1 Introduction 1.1 What is embossing?
Functionally based virtual embossing Alexei Sourin School of Computer Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, e-mail:
[email protected]
Embossing is the art of decorating metals in relief from the reverse side. This article describes how virtual embossing can be done using a functionally based representation of the metal plate and the tools. The program is implemented as an interactive shape modeler where a functional model of the metal plate is subsequently modified with offset and settheoretic operations. For visualization, interactive ray tracing is used. Bounding boxes together with the spatial organization of the functional model provide the required fast function evaluation that is usually a bottleneck for functionally based shape modeling systems. The program runs on a personal computer. Key words: Computer art – embossing – virtual reality – functionally based shape modeling – F-rep.
Embossing is the art of decorating metals. In this technique, the ornament is raised from the back of the metal by means of hammers and punches followed by hammering from the front, which is called chasing. Embossing has been used extensively throughout the history of metalworking. It achieved widespread popularity in Europe during the 16th, 17th, and 18th centuries. One of the places where this art originated from is the Caucasus Mountains. In Georgia and Dagestan, it is traditional folk art counting hundreds of years back (Fig. 1). For more embossed pictures, refer to Georgian Embossed Art. The author used to emboss when he was a schoolboy. In this article, he recalls his hobby, and proposes a functionally based approach to making virtual embossing. Embossing is performed on a sheet of metal about 0.3–1.0 mm thick. It can be copper, brass, aluminum, silver or any other soft and flexible metal. The tools used for embossing (Fig. 2) are hammers with specially shaped handles and faces, and different punches used for raising metal from the back as well as for chasing it from the front. The punches are so shaped that they are capable of producing any effect that may be required. There are also tracers that are used for making contours of the drawings onto the metal. A sheet of raw rubber or an asphalt block is also needed as a foundation. And last, some chemicals to process the metal after the embossing are required. With these chemicals, different tinges from black through brown and green to golden yellow can be given to different parts of the image. For example, when nitric acid is applied to the surface of copper or brass and then heated, green and black tinges will be achieved. The design is first drawn on the surface of the metal, and the motifs are outlined with a tracer, which transfers the essential parts of the drawing to the back of the plate (Fig. 3). The plate is then embedded face down in a rubber sheet or an asphalt block, and the portions to be raised are hammered down into this yielding foundation (Fig. 4). Next the plate is removed and re-embedded with the face uppermost (Fig. 5). The hammering is continued, this time forcing the background of the design into the foundation. By a series of these processes of hammering and re-embedding, followed finally by chasing from the front, the metal attains its finished appearance. After that, the coloring with chemicals remains to be done. The Visual Computer (2001) 17:258–271 c Springer-Verlag 2001
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Fig. 1a,b. Embossing by Georegian artists. a “Dancer” by I. Ochiauri; b “Dolphin” by K. Gurili Fig. 2. Tools for embossing Fig. 3. Transferring a drawing to the back of the metal
There are several reasons that prevented the author from coming back to his hobby. First, it is very noisy. Second, processing with chemicals requires special premises and facilities and often develops mephitis (e.g., laughing gas). So, the author has decided to “escape” to virtual reality, and simulate embossing with a computer.
