 227 223 221 220 219 218 217 217 218 218 220 222 225 228 232 237 242 247 253 256 258 263 267 271 273 276 278 279 280 280 280 280 279 278 277 275 273 270 268 265 262 259 255 252 251 252 252

259 260 262 264 265 266 268 270 271 272 274 276 277 278 280 282 283 285 286 288 289 291 292 294 295 297 298 300 301 303 304 306 307 309 310 312 313 315 316 318 319 321 322 324 325

252 252 252 252 251 251 251 251 250 250 250 250 249 249 249 249 249 249 249 249 249 249 250 250 251 251 252 253 254 256 257 259 261 263 265 267 270 273 276 279 283 287 291 295 300

300 295 285 275 266 257 248 239 231 223 216 210 205 200 200 196 193 191 190 189 189 189 190 192 194 196 199 200 201 204 208 211 215 219 223 227 231 236 240 245 250 250 255 260 265 270 275 279 284 288 291 295 297 299 300 301 301 302 301

209 211 213 215 217 219 221 223 225 225 227 229 231 233 235 237 239 241 243 245 247 249 250 251 253 255 259 261 263 265 267 269 271 273 275 275 277 279 281 283 285 287 289 291 293 295 297 300 301 305 307 311 313 315 317 319 321 323 325

300 299 297 295 292 290 287 283 280 280 277 273 270 266 263 260 257 255 253 251 250 250 250 250 251 252 256 258 259 261 262 263 263 262 260 260 257 254 249 244 240 235 230 226 223 220 219 220 221 229 235 250 258 266 274 281 288 295 300

69

Form the table and figures above, one can see the difference between the methods of interpolation. If we take a small section for the first 4 control points from each figure, we can get the following information:

Lagrange

Divided difference

Neville’s

Least Square

Chebychev

B-Spline

Bezier

Cubic Spline



 









Figure (3-8) Comparison between methods of interpolation for the first 4 control points. Due to the small set of control points used, we can see that Lagrange method is a suitable method for interpolation. But for a big set of control points the interpolated values tend to draw a vibration curve. We can make use of such a vibration in designing a curve that is very difficult for any one to guess its control points. Divided difference gives an interpolated data that are near to the real data but are unstable in its curvature. Neville’s and Chebychev methods give almost the same convergence to the data, and are considered as suitable as good methods for small set of control points but these methods are so much large algorithm to due and takes a big memory space especially for a big set of data. A least square method tries to approximate the real data but it needs very complicated calculations especially for the big set of data. B-spline method is a simple, efficient and good method but its interpolated points pass between control points except for the first and last control points. Bezier method is used by most of the architecture programs, because of its simplicity and its ability to make control over the whole curve using 0 and 1 mentioned earlier. Cubic spline method is a very effective method for the cases that need a curve which passes exactly through the control points, and 70

gives exact fitting for all the data with smooth curvature form and no vibration along its path.

3.4 Coordinate Planes Mathematically, there are three types of coordinate systems, these are, Cartesian, Polar and Parametric systems, described as follows :3.4.1 Cartesian coordinates Points in a plane can be placed in one-to-one correspondence with pairs of real numbers by using two perpendicular coordinate lines that intersect at their origins. Usually, one of the lines is horizontal with its positive direction to the right and the other is vertical with its positive direction up. The two lines are called coordinate axes; the horizontal line is called the x-axis, the vertical line is called the y-axis, and the coordinate axes together form what is called a Cartesian coordinate system or sometimes a rectangular coordinate system [Anton 1988]. The point of intersection of the coordinate axes are called the origin of the coordinate system.

Figure (3-9) Cartesian System If P is point in a coordinate plane, then we draw two lines through P, one perpendicular to the x-axis and one perpendicular to the y-axis. If the first line intersects the x-axis at the point with coordinate a and the second line intersects the y-axis at the point with coordinate b, then we associate the pair (a, b) with the point P (Figure (3-10)).

y

P(a,b)

b

x a

0

Figure (3-10) Point in plane system The number a is called the x-coordinate or abscissa of P and the number b is called the y-coordinate at the ordinate of P; we say that P is 71

the point with coordinates (a, b) and denote the point by P(a, b). The process of locating the position of a point in a coordinate plane is called plotting [Hill 2001]. The coordinate axes divide the plane into four parts, called quadrants. These quadrants are numbered from one to four, It is easy to determine the quadrant in which a point lies from the signs of its coordinates. A point with two positive coordinates (+, +) lies in Quadrant 1, a point with a negative x-coordinate and a positive y-coordinate (-, +) lies in Quadrant II, and so on. 3.4.2 Polar Coordinates To form a polar coordinate system in a plane, we pick a fixed point O, called the origin or poles; and use the origin as an endpoint, then construct a ray, called the polar axis. After that associate with any point P in the plane a pair of polar coordinates (r, θ), where r is the distance from P to the origin, and θ measures the angle. The number r is called the radial distance of P and θ is called a polar angle of P.

Figure (3-11) Polar System Frequently, it is helpful to use both polar and rectangular coordinates in the same problem. To do this, let the positive x-axis of the rectangular coordinate system serve as the polar axis for the polar coordinate system. When this is done, each point P has both polar coordinates (r, θ) and rectangular coordinates (x, y). As shown in Figure (3-12), these coordinates are related by the equations: x= r cos θ , y = r sin θ and r2=x2+y2 such that tan θ = y/x

Figure (3-13) Relationship between polar and rectangle systems 72

3.4.3 Parametric Coordinates Most of the function graphs can be the represented as an equation of y = f(x) whose graph is any given curve. However, there are graphs of functions that are specialized curves in the sense that no vertical line can cut such a curve more than once. Curves that are not graphs of functions can often be specified by using a pair of equations x= x(t) y= y(t). to express the coordinates of a point (x, y) on the curve as functions of an auxiliary variable t. These are called parametric equations for the curve, and the variable t is called a parameter. Parametric equations arise naturally if one imagines a plane curve C to be traced by a moving point. If we use the parameter t to denote time, then the parametric equations x = x(t), y = y(t) specify how the x- and y-coordinates of the moving point vary with time, as in the following figure.

Figure (3-12) Parametric system

3.5 Choosing the Suitable Coordinate Systems It is the designer’s decision to choose the suitable coordinate system according to the control points he specifies. Choosing control points and suitable coordinate system allows the designer to fashion a large variety of shapes simply by transforming and altering the sequence of control points. The sequence of control points is often called the control polygon. The designer enters the control polygon on the basis of a lot of experience. Along with a clear understanding of the characteristics of the curve-generation algorithm-the algorithm that will later be used to regenerate the curve from the data points. The designer wishes to create a computer representation of the curve that might be a part of an emerging design for a car fender, a turbine blade, or the casing of an electric drill. Or it might be the trajectory of a camera as it sweeps through a scene taking snapshots. The goal is to capture the shape of the curve in a form that permits it to be reproduced at will adjusted in shape and size as desired and sent to a machine for automatic cutting or mold etc. 73

So, the purpose is to find the best way to represent the curve of the given control points, such that if the points are taken to be in sequence (i.e. there is a unique value y for each x in the equation y = f(x)) then the Cartesian coordinate is the ideal method to represent such a curve. Examples of such a case are trigonometric functions and exponential equations and user-defined in sequence points, as in the figures.

(B)

(A)

Figure (3-14) (A) control points with sine function (B) control points of exponential function mixed with sine function If the points are represented as many values of y according to the same x (this means a vertical line x passes through many points of y) then polar or parametric systems are preferred. If the shape produced from control points is uniform (according to a specific degree and specific radius) then polar coordinate system is the best, while if the shape is not uniform then it is suitable to represent it in parametric equations.

Figure (3-15) Examples to show the control points of curves plotted with polar coordinates

(A)

(B)

(C)

(D)

Figure (3-16) shows (A) control points in a parametric form. (B,C,D) shapes produced using the same control points with some alteration in their positions. 74

Chapter Four DEVELOPMENT OF CURVE SECURITY TECHNIQUES 4.1 Introduction Counterfeiting is a growing threat in recent years, especially in light of the proliferation of digital scanners, color copiers and high quality printers. New methods and techniques must be established to stop this growing threat. Curve security is a new and important field for detecting and protecting curve from being counterfeited. Any document could be composed of different kinds of curves (geometrical shapes, letters (which are also a kind of curves) in addition to illustrations and graphs, which give the document of the final figure. Curve security involves the process of protecting the shape of curve from being reproduced and as a result, protecting the whole document from being regenerated by any counterfeiting person. The shape of the curve is basically based upon a set of control points that fundamentally describe its properties and its curvature. The algorithms that are used to generate the curves are primarily based on these control points. Thus if the intruder knows the set of control points, it may lead to discover the shape of the curves with a trial and error on the methods or algorithms that were originally used to produce the curve. To demonstrate this problem in more detail, let’s take an image of a curve scanned by a desktop scanner (See Figure (4-1)). The original curve form can be used in many other applications and documents as an image but not as a stand-alone curve. Trying to regenerate the curve alone without knowing the generation function or the control points of the curve will face many problems as shown in figure (4-2). Original curve form

Original Control points of curve

Figure (4-1) A scanned curve with its original control points 75

The original set of control points generates the curve in a smooth fashion and in a suitable curvature form. Potential counterfeiters who would like to reproduce the original curve with any other set of control points, will be unable to eliminate the undesired variations and change on curve form produced by the change in location of the control points. Choosing arbitrary set of control points

Figure (4-2) choosing arbitrary set of control points From the above figures, we conclude that the basis of curve generation is the control points and thus, there must be a way to protect these control points from being known by any one trying to generate the original form. According to this aspect we will introduce new methods that provide the security features to the curve so as not to be reproduced even if the counterfeiter knows the set of control points. These methods can be listed here in detail as: 4.2 Parameterization Method A parametric form for a curve produces different points on the curve, based on the value of a parameter. Parametric forms can be developed for a wide variety of curves, and they have much to recommend them. A parametric form suggests the movement of a point through time, which we can translate into the motion of a pen as it sweeps out the curve. The path of a particle travelling along the curve is fixed by two functions (X(t),Y(t)) as the position of the particle at time t. The curve itself is the totality of points ‘visited’ by the particle as t varies over some interval.