1.2 Computer-assisted art and virtual computer art Two different trends in computer art can be observed. The first one assumes a computer to do the whole job for the artist. For example, a computer can turn
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Fig. 4. Raising up the design Fig. 5. The result of bossing up the design
a photograph into a watercolor, charcoal, colored pen, oil paint picture, or engraving leaving the user an opportunity of controlling the appearance of the picture by adjusting the control parameters. Also, some absolutely new forms, shapes, and expressive techniques, not available in real life, can be created. The user of such software need not be an artist skilled in the original art to achieve outstanding visual results. The second direction in computer art assumes using a computer as a virtual tool that lets the artist work in the virtual environment exactly like, or at least as close to working in real life as possible, without taking over even for the simplest operations. The work of art is to be created with virtual models of the familiar tools, and familiar real world techniques are to be used. A 3D model rather than just a 2D picture often results in this virtual computer art. The advantages of virtual computer art are that the object being created is contained entirely in the virtual space and can be made from any virtual material with any tool needed. This is very essential for the arts that require special workshops or other conditions that may be inconvenient to have in modern houses. Considerable efforts have been made in the first area of computer art. Winkenbach and Salesin 1996 propose how to render parametric free-form surfaces in pen and ink. Salisbury et al. 1997 introduce interactive creating pen-and-ink line style drawings from gray scale images. Curtis et al. 1997 describe the various artistic effects of watercolor and show
how they can be simulated automatically. Dooley and Cohen 1990; Elber 1995a; Elber 1995b; Elber 1998; Lansdown and Schofield 1995; Pnueli and Bruckstein 1994 work on line art drawings. Haeberli 1990; Meier 1996 develop expressive rendering. Ostromoukhov 1999 introduces digital facial engraving, which imitates traditional copperplate engraving starting from a digital photo of a person. Chua et al. 1997 and Pasko et al. 1998 propose methods of carving and sculpting based on 2D images, where the color of each point defines how high or deep the elevation of the corresponding 3D point should be. As for embossing, there are software tools that create embossed-like pictures from the image provided as input data. For example, Ulead PhotoImpact (Ulead Systems, Inc) lets the user make the image appear as if it were stamped or imprinted on a solid surface, and Corel PHOTO-PAINT (Corel Corporation) has the filter that makes the image details appear as ridges and crevices on a flat surface. With these tools, one can manage to transform a photograph into an embossed-like 2D image by varying the photo properties and the command parameters, although to achieve more realistic appearance the underlying image is to be specially edited first. In Fig. 6, the author converted his photograph into the embossed-like picture with PhotoImpact. In virtual computer art, various interactive sculpting and carving techniques were proposed in Rossignac 1994; Wang and Kaufman 1995; Bærentzen 1998.
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Fig. 6. An example of conversion of a photograph into an embossed-like picture Fig. 7. The author’s exercise with a touch sensitive graphic tablet
Galyean et al. 1991 and Avila 1996 propose interactive local modifications of the basic voxel shape using a modeled carving tool and set-theoretic operations. Pasko et al. 1998, 2000 discuss functionally based shape modeling tools for interactive carving of the underlying model. Mizuno et al. 1998 propose an interactive modeling CSG technique to form solid objects with curved surfaces as if they were sculpted so that the generated objects look like real wooden sculptures. Carving with chisels can also be done interactively with a Wacom graphics tablet with using Wacom PenTools. These tools realistically simulate the depth of penetration of the chisel when a pressure sensitive graphics tablet is used (Fig. 7). The author could not find any reports on virtual embossing and proposes a functionally based approach to it in this article.
2 Making virtual embossing 2.1 Physics versus geometry When the design is bossed up from the back, and the background is obtained by beating down the adjacent areas, basically the same physical process
occurs. A hand-held punch, a tracer, or a face of a hammer deforms the metal surface plastically either in relief or in intaglio (incising beneath the surface of the metal) so that the imprints look like the tool shape. Due to the ductility of the metal, they have slightly slopping boundaries. The amount of slope varies depending on the force of hammering or pressing. The project aims to simulate the process of embossing so that it can be done interactively with virtual tools on a virtual sheet of metal with photorealistic appearance. The author wanted to develop a software tool that would be able to run on a common PC so that one would be able to do embossing virtually everywhere, even while flying in an airplane or sitting in the backseat of a car. When developing common VR systems, the following is usually required: 1. Realistic 3D geometric models with behavior and constraints. 2. Real time simulation including collision detection, sounds, and so forth. 3. Real-time 3D rendering. 4. VR rendering and input techniques based on special hardware devices.
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Since the scope of this project is to develop a desktop VR embossing system capable of running on PCs including notebooks without compulsory use of VR hardware, more attention has been paid to the first three tasks at the current stage of the project. For realistic modeling of embossing, a direct physically based simulation could be implemented but our feasibility study proved that it promises to be computationally expensive for our purposes. Alternatively, a pseudo-physical simulation of this process could be done entirely geometrically if the appropriate model of geometric deformation can be defined. This model is proposed in Sect. 2.2, real-time 3D rendering and immersion issues are discussed in Sect. 2.3 and conclusions and further plans are given in Sect. 3.