76

As an example, if we take the following data that represent a simple curve (represents the letter B): Table (4-1) shows the control point of a simple figure (letter B). I t X(t) Y(t) Control point of letter B 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

200 250 280 250 200 250 280 250 200 200

200 200 240 280 280 280 320 360 360 200

From the figure above we can see that for the same X (i.e. X=200) there are many values for Y (i.e. Y=200, 280, 360). Therefore the interpolation can only be applied between (t and X) for the first time and then (t and Y) for the second time, the results produced from the interpolation of t and X are plotted with the results produced from t and Y to represent the final curve. Now, according to the given values of parameter t the final curve is formed. For the above values of t =1,2,3,…10 , where ∆t = (ti+1 – ti) = 1, interpolating the above figure gives Table (4-2) Interpolation of letter B with ∆t=1 t

Interpolated figure

1 2 3 4 5 6 7 8 9 10

77

For the same control points, if we now take t = 2, 4, 6, ….,20, such that ∆t = (ti+1 – ti) = 2, and also take another interval of t such that t = 10, 20, …,100 where ∆t = 10, then the above figure will be more and more smoother as the value of ∆t increases, Table (4-3) shows interpolation of the above control points with two different intervals of t t Interpolated figure t Interpolated figure 2 4 6 8 10 12 14 16 18 20

10 20 30 40 50 60 70 80 90 100

The ideal interpolation figure is given when there is no fixed interval applied with ∆t as shown in the following table Table (4-4) shows the interpolation of the ideal curvaturel figure T Interpolated figure 1 20 40 41 42 62 82 83 84 85

This comes from the fact described above that the straight line between P(X[1],Y[1]) and P(X[2],Y[2]) can be achieved only when (t2 – t1) = 1. The same thing is applied to p(X[4],Y[4]) , P(X[5],Y[5]) and also to p(X[5],Y[5]) , P(X[6],Y[6]) and so on. Notice that, changing value of any of the t’s leads to a great change in the curvature of the whole figure as shown 78

Table (4-5) shows interpolation result of the control points When changing values the of t t (A) t (B) 20 40 60 70 110 115 140 160 180 200

20 40 60 80 100 120 140 160 170 200

Table (4-5)(A) shows that ∆t=20 and it is fixed for all t’s except for t4,t5,t6,t7 , where different values are taken from 20, figure (B) shows that ∆t=20 for all values of t except for t9 = 170 where it is supposed to take value of 180. From all of the figures above we can see that there is no continuity in the curvature between P10 and P1. Therefore we need a method to extend our figure to be drawn as a closed graph with a degree of continuity between the points of the figure, this can be achieved with the following algorithm: Algorithm : algorithm to generate continuity between control points. Input : The original set of points is Pi , where i = 1 .. 10 . Output: Drawing figure with required continuity. Step 1: Add additional points Pj , where j = 11 .. 20, such that Pj =Pj-10. Step 2: Apply the interpolation process to the original points with the new additional points. Step 3: Now draw the curve from P2.. P12. Step 4: End. interpolated Figure

Figure (4-3) continuity between last and first control points. 79

Extending to close graph gives additional curve security in that if any one knows the set of control points, then he does not know where to start drawing of the graph because it’s a continuous curve with no start and end points. Another form of parameterization is normally performed when using Bezier method for curve generation. Bezier method has the property that it interpolates the first four pointes then the second four points and so on, according to its equation described in the previous chapter. If we assume for any segment of the curve that ro = first control point , r1 = second control point , r2 =third control point , r3 =last control point. then the curve described by Bezier form passes through the points r0 and r3 has a tangent at r0 in the direction from r0 to r1, and at r3 has a tangent in the direction from r2 to r3. The significance of these tangents vector is that the direction and length of each vector determine the curvature of Bezier curve. Changing the direction of a vector changes the direction in which the curve curves. On the other hand, changing the length of a vector changes the amount of area affected by that vector. Changing the value of the tangent in the direction between r0 and r1

Original curve form

Figure (4-4) Using of bezier curve The change in the direction of the tangent gives another form of security for the curve since the change does not affect the control points of the curve, while a change of the curve shape happens. 80

Each of the cases above gives an indication on how parameterisation greatly affects curve shape, and thus adds a security feature that cannot be predicted by any counterfeiter designer. To achieve a great security on the curve parameters, it is possible to assign a mathematical function to the value of parameter t, such as using one of the trigonometric functions (sine, cosine, tan,..,etc) or a function of X such as X3, 4X+2 or use an exponential function that gradually increases as moving from the first point to the last point, or use mix of these functions mentioned right now.

4.3 Arbitrary Point Control (Area Parameterisation) This method introduces a new concept that interactively modifies the shape of the generated curve used in computer aided design (CAD) until the desired curve is obtained, such that, the designed curve has an acceptable fitness to the input points and gives the required curve security. The control over the curve geometry is obtained by modifying the parameterisation of the input data using an outside arbitrary point. The control of the curve geometry is obtained by compression of the area defined using input data points and outside arbitrary point, which we call the guide of parameterisation. The motion of the guide will produce a global effect on the geometry of the curve. To define parameterisation of data using areas we choose an arbitrary point G= (XG, ,YG) called the guide of parameterisation, then we define the values of ti to be to= 0 where,  i 

, ti=ti-1 + |δi|/ D

1 Xi  XG 2 X i 1  X G

Yi  YG Yi 1  YG

for i = 1 ,……,N , for i = 1,….., N

And N

D

|  i | i 1

The following figure (4-5) illustrates the values of the δi (i=1,…..,4) for a given set of data points (Xi,Yi) , i = 0,……,4 and for the guide previously chosen. The symbols “‫ ”ٱ‬and “Δ” denote the input data points and the guide positioning respectively. 81

Figure (4-5) Guide of parameterisation So, we can see that, for all δi , i # 0 , the values ti are distinct and monotonic with i, if the choice of G is such that G is collinear with the consecutive data points, then the corresponding δi vanishes. As the position of the guide G is left to the user, it is possible to fix the guide such that δi # 0 for all values of i, to enforce the condition t0 XCentre then slope = -1 * slope.

85

Step 6 : Now find θ that corresponds to each coordinate lying on the diameter of the circle using the equation θ = arctan(slope), where arctan is the tan inverse of the degree. Step 7 : The points of the circle are then XCircle = Raduis * Cos(θ) and YCircle = Raduis * Sin(θ ). Step 8 : At this stage each point of the curve is connected to its correspondening point of the circle. Step 9: End. The following table shows the previous stages :-

I

t

X

Y

1 20

200

200

2 40 3 60

400 400

200 300

4 80

200

300

Table (4-9) Radius Method Control points Curve of control point

Curve with circle and connected lines

From the table above, we can see that each point of the curve is tightly connected to each point lying on the diameter of the circle. Now, if we scale up or down the radius of the circle, then each point of the curve is affected by the same scale and the whole shape will be changed as in the following figures:-

86

Scaling radius up and interpolate

Scaling radius down and interpolate

Figure (4-7) Curve interpolating with radius scaling up and down The regions of concave or convex seen in the figures above occur because of the control point regions where they are not affected by the scaling factor.