2.2 Functionally based modeling A functionally based approach to shape modeling has been used in this project. Each tool, a sheet of metal, and a final embossed picture are defined with the Function Representation or just F-Rep (Pasko et al. 1995). With the F-Rep model, a complex scene can be defined as a union of functionally defined shapes where, figuratively speaking, the functions are meant as geometric DNAs constituting the shapes and their properties. Each individual function in the F-Rep is an inequality f(x, y, z) ≥ 0 that is greater than zero for the points inside the respective shape, equal to zero on the surface of the shape, and less than zero for the points outside the shape. The resulting function is an inequality as well. It is a superposition of other functions representing shapes and operations over them. Using functionally based approach for virtual embossing lets us have a 3D model of the embossed picture rather than its 2D image. This model can later be converted to polygonal mesh or any other representation for fast visualization or rapid prototyping purposes. The marching cubes algorithm is normally used for converting to polygons. The details of the conversion process are well studied in computer graphics and beyond the scope of this article, though it must be mentioned that when converting to polygonal mesh, the precision of representation may suffer because of the finite size of the polygons. In our case, background patterns created by small imprints of a hammer may create artifacts since the size of the imprints is about 1 mm. In computer graphics when
using polygons, such artifacts are normally avoided by using texture mapping but this solution contradicts with the goal of fully geometric simulation of embossing. Alternatively, a very large number of polygons will be required even when using adaptive polygonization. The program is implemented as an interactive solid modeler where the functional model of the metal is subsequently modified with offset and/or settheoretic operations. The final object is represented in the data structure as a binary tree where each node is an operation and the leaves are the tool shapes. When doing embossing, the virtual tools are selected from the set of tools with predefined shapes and sizes. Custom made tools can be defined by varying geometric parameters of the tool models. The user acts as if doing real embossing. The user chooses the tool, hits or forces down the metal, and observes the result. If the result is not acceptable, a multilevel undo operation can be used – a rather charming bonus compared with real embossing where one wrong stroke can ruin hours of work. Let’s see how the functionally based virtual embossing works step by step. We’ll try to re-make virtually the picture that the author embossed many years ago (Fig. 8). First, let’s represent a sheet of metal of size 2w × 2h × 2d as a thin solid plate by intersecting six plane half-spaces as follows: f embossed = f(x, y, z) (1) = min(x + w, min(w − x, min(y + h, min(h − y, min(z + d, d − z))))) ≥ 0 The intersection operation is implemented with the min function. Implementation of the intersection operation with the R-functions can be used as well but it is computationally more expensive. The plate is rendered with an optional drawing mapped on top of it to facilitate further work. Alternatively, the drawing can be placed on a graphics tablet that is in fact more convenient. Next, the contours of the drawing are outlined by dragging lines with a mouse or a pen. Mathematically, each curve drawn on the surface of the plate is interpolated by segments of straight lines, where for each segment the negative offset operation is applied along the normal to the surface. The “Witch of Agnesi” function (Fig. 9), which resembles a profile of the traced contour, has been used for simulating the tracing. Therefore, for each segment of a straight
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Fig. 8. “Girl with a candle” by A. Sourin Fig. 9. The offset function used for simulating embossing Fig. 10. Implementation of tracing
line joining two points P1 and P2 , and for any arbitrary point P (Fig. 10), the following is to be done: P = P − P1 , P12 = P2 − P1 |P12 · e y | |P12 · ex | , s= , c= |P12 | |P12 | c −s T= , P = P · T s c a3 if 0 ≤ |P · ex | ≤ |P | ·e |2 +a2 |P y f offset (P) = 0 otherwise (2) f embossed_new = f embossed − f offset f embossed = f embossed_new f embossed ≥ 0 where a is a parameter defining the size and the shape of a tracer. The result of application of such an offsetting operation is illustrated in Fig. 11. For raising contours up from behind, the positive offset is to be used: f embossed_new = f embossed + f offset
Note that (2) neglects the endpoints of the segment. To avoid possible artifacts at the connection points, the same function is to be applied to the endpoints thus surrounding the whole segment. Let’s return to the “Girl with a candle”. By applying the offset function (2) subsequently to all the segments interpolating the drawing, all the contours have been made (Fig. 12). Next comes raising up the relief regions. This also can be modeled with the offset operations and/or the set-theoretic operations over the plate and the shapes representing the tools. In our case, for bossing up the portions of the plate by hammering or pressing it from behind with the punches, the offset is the most appropriate method. For each application of the punch to point P1 , the following is to be done for any point P: P = P − P1 pa3 f offset = (3) q|P |2 + a2 f embossed_new = f embossed + f offset where a, p, and q are parameters defining the size of the affected region and the height of embossing.
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In real embossing, there are two ways for raising up the relief regions. The plate is to be embedded face down, and the portions to be raised up are either hammered down, or forced down by pressing the metal with the hand-held punch. In both methods, the portions closer to the contour raise first so that the middle region will raise following the boundary regions (Fig. 4). If a large region is to be raised up, than the middle portion also will be raised later on by the same means until the desired elevation is achieved (Fig. 5). In virtual embossing, we follow the same directions. Either individual points where the offset (3) is to be applied are selected thus simulating strokes of the punch, or the path of pressing is outlined with a mouse or a pen inside the contour and near it (Fig. 13). In the second case, either the offset defined
Fig. 11. Tracing drawings with the offsetting Fig. 12. Making virtual “Girl with a candle”: the contours have been traced Fig. 13. A diagram of raising up the relief portion of the design
by segments (2) will be used, or the points defining the offset (3) will be calculated on the path by the program so that the smooth surface will be resulting. Fig. 14 illustrates the result of application of such an operation. In this example, the drawing is traced first. Then, the internal area is raised up by moving the virtual punch near the boundary and inside it. Next, the adjoining area is slightly lowered down by moving another virtual punch near the boundary and outside it thus simulating chasing (Fig. 13). The order of operations corresponds to real embossing. For raising up large regions, this method may not work efficiently because the number of individual functions contributing to the resultant shape can be quite large. For such cases, one single function for raising up large regions has been introduced. The contour is to be outlined following the path of a punch.
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Fig. 14. Raising up the relief portions of the design with the offsetting
Fast inside-outside odd parity rule test is executed for each rendered point. For the points inside the outlined contour, a uniform offset is applied to the function. For the points lying outside the contour but within a certain distance from it, a non-uniform descending offset similar to (3) is applied. In this case, the distance to the contour will be taken into account. A union with blending (Pasko and Savchenko 1994, Pasko et al. 1995) can be used as an alternative to the offsetting when fancy shaped punches are applied. For example, when bossing up the metal with a semispherical punch for each application of the punch to point P1 , the following is to be done for any point P: P = [x y z], P1 = [x 1 y1 z 1 ] f embossed (x, y, z) ≥ 0 f tool = f sphere (x, y, z) = r 2 − (x − x 1 )2 − (y − y1)2 − (z − z 1 )2 ≥ 0 f embossed_new = f embossed + f tool a1 2 2 + + f embossed + f tool 2 2 f tool 1 + fembossed + a2 a3 (4) f embossed = f embossed_new f embossed ≥ 0 where a1 , a2 , and a3 are the parameters defining the amount of blended material. For other punch shapes, the appropriate function f tool is to be used.