4.6 Steganography and Curve Hiding This section is concerned with protecting objects (curves and texts) displayed on screen during design process with a method called Steganography. This method is the art of hiding information in ways that prevent the detection of hidden objects. Steganography, derived from Greek, literally means "covered writing”. It includes vast array of secret communications methods that conceal the message's very existence. These methods include invisible inks. microdots, character arrangement, digital signatures, covert channels and spread spectrum communications. Steganography and cryptography are cousins in the spy craft family. Cryptography scrambles a message so it cannot be understood. Steganography hides the message so it cannot be seen. A message in cipher text, for instance, might arouse suspicion on the part of the recipient while an "invisible" message created with steganographic methods will not. 4.6.1 Image Files To a computer, an image is an array of numbers that represent light intensities at various points (pixels). These pixels make up the image's raster data. A common image size is 640 x 480 pixels and 256 colors (or 8 bits per pixel). Such an image could contain about 300 kilobit, of data. Digital images are typically stored in either 24 bit or 8-bit files. A 24-bit images provides the most space for hiding information. All color variations for the pixels are derived from three primary colors: red, green, and blue. Each primary color is represented by 1 byte: 24-bit images uses 3 bytes per pixel to represent a color value. These 3 bytes can be 87

represented as hexadecimal, decimal, and binary values. A white color would have the value FFFFFF: 100 percent red (FF), 100 percent green (FF) and 100 percent blue (FF). Its decimal value is 255 255 255, and its binary value is, 11111111, 11111111, 11111111 which are the three bytes making up white. There are many types of file formats that are used to hold the hidden information. The simplest and efficient type is the BMP file format because, it is a kind of lossless compression that lets us reconstruct the original message exactly without any loss of its information. Therefore, it is preferred when the original information must remain intact (as with steganographic images). 4.6.2 Types of Data Embedding In our approach, we have proposed three methods of information hiding, these three methods are:  Embedding curve within image file.  Embedding text within an interpolated curve.  Embedding curve points within another curve. In these three types of embedding, an innocent looking image is used to hold the hidden information, called the cover image. The curve combined with the cover image, makes a stego-image. A stego key (a type of password) may also be used to hide, then later decodes, the hidden information. 4.6.3 The Proposed Methods of Information Hiding Information can be hidden in many different ways within objects. To hide information, straight object insertion may encode every bit of information in the image or selectively embed the object in "noisy" areas that draw less attention-those areas where there is a great deal of natural color variation. The object may also be scattered randomly throughout the image redundant pattern encoding "wallpapers" the cover image with the object. A number of ways exist to hide information in digital images. Least significant bit (LSB) insertion is a common, simple approach to embedding information in a cover file. If we use 24-bits image and we want to hide an image in the LSBs of each byte of a 24-bit image, then we can store 3 bits of data in each pixel. For example, the letter A can be hidden in a three pixels. The original raster data for 3 pixels (9 bytes) is:88

Table (4-10) Original Raster Data Pixel 1 Pixel 2 Pixel 3

Red

Green

Blue

00100111 00100111 11001000

11101001 11001000 00100111

11001000 11101001 11101001

The binary value for A is 10000011 inserting the binary value for an A in the three pixels would result in: Table (4-11) Resulted Raster Data Pixel 1 Pixel 2 Pixel 3

Red

Green

Blue

00100111 00100110 11001000

11101000 11001000 00100111

11001000 11101000 11101001

The underlined bits are the only three actually changed in the 9 bytes used. This process can be explained as taking every three bits of letter A form left side, and insert them within the LSB of each pixel bytes from the right side. On average, LSB requires that only half the bits in an image be changed. We can hide data in the least and second least significant bits and still the human eye would not be able to discern it. 4.6.4 Embedding Types and Applications Delphi language that we use in our program provides us with a 24bit colors image or a 16777216 colors enough to simulate the colors that the human eye can see. Using the method of LSB, we can implement the embedding process using 3 bits of each pixel, such that a large number of data can be hidden in this way. The methods of embedding can be described as followings :4.6.4.1 Curve Within Image Any curve is composed of control point and a method of interpolation. In our program we give a code for each method of interpolation, as follows:       

Lagrange interpolation is represented by 000. Divided difference method is represented by 001. Nivells method is represented by 010. Least square method is represented by 011. Tshebyshev method is represented by 100. B-spline method is represented by 101. Bezier method is represented by 110. Cubic spline method is represented by 111. 89

Now, the process of hiding curve information involves hiding only the control points and the code of the method used to interpolate the curve. Hiding these information is not a random operation, but follows a an algorithm that is :Algorithm: algorithm for performing Steganography. Input : Curve to hide Output : Hidden curve within an image. Step 1: Encode the coordinate of the first and the last control point of the curve using the following equations (proposed by us):X-position = N *length + (-1)N * length /(length /100)……(4.1) Y-position = M *width + (-1)M * width /(width /100) Where N and M ε [0,1], thus the above set of equations gives us four positions on the screen, (100,60), (700,60), (100,540) and (700,540), this is in case that the image file has a resolution of 800 X 600. These four positions are less interesting than one’s of the image where a less detailed picture are concentrated here. Step2 : In these four positions, the first and last control point of the curve are stored. While each coordinate is represented by three digits we need a stego key to distribute the bits of these three digits around the 4 neighbors pixels of each of the four coordinates specified by eq. (4-1) (since each pixel can hold three bits and that each digit is represented by 4 bits, thus 4 bits x 3 digits = 12 bits which can be distributed on 4 pixels). This combination of the stego key is either (0,2,4,6) or (1,3,5,7) as shown in the following figure

Figure (4-8) stego-key Step 3 :After accessing the position of the first control point, its 8neighbors give us the position of the second control point (xposition and y-position) , and the 8-neighbors of the second control point give us the position of the third control point and so on. Till we reach the last control point, at that time, the pixel 90

at position 0 contains the 3 bits that represent the interpolation method used to interpolate the curve. Step 4 : End. To extract the curve form the image, these three steps must be repeated in reverse. 4.6.4.2 Text Within Curve The same three steps described above will be used here. A cubic spline method is used to distribute the bits of the hidden text. This can be done by the following steps :Algorithm: algorithm for performing Steganography. Input : text to hide Output : Hidden text within a curve.

Step 1: First of all, we must locate the control points of the curve that will hold the text information. These control points are interpolated using a cubic spline method. Step 2: The new points that are produced from the cubic spline method will hold the information according to the stego key proposed above. Step 3: The hidden text is converted into binary form, each 12 bits are stored in 4 neighbor pixels of the new interpolated point according to the stego key sequence proposed in step2. Step 4: The last control point of the stego-curve contains the code 1000 to represent that it’s a hidden text. Step 5: End. 4.6.4.3 Curve Within Curve Steps mentioned above in text within curve hiding, are used here with the same details but the last control point of the stego-curve must contain the code of interpolation methods of the hidden curve, this code as mentioned above is either 000 or 001 or 010 or 011 or 100 or 101 or 110 or 111.

91

Chapter Five BANKNOTE SECURITY AND DESIGN

5.1 Document Security Counterfeiting is a serious problem worldwide that involves all kinds of official and other non-official documents. And besides the document of banknotes, counterfeiting extends to a variety of products such as designer clothes, watches, compact discs and computer products. Almost anything that can be copied will be, so long as someone sees a commercial advantage in it for themselves. There has always been counterfeiting and, in all likelihood, always will be. Technically, we can define the term printed document security as the inability to reproduce the document even if all technical printed capabilities are supported to the counterfeiting party, where these facilities are the same used by the authorized party to produce the authorized authentic document issue. This can be achieved by the use of specialized security features performed in many ways and in many applications. What is important to us for the time being is the banknote and the security features applied to preserve the content of this kind of documents as a valuable content accepted by all people of the country. The aim of this research is to concentrate on how to generate a secure technique that handles the contents of the banknote or any valuable document in a way that make them difficult to reproduce. This can be done by using parallel layers of curves (since all the banknote content are figures consists of a set of curves) each layer could be printed in different printing techniques mentioned earlier. Therefore a method is needed to generate parallel set of curves (using interpolation process), such that these curves passes from a point printed in a one printing technique (like offset) and ending with a point printed in other printing technique (like gravure). The controlling process over the whole operation is easily performed since all the control points and the extra interpolation points are known and recorded in the systems program. 92

5.2 Security Features in Banknotes Security is a prime requirement of all banknotes. As an anonymous medium of exchange of a valuable negotiable document, it must inherently display exceptional security to gain the confidence and trust of the general public. A wide range of security features available for banknotes are classified into the two main categories: Overt and Covert security features. Most importantly, banknotes must possess easily recognizable overt security features for the person in the street. These features must be difficult to counterfeit or simulate, and should be easily recognizable as genuine in the short time available during a normal transaction, ideally without the need for an additional device. Covert security features, generally protected by secrecy and only detectable with the aid of special devices, are often made use of by automatic cash handling machines and high volume cash handling personnel. Modern banknotes contain a range of these features, with an even higher-level security feature reserved exclusively for the issuing authority.

5.3 The Use of Security Features in Banknotes Security features are incorporated in four distinct areas of a banknote:  Substrate: - involves watermarks, security threads discussed in chapter two.  Design;- This part is our concern in this chapter, which involves portrait design, design of banknote backgrounds, decoration shapes, boarders and banknote letters.  Printing: - includes offset printing, gravure and letterpress printing. These printing methods are also mentioned previously in chapter two.  Machine-readable features: - Includes High Level Authentication System (HLAS) used in central banks to verify the validity of banknote issue.

5.4 Banknote Design Besides the importance of the currency as a means of circulation, the banknote design must achieve many other goals (security, aesthetics appearance, valuable content, etc.) since it is a document which represents a historical, informative, cultural and creative properties that give the power to the local economy and through which, a power to the whole country which uses it. The banknote must be designed according to the distribution of the fundamental components (optical illustrations and 93

color space areas) in a way that preserves a comprehensive construction formed around a branch details working together in interaction to give the viewer an integrated perspective and the aesthetic attraction to the banknote valuable contents and to the banknote signs that represent the important country manifestations. Many designable secure components of the banknote can be performed through graphical applications with the aids of the methods of curve interpolation and curve security mentioned in the last two chapters. These components can be listed in details and include: -

5.4.1 Family of Curves A security complex patterns of lines, points, arcs, and other shapes make documents difficult for counterfeiters to fake. Some patterns cannot be reproduced accurately by photocopiers, thwarting easy counterfeiting. It is an important feature used to give a decoration aestheticism to the banknote during the design process.

Taken from 25 Dinars issue 1986

Taken from 1 Dinar issue 1979

Taken from 1 Dinar issue 1979

Taken from 25 Taken from 25 Dinars Dinars issue 1986 issue 1982

Taken from 100 Dinars issue 2002

Figure (5-1) shows some family of curves figures taken from Iraqi banknotes 94

Family of curves procedure can be performed using a single interpolated curve (which consists of a set of control points) applied with a set of basic transformation operation such as translation; scaling, rotation and reflection. These basic transformations are applied in much more effects to a copy of this single curve so as to produce a set of curves. The methods of curve security mentioned in chapter four are allapplicable within this set of family of curves so as to make control over the hole curve and to produce a more effective secure technique, in which the curve can not be regenerated even if the set of control points curve are discovered. For more details about basic matrix transformations see [Mitchell 1987]. The following figure shows the use of single curve and then generates a set of family curves according to that single curve.

Interpolated control points

(A)

(D)

Family of curves using the same control points

(B)

(C)

(E)

Figure (5-2) (A) shows a set of control points (B-E) are family of curves produced using control points in (A).

95

Another example of curves is illustrated with the following figure Control points

Family of curves figures

(A)

(B)

(C)

(D)

(E)

(F)

Figure (5-3) (A) set of control points. Figures from (B-F) are family of curves based on control points in (A).

5.4.2 Portrait Reproduction It is a security feature that is difficult to capture by any counterfeiting techniques. It represents one of the structural components that participate with other components in the integral building of banknote design. These structural components are invented from the philosophical mathematical treasure, based on the local urban environment and that gives an obvious cultural national signs for the banknote about the country it represents. It also participates through the optical geneses to arrange the suitable partitions of the color space areas gathering them in a relation which leads to the comprehensive form of the final printing design. A banknote must be designed to be clearly distinguishable from other printed matter, so that it is accepted immediately as a document of value. On choosing motifs for the banknote series it is important to have a good original in the form of a portrait, which is a good likeness. Both men and women are included, either in profile or as full-face portraits. Varying head coverings also contribute to this diversity. The photographs 96

or paintings chosen serve as the original for the printing in intaglio on the banknotes. Some images are engraved by hand into metal copper plates, whilst others are created using a Computer Aided Design (CAD) system and are drawn onto film by a laser beam. When finished, the images are duplicated many times onto printed plates ready for the presses.

Figure (5-4) shows engraving portrait used in banknotes Professional copper plate engravers are rare today, and the cost of true engravings is simply too prohibitive to be used in everyday printing. At the same time, traditional face engraving has no doubt very specific 97

appeal: its neat, sharp appearance distinguishes it advantageously from photos. Now, the goal is very precise: starting from a digital photo of a person, trying to reproduce it faithfully suing curves and lines with dark and shadows effects, relying on the technical achievements and techniques that traditional engraver used in the past. The resulting digital engraving should be visually pleasant, and the person must be recognizable. Visibly, the main rule for creating facial engravings is: the directions of the engraving lines should somehow follow facial features. Somehow means: just loosely related to large facial surfaces.

Figure (5-5) An enlarged section of a portrait shows that the details of the portrait are totally composed of curves and small lines. 5.4.2.1 Portrait Implementation Method The implementation method includes image-processing techniques and graphical algorithms so as to deal with a real photograph image. The real photograph used here is composed of 256 gray shades. The implementation method is divided into four main steps performed in sequence depending on the input image, these are:  Extracting image contour lines.  Performing pixel connectivity on image contours to locate the specific interested gray level regions.  A mesh of parametric interpolated curves with some basic rules applied over the original image in the regions that match the regions in the image produced from these predecessor two steps, such that the mesh is applied over the required regions of interest.  Superimposition of separate mesh layers to construct the final form of the portrait. 98

Each of these steps are described in detail as: 5.4.2.2 Contour Lines A quantized image is considered to be composed of layers of planes each of constant gray level. The image may then be represented by the boundaries or contours of the gray levels in each plane. These layers of gray level intensity caused by the amount of light reflected from the objects within the image exposured by the direct light from a light source. Figures (5-6) show different shades of gray in each picture created on the same object (human face in this figure) with different located light sources.

Figure (5-6) Variable shades of gray depending on the source of light If a continuous image is defined by the function F(x, y), that varies smoothly from high gray level, at the center to low gray level at the borders, then we can select some gray level F1, and define a set of contour lines connecting all points in the image with value F1. The resulting contour lines form a closed curves that surround regions in which the gray level is greater than or equal to F1. A second contour line has been drawn at a higher gray level F2 and so on. A1 is the area of the region inside the first contour line, and similarly, A2 is the area inside the second line. Contour lines provide an effective way to establish the boundary of a simple object within an image according to its gray level. The threshold area function A(F) of a continuous image is the area enclosed by all contour lines of gray level F. This threshold divides an image into disjoint regions on the basis of gray level as we can see with the following figure:-

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Figure (5-7) shows contour lines of human face 5.4.2.3 Pixel Connectivity Pixel connectivity is a central concept of both edge- and region-based approaches to segmentation and classification. Connectivity defines which pixels are connected to other pixels. In an image with a normal, rectangular sampling pattern, we may define two types of neighborhood surrounding a pixel. A 4-neighbourhood contains only the pixels above, below, to the left and to the right of the central pixel. An 8-neighbourhood contains all the pixels of a 4-neighbourhood, plus four diagonal neighbors.

(A)

(B)

Figure (5-8) (A) 4-neighbors of a pixel. (B) 8-neighbors of a pixel. The type of neighborhood chosen affects the number of objects found in an image and the boundaries of those objects. A 4-connected path from a pixel p1 to another pixel Pn is the sequence of pixels {P1, 100

P2,…., Pn}, where Pi+1 is a 4-neighbour of pi for all i = 1 . . . . . n-1. The path is said to be 8-connected if Pi+1 is an 8-neighbour of Pi. If we have a set of pixels, we can identify at least one 4-connected path between any pair of pixels from that set, we can say that the set is a 4-connected region. An 8-connected region can be defined similarly. Figure (5-9) shows a curve going from pixel A to pixel B. This curve is 8connected but not 4-connected since it moves diagonally in addition to vertical and horizontal steps.

Figure (5-9) A curve that is 8 connected but not 4 connected Armed with these definitions of connectivity, we can solve the problem with thresholding noted earlier, namely that it groups together pixels with gray levels above the threshold, despite the fact that they may not be connected. What we must do is to find each connected region of pixels that were detected by thresholding and give all the pixels in that region their own unique label. An algorithm is applied to scan the image pixel-by-pixel, and invokes a recursive labeling procedure whenever a required pixel is found. This procedure starts at the pixel, and that it propagates to any of the 4 or 8-neighbor pixel's that were also detected by thresholding. Whenever the procedure is started, the pixel is labeled within the input image so that it cannot be visited again. At the end of procedure all pixels belonging to a region have been set to a label in the image making then distinguishable from the other labeled regions and the corresponding pixels in the output image have been assigned to a region number. The region number is then incremented ready for the next connected region.

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5.4.2.4 Parametric Mesh If we suppose that the basic engraving layer is defined on a unit square in the uv coordinate system, as shown in Figure(5-10), the layer is built of a sequence of threshold structures made up of uniformly spaced waves, as shown in Figure(5-10)(b). The cross-section of each wave has a simple saw shape, directly inspired by the shapes of the furrows. The directions of the waves are not necessarily parallel to axes u and v.

Figure (5-10)(a) Parametric grid defined on a unit square in parametric space uv is transformed into morphed parametric grid (b) As we want the engraving lines to somehow follow the directions of the features in the original image, we naturally build the border curves taking into account the borders of the features such as nose, eyes, cheeks, lips etc. The border curves are built of an arbitrary number of straight line and/or Bezier curve segments. Each curve has to be re-parameterized in order to preserve the uniformity of the curve’s length when the parameter uniformly moves in the range of the image. The re-parameterization permits a smooth and uniform interpolation between the curves built of a different number of segments, of different lengths. Any basic engraving layer defined in the parametric space is accordingly transformed into a warped engraving layer in the image space. 102

5.4.2.5 Superimposition of Separate Layers Now, our task is to establish basic rules for the superimposition of several transformed engraving layers. The superimposition of several layers is performed sequentially, one layer after another. For this reason, it is important to define a set of basic rules for superimposing two layers, the extension to several layers being straightforward. Imposing engraving layers consists in consecutively merging the Current Layer (CL) into the Resulting Layer (RL). The merging is performed according to the layers needed to form the shape sequentially one after the other. Figure (5-11) illustrates the use of merging modes.