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The offset and the blending parameters must be functions of the geometric size of the punch and the metal plate properties (ductility) to achieve pseudophysical simulation. E.g., parameters a1 , a2 , a3 from (4) must increase linearly with the tool size, and an independent increase of parameter a1 simulates hard metals. The benefit of the offset operations comparing to the set-theoretic operations is that with the offsetting, the contours can be made on the relief portions of the design as well as on the flat surface that is very essential for the further phases of embossing. Besides that, the offsetting deforms the shape rather than adds or subtract the material. The offset operations have a disadvantage that must be acknowledged. A negative or positive offset applied to the plate from the front causes a similar offset on the other side of the plate. To avoid these “mirror” offsets, the Z-coordinate of the points must be taken into account. At last, the background is to be made by beating down the metal with differently shaped hammers and punches. To simulate the stroke of the punch with a semi-spherical tip, the offset and/or the settheoretic operations similar to those discussed above can be used as follows. Offsetting: f embossed = f embossed − f offset ≥ 0, where f offset is from (3) Subtraction: f embossed = min( f embossed , − ftool ) ≥ 0, where f tool is from (4) Subtraction with blending: f embossed_new = 2 2 f embossed − f tool − f embossed + − f tool a1 − 2 2 , f embossed − f tool 1+ + a3 a2 f embossed = f embossed_new f embossed ≥ 0 The process of embossing continues if other contours, raised regions, and background patterns are to be made. In Fig. 15, all the raised portions and the background of the “Girl with a candle” have been made. About 850 individual offset operations are involved in its functional model. To finish this work of art, the col-
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Fig. 15. Making virtual “Girl with a candle”: the relief portions and the background have been made Fig. 16. “Seashells”. Virtual embossing made with the settheoretic operations Fig. 17. The real clone of the virtual embossing “Seashells”
oring and finishing remain to be done that will be discussed in Sect. 2.3. In Figs. 16 and 17, another virtual embossing and its real copy are presented. Here, only the set-theoretic operations with blending (4) have been used for bossing up the relief portions of the picture. Although subtraction and addition of material is more suitable for sculpting rather than for embossing which only deforms the material, they also can produce an attractive result in certain cases.
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In all the above examples, the flat surface defined by (1) has been used for embossing. The same mathematical models work with any shape of the workpiece. Just the appropriate function defining the required shape is to be used in place of the one in (1). The program offers several predefined shapes and lets the user import any shape that may be required. The user can rotate the work-piece to the desired location so that any point on its surface can be reached with the tools.
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2.3 Achieving interactivity, photo-realism and immersion For visualization, interactive ray tracing has been used. Assuming a typical model may contain several thousands of shapes/operations, the ray tracing of it can take quite a long time since it implies many function evaluations for each ray cast. The most effective acceleration techniques developed to reduce ray tracing’s high computational cost are based on space coherence: bounding box hierarchies and space subdivision (Glassner 1989). During common ray tracing, a space subdivision algorithm associates objects with the bounding shapes in which they reside, and tests each ray for intersection only with the objects inhabiting those shapes. To make ray tracing interactive, only the region that has been affected by the most recent application of the tool is to be redrawn. This method ensures the required fast rendering time of the affected regions, and thus provides both interactivity and photorealism that are so important for our purposes. To estimate the size of the affected region and to detect which tool instances are involved, the bounding boxes for the tools, and the spatial organization of the model are used. The size of the bounding box is about the size of the tool for simple set-theoretic operations. It requires more complicated estimation of the size of the affected region when the offset operations and the set-theoretic operations with blending are used, since the result of these operations expands beyond the region of the direct impact of the tool. The projection of the bounding box onto the viewing plane defines the region of the image on the screen that is to be updated. For the punches with spherical and other symmetrical shapes, axis-aligned bounding boxes projecting into axis-aligned rectangles can be used (Fig. 18a, b). For the segments interpolating contours, the use of the axis-aligned rectangles is not feasible since these segments can be long which may require re-drawing of large regions. Instead, the bounding rectangles aligned with each segment are used for updating the image (Fig. 18c). Calculation of the initial and final coordinates of each scan line for these rectangles is done using the Bresenham’s line scan conversion algorithm. The coordinates of the ray tracing scan lines are calculated by increasing/decreasing by an integer value δ the respective coordinate of each pixel representing the segment (Fig. 19). The use of the Bresenham’s scan
Fig. 18. Bounding rectangles for different shapes