Figure (5-10) merging modes

Figure (5-11) The effect of merging superimposed layers One may notice that the tone reproduction curve of two superimposed layers is no longer linear, even if both layers forming the superposition have a linear curve reproduction behavior. This means that when several layers are superimposed, the resulting engraving may appear locally darker or lighter than what is expected. Now, let us illustrate the techniques described in the previous section showing an example of gray scale engraving of real photo. Many separate engraving layers for various parts of the face have been created 103

depending on the structure of contours found within image that divides the image into disjoint regions, each of which is with specific gray level. The borders of the layers are arranged in such a way that the layer grids loosely follow the key features of the image: the nose line, the cheek profile, the eye shape, etc, arranged according to the gray level of the human face regions. Now, The steps of the portrait technique can be listed as:Algorithm: algorithm for generating a human face portrait Input : An image of a BMP file format with 256 gray level. Output: Engraved human face as a portrait Step 1: Open a file of BMP format as an image with 256 gray level of colors, figure (5-12)(A). Step 2: Find image contours that will divide the image into disjoint regions according to the gray levels of the image, see figure(5-12)(B). Step 3: Find out the boarders of each region using the technique of pixel connectivity. Keep the points of the boarders within an array for each contour for further use. Step 4: Apply a set of layers each composed of a set of interpolated curves above the specified regions that we’ve already found using step 3 such that the points of these layers must not exceed the boarders of the regions (clipping at the boarders of the regions, since we know the points of the boarders) see figure (5-12)(C,D). Figure (5-12)(C) represents the portrait generation with the first layer of curves that passes from the left to the right. While figure (5-12)(D) represents the same portrait with only the second layer of curves that are considered as a complementary layer to the first one. Figure(5-12)(E) represents the final portrait after applying the first and second layers together. Step 5: End. The final output may not be much satisfactory, that it may not simulate the artist sensation who does the engraving by hand.

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(A)

(B)

(D)

(C)

(E)

Figure (5-12) shows the steps of Portrait Engraving process 105

5.4.3 Background Shadow Effects : Complex patterns of lines and wavy curves built according to a mathematical model are used as a decoration background to simulate the shadow of the relief lines found in banknote. This technique uses the same set of layers and rules used to create the portrait in the previous section. According to the source of the light, the layers over a template are composed. The template can be line work such as text or a logo, but also a halftone image. This technique extends from simple objects composed of simple line (or curve ) arrangement and repetition, to more complicated figures composed of overlapped objects that gives the final result.

Figure (5-13) Simple backgrounds which use simple objects To simulate relief printing, a template is used as a basis under the background mesh to gain the effect of object shadow.

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Background method (horizontal lines)

Template

Figure (5-14) shows a horizontal background using template The same is done with vertical lines, inclined (lines drawn with a specific degree) backgrounds that gives a beautiful relief appearance as shown with the following example Incline background with Template 45 and 135 degree line direction

Figure (5-15) shows relief appearance using inclined background lines More complicated patterns of interpolated curves can be used here. A mesh of interpolated curves over a template may be used to give the wavy shadowed appearance. 107

Template

Mesh of interpolated curve Background

Result

Figure (5-16) Mesh of curves applied over a template

Seawave background

Result

Double Seawave

Result

Figure (5-17) Mesh of curves applied over a template

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5.4.4 Frames: Frames are the boarders that surround the objects in banknote paper. These are complex symmetric patterns performed using lines and parametric curves, which may take different wavy characteristics with different shapes. It’s very complex to generate because of its object overlapping and deformation along the path. Typical of a normal deformation is the compression and the expansions always occurs perpendicular to the direction of the frame. A nice design feature is a deformation that isn’t perpendicular but slanted. This kind of deformation is called slanted deformation. We can create this kind of deformation by changing the positions of the control points of the deformation wave. Most of the following frames are performed on Bezier curves while the others are cubic spline curve interpolation.

Figure (5-18) Frame examples

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5.4.5 Guilloche: Many printing methods are used in the production of banknotes, engraved printing, color, print registry, serial numbers, micro printing, and latent imaging. Today the most important parts of bank notes are generally printed in a method known as intaglio printing. This starts with a master engraver, engraving the art into steel plates, from which the production plates are made. Then ink is applied to the plates, wiped clean and the remaining ink in the groves and fine lines is applied under enormous pressure to the paper, this gives the printed surface of the note a raised feeling. The use of circular or symmetrical lines on the engraved plates, called guilloche, are made by machine or laser and Computer Added Design (CAD). These fine line designs are extremely difficult to produce by hand. Some countries also use this feature of intaglio printing to build up some areas of the note to assist the blind or visually impaired, by placing raised marks on the notes to distinguish which denomination the note is. Here are some examples of guilloche:

Figure (5-19) Examples of Guilloche Using the graphical methods and curve interpolation techniques, it is possible to make such ornamentation, extending from simple objects that needs only changing the number and position of control points, with some basic operations such as rotation and transformation, extends to much more complicated patterns that need complicated calculations to count the next position of the points that the line passes through.

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Figure (5-20) Simple forms of guilloche The most complicated type of guilloche is the type where another guilloche passes through the points of the first one, counting for each

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point of the first, where the points of the second guilloche must be located. This type is called multi stencil guilloche.

Figure (5-21) Complicated shapes composed of many Guilloche in each figure. 5.4.6 Decorative Alphabets (Text and Type) : The ability to use type effectively is an essential skill for successful graphic design. Just a few basic principles open the way to an infinite variety of design possibilities for all kinds of printed products. Graphic designers must make type work hard, in harmony with other graphical elements, such as illustrations,

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photography, and color. They are dealing with practical situations, in the real world of tight deadlines, specific briefs, and competitive pitches. To be able to choose the right typeface for the job, one must first know something about how typefaces are constructed and classified (Fig. 5-22).

Figure (5-22) Each letter has its own anatomical details, and knowing the names for the component parts of a letterform is a great aid to identifying and specifying a particular typefaces. Each letter has its place in the graphic designer's toolkit: for a bank's annual report, for example, you may wish to use a well established "classic" face like Garamond to convey tradition and solidity; a music magazine aimed at young people will look better with a fashionable type like copper. Some typefaces are chosen for practical reasons. Newspapers tend to use faces with large x-heights and open counters, because the ink spread on low grade paper would fill in less robust faces. Typefaces (Fonts) Garamond Italic Copper Black Verdana Lucida Handwriting Arial Black

Example

Elegant Fun and Friendly Professional Establishment powerful

Figure (15-23) Some typefaces The shape of each character can be defined by a polyline (or more complicated curves, such as Bezier curves as shown in Figure (5.24a), or by an arrangement of dots or pixels. as shown in Figure (5-24b). Graphics packages come with a set of predefined fonts, and additional fonts can be purchased from companies that specialize in designing them.

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(A)

(B)

Figure (5-24) (A) shows how characters are built using Bezier curve . (B) bitmap font uses pixels to form character shape Bitmapped fonts still exist, but nowadays hardly anybody prints directly from bitmaps. A resolution of 72 dpi (or even the 144 dpi provided by the ImageWriter’s Best-quality mode) is unsuitable for high-quality printing. The notorious jaggies; the stair-step effect caused by the relatively large size of the dots that make up bitmapped fonts-make characters appear coarse and chunky. Also, bitmapped fonts come in a limited selection of sizes. The alphabet that we are trying to perform is a mathematical model which is made up of curves and control points, so as to be a scalable and resolution-independent model and that can generate printed alphabet from as small as 1 point in font size to more than 1000 points. This model must contain the information necessary to render the subtle curves, strokes, and line-weight variations that make up the characters of a typeface.

Figure (5-25) mathematical model The mathematical model depends entirely on the methods that draw a smooth curve according to a set of control point, keeping the optimal 114

shape of the letter and its peculiar curves. Cubic spline interpolation can be used to generate letter curves since it fits a smooth curve to the points of the letter it passes through. After designing the suitable mathematical model for the alphabet, it is now required to design a decorative alphabets or letters filled with complex patterns and ornamentation. To achieve this aim, a procedure must be performed on the desired letter shape , this procedure includes :Step 1: - Take a letter and outline it (extract the boarders of the letter). This is done using edge detection that is one of the important image processing techniques. The detected edge gives a bright spot at the edge and dark areas everywhere else and vice versa. Calculus fans will note the detected edge as the derivative of the edge. This means it is the slope or rate of change of the color levels in the edge. The slope of the edge is always positive or zero, and reaches its maximum at the edge. In our case Sobol operator mask is used to look for edges in both the horizontal and vertical directions and then combines the information into a single metric. The masks are as follows:

Figure (5-26) Sobol operator At each pixel location of the letter we now have two numbers: Sl, corresponding to the result from the row mask, and S2, from the column mask. We use these numbers to compute two metrics, the edge magnitude and the edge direction, which are defined as follows: EDGE MAGNITUDE

=

S12  S 2 2

S  EDGE DIRECTION = tan 1  1   S2  The edge direction is perpendicular to the edge itself because the direction specified is the direction of the gradient, along which the gray levels are changing.

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Step 2 : - After getting the edges of the letter, these edges must be thinned to have a smooth thin line and curves. The thinning process is performed using what is called Skeletonization, that reduces all objects in an image to lines, without changing the essential structure of the image.

(A)

(B)

(C)

Figure (5-27) shows the process of (A) letter taken, (B)edge detection and (C) skeletonization Step 3 :- Choose the control points that specify the shape of the curves within the letter produced. This operation is performed by the designer who chooses the best locations for the control points. Step 4 :- A method of pixel connectivity is used to specify distinct boundary of the regions within the letter itself. Step 5 :- Filling-Regions :-Sometimes called "fill area” primitive, is a shape filled with some color or pattern from an image. The algorithm operates on interior-defined, 4-connected pixels region. It changes every interior pixel of color interColor to a new color, newColor. The algorithm starts out from the "seed" at (x, y)(which is part of interior region) , "looking for" pixels of interColor, and changing each one it finds to newColor. Apply the same process recursively to each of its four neighbors, otherwise do nothing. Procedure Fillarea (x, y, interColor: integer); // Start at (x, y); change all pixels of interColor to newColor. // begin if (getPixel(x,y) = interColor) then putpixel(x,y,newColor) Fillarea(x - 1, y, interColor); // fill left Fillarea(x + 1, y,interColor); // fill right Fillarea(x, y + 1,interColor); // fill down Fillarea(x, y - 1, interColor); // fill up End; Applying these five steps on letters can produce a beautiful effect within the letter shape, in addition to the capability of controlling the whole shape of the letter by scaling it down or up or deforming it in any suitable manner.

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Examples below shows how letters are merged with backgrounds fig(5-28). The letters can be filled with a picture as in fig (5-29)(A) or the capability of inserting decoration pattern with the letter itself using method of interpolation, fig(5-29)(B,C,D), or a letter itself could be part of an ornamentation that builds around the letter, fig (5-29)(E).

Figure (5-28) Filling letters with background relief effect Pattern

Letters

Result

(A)

(B)

(C)

(D)

(E)

Figure (5-29) Decorative letters 117

5.4.7 Special Anticopy Background Method: Anti-copy patterns are line patterns that make illegal copying of security jobs difficult. The concept is that the (color)copier handles certain combinations of line patterns differently and this results in a copy that looks different from the original document, therefore making it easier to recognize a counterfeited security document. There are different types of anti-copy patterns, but a lot of them are protected by patents. The Split Line operation creates very effective anti-copy patterns. It will cause a normal stroke line to split open on certain places. At first glance, you will hardly see the split because the overall color tone of the lines hardly changes. But when you try to make a photocopy, the Split Line really catches the eye since the split lines are enforced on the photocopy, thereby creating a different color tone in those areas. The split line process takes many parameters the must have accurate values, these parameters are: Split line:- Here we define the stroke width of the lines in the area where the line has split open. This value is valid for both upper and lower stroke of the Split Line. This value is a relative value( it means that the width value depends on the resolution of the machine producing the split line. It also depends on the resolution of the printer in addition to the resolution of the scanner or the copying machine).

Figure (5-30) Width stroke of the splitting line  Gap: - The Gap is the width between the splitted lines. The distance is expressed as a fraction of the original stroke width.

Figure (5-31) The gab of the splitting line

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 Stroke width: - With the stroke width parameter, we define the overall stroke width of the lines outside of the split areas. Again, this is a relative value.

Figure (5-32) Width of lines outside the split area  Slope: - We can control the Slope on steepness of the splitting effect. The higher the value, the smaller the slope of the split will be, whereas a very low value will make a very abrupt split.

Figure (5-33) Slope of the splitting line

This method is performed using a template that works as a blueprint for the Split Lines. The template can be a linework such as text or a logo, but also a halftone image. Then draw a set of lines on top of the template, which could be horizontal or vertical lines, whenever a black spot is found within the template, the line is splitting in a way that the width of the two splitting branches with the gap space between them must not much exceed the width of the original line. After generating the splitting process the final result must be minimized or scaled down till the spaces between splitting lines is no longer recognized by the human eye. When printed, the result is also not recognized. But when scanned or copied, the template appears obvious because of the reasons mentioned above.

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Template

Mesh of lines

Splitting line process according to the template

Figure (5-34) Special anti copy splitting line method

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CHAPTER SIX PRACTICAL WORK AND IMPLEMENTATION 6.1 Introduction Computer graphics can be defined as comprising modeling (describing an object in terms of coordinates, lines, surfaces or solids), storage (of the model in the memory of a computer), manipulation (changing the model in some way, for example by altering its shape or merging two models together), and viewing (the computer adopting a particular viewpoint, looking at the model from this viewpoint and depicting its screen what it sees). The Security Documents Design System (SDDS) (our proposed system) is a graphical application aims at providing high security printing models for the banknote, passport and special documents related to different major sides of the design and mathematical features. These features are the decorative backgrounds, regeneration of portrait, guilloche, decorative boarders or frames, decorative letters with the capability of hiding objects within the image or within each other. The system is provided with a means to print the designed work on the printer in a smooth curve forms and smooth output. The proposed system is designed to work in an interactive application manner. Interactive graphic applications are fast and support effective dialogue between the human user and the computer. It lets the user control the flow of a program by natural human motions, recall that when the user presses or releases a mouse button, moves the mouse, or presses a keyboard key, an event occurs. Security documents design is a special form of computer-aided design that offers enormous benefits. The designer can add new elements by selecting from a menu of icons (small pictures that represent the transformation operations performed on an object) and "dragging" the icon to the desired position. By means of simple pointing actions, the designer can add, delete or modify the elements or objects found in the design.

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6.2 System Requirement The proposed system is designed using a structural language that provides both, the suitable data structure needed to present system objects, and the algorithms used to build the internal model representation (physical code) of the whole activities and transformation operations that support the drawing of these objects, on a basis of interactiveness with the user requirements and that responds to the user instructions and demands. Our proposed system uses Delphi 5 language that provides the ease of use and the effective way to communicate between the user and the machine via suitable tools, which gives us numerous options of forms and shapes used to construct the final Graphical User interface (GUI). The system uses a computer supplied with a processor of 233 MHz or more and a memory capacity of 32 Mbytes of RAM.

6.3 System Implementation and Description System implementation represents the final phase of the system development, in which the design and the algorithms that are determined previously are translated into an interactive application interface supported with pull down menus and push-up buttons that perform the activities required to complete the document designs in a coordination manner between each other, taking into consideration, the ease of use and the aesthetic appearance of the forms and windows used for each part of the system applications. The following section describes in detail the nature of the system performance and implementation. The system starts working by displaying the main window that holds the main menu, the Secondary menu (operational menu), and the workspace area, shown in Figure (6.1). Each option of the main menu contains a submenu, which appears as a pull down menu that consists of many other options responsible for some activities and applications. The user can choose any option by moving the mouse pointer to the desired option and clicking the left mouse button on that option.

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Figure (6-1) Main system window

6.3.1 Main Menu The main menu consists of eleven options, each of which consists of other options. The main menu options are: 6.3.1.1 File option: This choice performs the basic operations that deal with file management operations such as save and open. Figure (6-2) shows in detail the pull down menu of the file option.

Figure (6-2) File option menu. A detailed description for each option of the File menu is given as :  New: This option prepares the workspace for new job. The system deals with many objects such as letters, curves pictures, etc. Each object is recorded as an entry in the systems database. Choosing the New option causes the 123

database to be cleared and all saved entries will be deleted, in addition to clearing the workspace area to receive new work.  Open: This system deals with two types of files. The first file type is of the extension .PNT (PNT is an abbreviation for points). This file type deals with the control points of the objects used in the system and saves only these control points in addition to saving the way these control points are represented (i.e. Lines between control points are represented by 1, Lagrange interpolation is represented by 2, cubic spline represented by 11 and so on, in addition to saving pictures and texts). The other file type used in this system is the BMP file format, which opens and saves the work as a silent picture. Thus Open option opens a file of objects loaded them to the system database, the system then deals and alters these objects as the user desires.  Open BMP as background: This option loads an image of type BMP as a background picture placed on the workspace area.  Save and Save As options: These options save the objects found in the system database and that appear on the workspace, to a file of extension .PNT described above.  Save As BMP: This option saves the work and objects in the database as an image in a file format of BMP extension.  Save As Vector Format: This option stores the work as vector graphics so that it could be used in other application programs.  Print: This option prints all objects, which appear in the workspace to the printer to show the final result of the document designs. 6.3.1.2 Edit : This options deals directly with the objects that are selected with the Selected Objects option found within the secondary menu. Figure (6-3) shows edit menu

Figure (6-3) Edit menu 124

 Copy option: Take a copy of the selected object.  Paste option: Pastes the object that was previously copied by the Copy option.  Delete option: deletes the selected object that is no longer needed. 6.3.1.3 Background:- This choice performs the imposing feature for the area selected by the user. The imposing feature can be performed in many ways as described previously in chapter five. Figure (6-4) displays the details of the background form: -

Figure (6-4) show background form  Shifting between lines option: describes how much distance between each line of the imposing feature method.  Distance: describes the space generated to produce the imposing, which depends entirely on the direction of light determined by the options, left, right, up and down.  Options Horizontal, Vertical, 45 degree, 45+135 Degree, Sea waves, Complex sea waves, 2D sine waves, Special anticopying: These options describe the background methods used to produce the imposing effects. These 125

methods are described in detail in chapter five, section on background (Section 5.4.3). 