conversion algorithm ensures the required fast processing time. Yet another way to accelerate the function evaluation for the offset defined by segments is to calculate and store the matrices T from (2) for each segment to be traced. The bounding boxes are used not only for defining the region for ray tracing after each individual operation. They, as well as other simple shapes like spheres and cylinders, are also associated with computationally expensive shapes/operations to accelerate the function evaluation when points are located with a mouse or a pen on the surface of the metal. On top of this spatial organization of the functional model, another acceleration structure – a regular grid – was used when a large number of shapes/operations was involved in the model. The bounding boxes together with the spatial organization of the functional model provide the required fast function evaluation that is usually a bottleneck for functionally based shape modeling systems. The final or interim model of the object can be saved for further high quality ray tracing with the de-facto
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20 19 Fig. 19. Calculating a bounding rectangle for the offset defined by a segment Fig. 20. “Girl with a candle”, virtual embossing
standard POV-Ray program or for later use with other models. The extension of the POV-Ray program by Suzuki capable of visualizing objects represented with isosurfaces is used in the project. At this point, the desired coloring is to be applied simulating both the metal used and the final chemical processing of the picture. Take a look at the final virtual “Girl with a candle” in Fig. 20 and compare it with the original one in Fig. 8. For better immersion, a graphics tablet has been used. The graphics tablet with a pressure sensitive pen lets the author control the depth of embossing almost in the same way as when doing real embossing. The depth of the tool penetration is a linear function of a pressure. The tip feel is to be customized interactively for each virtual metal. Since the author knows embossing, he simulated it following closely the process of real embossing, and fine-tuned all the respective parameters to achieve eventually the required feeling of “being there”. Perhaps the only difference when using a graphics tablet is that the pen is normally not held in a fist like a punch although
it could be done this way as well, and there was no haptic feedback. The Pentium II 300 MHz with the Wacom Intuos graphics tablet has been used for running the embossing program. As for the time spent for making the real embossed pictures and their virtual clones, it was about the same. One more virtual embossing is presented in Figs. 21 and 22. It exists only in digital form. It is made with both the offsetting and set-theoretic operations. 3500 individual operations/shapes have been used for making its model.
3 Conclusion and future work VR modeling of embossing, as well as other vanishing arts, will let us preserve them, and probably will give them another birth when works of art can be created in the virtual environment, easily duplicated, and exchanged through the Internet. Rapid prototyping would let artists make “physical” copies of their virtual works.
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22 Fig. 21. “Unruly horses”, virtual embossing Fig. 22. “Virtual embossing”. A POV-Ray scene with “Unruly horses”
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In this article, virtual embossing based on the function representation of the metal plate and the tools has been described. The program is implemented as an interactive solid modeler where the functional model of the metal is subsequently modified with the offset and the set-theoretic operations. The proposed offset functions simulate uniformly different embossing operations and provide pseudo-physical simulation of the real process. For visualization, interactive ray tracing is used. The program runs on a personal computer. The use of the function representation for modeling embossing ensures any desired precision of the simulation and thus avoids artifacts that are usual for polygonal representation. Besides, relatively “small” formulae are more attractive form of representation comparing to thousands of polygons. The use of the bounding boxes together with the spatial organization of the model provides us the required fast rendering time and lets us use ray tracing for the VR rendering purposes. Further work will be carried out in several directions. First, implementation of more tool shapes is being planned. Second, the platform independent version of the software will be developed and made available for embossing enthusiasts. Also, the presented techniques will be expanded to virtual modeling other decorative arts. Acknowledgements. Many thanks to my wife Olga and daughter Ania for their help and inspiration. The author also thanks the reviewers whose comments helped to improve the article.
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26. Suzuki R POV-Ray 3 isosurface patch. http://www.public.usit.net/rsuzuki/e/povray/iso 27. Wang W, Kaufman A (1995) Volume sculpting. Symposium on Interactive 3D Graphics, ACM Press, pp 151–156 28. Winkenbach G, Salesin D (1996) Rendering Parametric Surfaces in Pen, Ink. SIGGRAPH’96, Computer Graphics Proceedings, Annual Conference Series, pp 469–476
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A LEXEI S OURIN received his MSc and PhD degrees in Computer Science, both from the Moscow Engineering Physics Institute in 1983 and 1988 respectively. Currently, he is an Associate Professor at the School of Computer Engineering, Nanyang Technological University, Singapore. He is teaching Virtual Reality and Computer Graphics courses. His research interests include functionally based shape modeling, virtual reality and computer art. In the past, he was an Associate Professor at the Moscow Institute of Physics and Technology and a Research Scientist at the Moscow Engineering Physics Institute. For more information see http://www.ntu.edu.sg/home/assourin.