Options left, right, up and down: These options represent the direction of light falling on the background to perform the imposing feature.

6.3.1.4 Steganography:- This main menu choice is used to add a hidden object feature to the system, to construct a special method of privacy for the image files representing the document design. Figure (6-5) shows the details of the steganography form: -

Figure (6-5) Steganography option window  Hiding methods option: consists of three alternatives which are Object within object option used to hide curves within each other chosen from the options of first object and second object (see the above figure). First object and second object, take their input from the database of the system. The user then chooses which object to hide with the other. Option of Text within object is used to hide a string of text with one of the objects that the user chooses for the first object option. The user enters a text in the field of text to be hideden to perform the action. The third alternative is the option of 126

object within image that hides an object chosen from first object option within the background image which exists in the workspace area. 6.3.1.5 Find out: This main menu choice is used to discover whether there is any hidden object within the image opened immediately, finds which method of object hiding types are used, and prompts by sending a message to the user notifing him to extract the hidden object, so as to add it to the system database for further manipulation and modification. 6.3.1.6 Guilloche:- This choice adds as a new element represented by a decorative guilloche to the system. The guilloche window consists of ten major options which represent ten major types of guilloche used in the system. Each one of the ten types consists of many shapes that depend on the type of the interpolation method used, and the Number of Revolutions parameter and determines how many times the complete basic movement will be executed. It also depends on the Frequency parameter, which is the number of sine movements over the total length of the wave; and Amplitude parameter, which is the distance, from the center of the wave to its top. All of these parameters together contribute the final guilloche form displayed on the workspace window. Figure (6-6) shows the details of the guilloche window.

Figure (6-6) Guilloche window 127

 As we can see from the above figure, there are many types of guilloches displayed as buttons to be selected. These types rely on the mathematical generation model that can be classified into:  Stencil: When you want to create a guilloche that is not linear, circular or elliptical, but that follows a more irregular shape, that uses a template, this is called a stencil form.  In between stencil: is a guilloche that fits precisely between two stencils.  Multi Tour: Stencil that goes round more than once per turn of a guilloche.  Saw shaped: It’s a poly line shape represented by a waveform but with sharp edges and vertices.  Rosette: is a polygon with n-sides in which each vertex is joined to every other vertex.  Heart iterations: A fixed shape like heart shape, with some modification of its control points that can generate a family of guilloche.  Whirling: It’s a hexapolygonal figure with 6-sides wherein each successive segment is larger than its predecessor by a fixed amount and is oriented at some fixed angle to the predecessor.  Double Frequency: It’s a special set of deformation when the number of deformation is twice as high as the number of waves.  Poly spirals: is a polyline wherein each successive segment is larger (or smaller) than its predecessor by a fixed amount and is oriented at some fixed angle to the predecessor.  Slanted Deformation: Typical about a normal deformation is that the compression and expansion always occur perpendicular to the direction of the guilloche. A nice design feature is the deformation that is not perpendicular but slanted.  Preview option: the types classified above when selected, a pull down menu starts displaying the figures of each type according to their Interpolation method, frequency, 128

amplitude, shift between rounds of guilloche. Thus the preview option is used to demonstrate the figure of guilloche the user chooses, in the preview window specified for this purpose. 6.3.1.7 Portrait: This main menu choice displays a window which contains many options used to construct the portrait. These options are shown with the following figure

Figure (6-7) Portrait window  Load Picture option: This option is used to load the picture needed to perform portrait regeneration operation.  Position ; It is used to locate where to place the generated portrait .  No. of curves per layer : The generation operation is performed over a number of superimposed layers, each one consists of a set of curves. The option determines the number of curves in each set.  Shift between curves: This option provides information about the distance between each curve within the same layer.

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6.3.1.8 Boarders:- This choice works with frames that surround the document or image. These frames are designed using specialized forms of equations and functions supported with the methods of interpolation to form an aesthetic decorative boarder. It also uses trigonometric functions such as sine, cosine and tan functions with their specialized parameters of frequency (described above), amplitude, and shift parameter. The boarder window shows in detail the options used.

Figure (6-8) Boarders window  Accept, Left And Right Options : These are back and forth options used to display and choose the various types of boarders used in this system.  The four directions options: These options are used to guide us where and on which margin of the document (left, right , up or down) we will place the boarders selected.  Custom option: If we want to design our own boarder from the trigonometric functions like sine or cosine wave, then three other option values must be defined these are the frequency option, amplitude and shift options. 6.3.1.9 Letters option:-This choice uses a window with many options described in the following figure:-

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Figure (6-9) Letters window  A widow is used to display the control points of the letters entered by the user.  Picture option: If the user tries to fill the chosen letters with a background picture, then the user must press on picture option. This option causes a dialogue box to open, notify the user which background picture to choose and to display in the preview window.  Guilloche option: If the user tries to fill the chosen letters with a guilloche or a decoration figure, then this option must be chosen. This option causes an extra window to open, and notify the user which guilloche method to choose. 6.3.1.10 Help option : This choice gives a brief information about how the system works and learns the user how to use each part of the system. 6.3.1.11 Exit option : This choice ends the execution of the system.

6.3.2 Secondary Menu : This menu consists of many buttons used as transformation operations that deal with objects, so as to make any 131

required change or modification. With this menu the user communicates interactively with the objects, which exist in the workspace by choosing the desired menu buttons, doing the required operation on the object itself by clicking on the control points of the object to change them. The secondary menu consists of eighteen buttons, which can be shown in Figure (6-10).

Figure (6-10) Secondary Menu description 6.3.2.1 Object Rotation Icon: This option is used to rotate the object freely in any direction the user wants. This action is performed after clicking Rotate icon and then dragging the mouse pointer on any one of the control points of the selected object, and then moves the mouse up or down to rotate the object in any direction, the system then redraws the object with the new position. 6.3.2.2 Object Scaling Icon:- This option is used to scale the object freely in any scale ratio either increasing or decreasing. Dragging on any one of the control points of the selected object, moving the mouse up or down will perform scaling up or down as required. 6.3.2.3 Deleting Control Point Icon:- This option is used to freely delete any one of the control points of the selected object by just pointing on it, the system then redraws the objects after deletion operation. 6.3.2.4 Draw Line Icon :- This option draws a set of control points that are connected by lines between each other. This option adds a new entry 132

to the database of the system containing the set of control points defined by this option. 6.3.2.5 Move Object Icon :- This option moves the selected object to any position the user specifies by dragging the mouse pointer to any one of the control points and moves to any direction, then dropping the object, this will cause the object to reside in the new position. 6.3.2.6 Edit Object Icon:- If the user wants to change or modify the position of any of the control points of the selected object then, choosing this icon and dragging to any point and moving the mouse pointer will cause to change the position of the selected point. 6.3.2.7 Convert Line to Curve Icon :- Choosing this option by clicking the right mouse button will display a submenu which contains all the methods of interpolation that the user can choose to implemented on the selected object as shown on Figure (6-11). Any method can be applied to the selected object just by pointing on the method, and then the object will be redrawn with the new selected method.

Figure (6-11) curve menu 6.3.2.8 Convert Curve to Line Icon:- This options returns the status of the object from the curve form that is performed with any of the interpolation methods to the standard line form according to the user wish.

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6.3.2.9 Print icon :- This option sends the contents of the workspace to the printer to be printed. 6.3.2.10 Selected Area Icon:- This option is used by the user to select an area from the background image in the workspace to perform the operation of imposing selected by background option from the main menu. 6.3.2.11 Zoom in and Out Icons :- These options are used to zoom the workspace area In and Out to show its contents in detail. 6.3.2.12 Fix Label Icon:-This option is used to fix the location of the label text written within the Text Entrance option. 6.3.2.13 Switch Control Point ON/OFF Icon:- The figure above shows an object with its control points that are surrounded with red rectangles. These rectangles aid the user on selecting the right control point, thus switching on/off displays or removing these red rectangles from the objects. 6.3.2.14 Add and Delete Object Icon:- These options adds a new object to the database of the system or removes one object from the database. 6.3.2.15 Font and Text Entrance Option:- Options used to enter a text to be displayed on the workspace area with the required font size and type chosen by the user.

6.4 System Hierarchy: The system is designed with a structural programming language that provides a top-down design approach and that divides the program into separate modules, each with its own task to be performed (modular fashion). These modules consist of one or more subroutines each with its own function and instructions, these instructions refer to the lowest level of system hierarchy in which change control and modification are applied. The flow graph of the system hierarchy is illustrated below:

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Figure (6-12) represents the flow graph of the system (Main menu)

135

Figure (6-13) Represents the flow graph of the system (Secondary menu)

6.5 Case Study: In this stage, a real application is needed to demonstrate all the steps needed to design a model filled with a decorative frame and guilloches, using the main menu and the secondary menu options. This real application is a 5 Dinars Iraqi stamp that contains an engraved picture of the Mr. President Saddam Hussein placed at the right side of the stamp (using File  Open BMP As Background option and the choosing Portrait option, then doing the engraving with the specified 136

parameters). The stamp also contains two guilloches centered at the upper left and lower left corners, these guilloches surrounds the number 5 (using Guilloche  In Between Stencil option and Heart Iteration option). The whole stamp is surrounded with a frame chosen from a set of frames (using Boarders option). The word DINARS is repeated two times. At the first time the word is filled with a background picture (using Letters  pictures). The second time the word is written in Arabic. The imposing feature is created using the template of “Central bank of Iraq” message placed at the left side of the document (using Background  45-degree imposing method option). The number 5 is repeated two times. The first time within the in between stencil guilloche and the second time the number is filled with a guilloche chosen from the option guilloche that exists in Letters window. At this time the number. At this time the number is placed within the heart iteration guilloche. More examples are shown in the appendices section.

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Chapter seven CONCLUSIONS AND RECOMMENDATIONS

7.1 Conclusions From this research, we conclude that: 1) During our study, we have explored that there are two big international companies involved for many years in the market of high security prepress technologies, these are Jura and Barco. These two companies print most of the world’s secure documents like banknote, official documents and passports. From the publication catalogue of these two companies and from noticing all of the patterns created in this catalogue, we have found that after understanding some of the basic mathematics of trigonometric function, with the application of curve generation methods, most of these patterns are performed in our program with a very good performance and with suitable appearance like guilloches in its different types explained in chapter 6. The use of mathematical models of curve generation gives the power to design security graphical features used in protecting any document from malicious attack performed by a counterfeiter to regenerate the graphical features, which exist within the forgery document. 2) Most of the banknote security features are printable feature and can be designed using special programs like Illustrator, Freehand and Photoshop. Our program is a trial to build the basic elements of the banknote designs and to simulate the work of these programs with the addition of some features that are not found with these programs like Portrait generation, Steganogrpahy, Guilloches, Decorative letters and numbers. 3) Curve security is performed in many ways, each of which is characterized by special features to perform the security and each of which produces a different result from the others. Curve 138

security is the basis of document security since the patterns found in the document are unknown through the mathematical formulas. So, even if the counterfeiter is capable of determining the generation formulas, he cannot regenerate the patterns due to the additive feature performed by the curve security techniques. 4) Working with our research leads us to discover a world wide problem which is “Bitmap images and patterns to Vector Conversion”. Drawing programs such as Adobe Illustrator, free hand creates vector graphics, made of lines and curves defined by mathematical objects called vectors. Vectors describe graphics according to their geometric characteristics, such that each vector is defined with a certain radius set at a specific location (specific degree), filled with a specific color, that you can move, resize, or change the color without losing the quality of the graphic. A vector graphic is resolution-independent that is, it can be scaled to any size and printed on any output device at any resolution without losing its detail or clarity. As a result, vector graphics are the best choice for type (especially small type) and bold graphics that must retain crisp lines when scaled to various sizes. The graphical designs that we produce in our program are printed as a silent image composed of pixels that cannot be activated and modified. Thus we have created a method of conversion makes the ready drawing programs accept our designs and alter them as required and prints them in any size smoothly without any stair step effect due to screen resolution. 5) The proposed system have unlimited designable capabilities especially these concerns relief background, guilloches and decorative alphabets. The system is characterized with the simplicity of use, the accurate result designable models and the secrecy in figures generation. In addition to its capabilities to produce result that can be directly accepted in other graphical programs through a special option specially prepared for this purpose.

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7.2 Recommendations for Future Work Many recommendation points are considered here, these include: 1) The generation of three-dimensional decorative models by using complex mathematical techniques to generate a surface composed of multiple curves in many layers by which we get high security design models. 2) Use of more complicated algorithms for suitable control points extraction from a figure or a set of curves, since this operation is very important in forming the final curve shape during the interpolation process (curve regeneration such as the operation of portrait regeneration), because as we have described in chapter 4 choosing of control point leads to change in curve shape every time the set of control points have changed for the same curve or set of curves. The process of control point extraction must take into consideration extracting a minimum number of control points in a set that achieves the conditions of curve smoothness and forming the required suitable shape of curves. 3) Portrait generation is much more complicated to perform than the

method we propos, so, much work must be performed to design algorithms that simulate the engraving process of portrait generation in a accurate fineline technique performed on a steel die engraved with industrial machines like CNC machines, that drill a steel die in ten’s of millimeters or much less to simulate finelines technique. This type of line structure appears normal to the human eye but is difficult for current copying and scanning equipment to resolve properly.

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This section demonstrates some of the figures performed with the SDDS program as apart of its capabilities and that can be used as a partial components participating in the design of banknote document or any other printable documents.

Appendix ( A ) : Family of curves.

1

2

Appendix ( B ) : Guilloche Types . Appendix ( B-1 )

Saw Shaped Guilloche Figures

3

Appendix ( B-2 )

Rosette And whirling Guilloche Figures

4

Appendix ( B-3 )

Poly Spirals Guilloche Figures

Appendix ( B-4 )

Heart Iterations Guilloche Figures

5

Appendix ( B-5 )

Double Frequency Guilloche Figures

Appendix ( B-6 )

In Between Stencil Guilloche Figures

6

Appendix ( B-7 )

Slanted Deformation Guilloche Figures

7

Appendix ( B-8 )

Slanted Deformation Guilloche Figures

8

Appendix (C) : Frames.

9

Appendix (D) : Backgrounds.

10

Appendix (E) : Decorative Letters And Numbers

11

An example of a one-dinar banknote design

A stamp designed in the occasion of 21 th Martyr annual day

‫ﺟﻤﮭﻮرﯾـﺔ اﻟﻌـﺮاق‬ ‫وزارة اﻟﺘﻌﻠﯿﻢ اﻟﻌﺎﻟﻲ واﻟﺒﺤﺚ اﻟﻌﻠﻤﻲ‬ ‫اﻟﮭﯿﺌﺔ اﻟﻌﺮاﻗﯿﺔ ﻟﻠﺤﺎﺳﺒﺎت واﻟﻤﻌﻠﻮﻣﺎﺗﯿﺔ‬ ‫ﻣﻌﮭﺪ اﻟﻤﻌﻠﻮﻣﺎﺗﯿﺔ ﻟﻠﺪراﺳﺎت اﻟﻌﻠﯿﺎ‬

‫ﺗوﻟﯾد اﻟﻣﻧﺣﻧﯾﺎت ﻏﯾر اﻟﺧطﯾﺔ ﺑواﺳطﺔ‬ ‫ﺗطﺑﯾﻘﺎت اﻟﺣﺎﺳﺑﺔ‬ ‫أطﺮوﺣﺔ ﻣﻘﺪﻣﺔ إﻟﻰ‬ ‫ﻣﻌﮭﺪ اﻟﻤﻌﻠﻮﻣﺎﺗﯿﺔ ﻟﻠﺪراﺳﺎت اﻟﻌﻠﯿﺎ ‪ /‬اﻟﮭﯿﺌﺔ اﻟﻌﺮاﻗﯿﺔ ﻟﻠﺤﺎﺳﺒﺎت واﻟﻤﻌﻠﻮﻣﺎﺗﯿﺔ‬ ‫وھﻲ ﺟﺰء ﻣﻦ ﻣﺘﻄﻠﺒﺎت ﻧﯿﻞ ﺷﮭﺎدة اﻟﺪﻛﺘﻮراه ﻓﻠﺴﻔﺔ ﻓﻲ ﻋﻠﻮم اﻟﺤﺎﺳﺒﺎت‬

‫ﺗﻘدم ﺑﮭﺎ‬

‫ﻓﺮاس ﻫﺸﺎم ﻣﺤﻤﺪ أﻣﻴﻦ اﻟﻤﺨﺘﺎر‬

‫ﺑﺈﺷراف‬

‫أ‪.‬د‪ .‬ﻫﻼل ﻣﺤﻤﺪ ﻳﻮﺳﻒ‬

‫د‪ .‬ﻋﺒﺪ اﻟﻤﻨﻌﻢ أﺑﻮ ﻃﺒﻴﺦ‬

‫ﻣﺎرس ‪٢٠٠٣‬م‬