such fields as art and technical illustration to develop automatic methods to ... traditional volume rendering system, and Diagram 2, our volume illustration.
PROCEDURAL VOLUME MODELING, RENDERING, AND VISUALIZATION
David Ebert
Penny Rheingans
Purdue University
University of Maryland Baltimore County
1.
INTRODUCTION
Volume visualization techniques have advanced dramatically over the past fifteen years. However, the increase in scale of visualization tasks has been increasing at even a faster rate. Today, many problems require the visualization of gigabytes to terabytes of data. Additionally, the number of variables and dimensionality of many scientific simulations and observations has increased, while the resolution of computer graphics displays has not changed substantially (still a few million pixels). These factors present a significant challenge to current visualization techniques and approaches. We propose a new approach to visualization to solve these problems and provide flexibility and extensibility for visualization challenges over the next decade: procedural visualization. In this approach, we encode and abstract datasets to a more manageable level, while also developing more effective visualization and rendering techniques.
1.1
Background on Procedural Techniques
Procedural techniques have been used throughout the history of computer graphics. Many early modeling and texturing techniques included procedural definitions of geometry and surface color. From these early beginnings, procedural techniques have exploded into an important, powerful modeling, texturing, and animation paradigm. During the mid to late 1980s, procedural techniques for creating realistic textures, such as marble, wood, stone, and other natural material, gained widespread use. These techniques were extended to procedural modeling, including models of water, smoke, steam, fire, planets, and even tribbles. The development of the RenderMan1 1
RenderMan is a registered trademark of Pixar.
shading language [Pixar89] in 1989 greatly expanded the use of procedural techniques. Currently, most commercial rendering and animation systems even provide a procedural interface. Procedural techniques have become an exciting, vital aspect of creating realistic computer generated images and animations. As the field continues to evolve, the importance and significance of procedural techniques will continue to grow. Procedural techniques are code segments or algorithms that specify some characteristic of a computer generated model or effect. For example, a procedural texture for a marble surface does not use a scanned-in image to define the color values. Instead, it uses algorithms and mathematical functions to determine the color. One of the most important features of procedural techniques is abstraction. In a procedural approach, rather than explicitly specifying and storing all the complex details of a scene or sequence, we abstract them into a function or an algorithm (i.e., a procedure) and evaluate that procedure when and where needed. We gain a storage savings, as the details are no longer explicitly specified but rather implicit in the procedure, and shift the time requirements for specification of details from the programmer to the computer. This allows us to create inherently multi-resolution models and textures that we can evaluate to the resolution needed. We also gain the power of parametric control, allowing us to assign to a parameter a meaningful concept (e.g., a number that makes mountains "rougher’’ or "smoother’’). Parametric control also provides amplification of the modeler/animator’s efforts: a few parameters yield large amounts of detail (Smith [Smith84] referred to this as database amplification). This parametric control unburdens the user from the low-level control and specification of detail. We also gain the serendipity inherent in procedural techniques: we are often pleasantly surprised by the unexpected behaviors of procedures, particularly stochastic procedures. Procedural models also offer flexibility. The designer of the procedures can capture the essence of the object, phenomenon, or motion without being constrained by the complex laws of physics. Procedural techniques allow the inclusion of any amount of physical accuracy into the model that is desired. The designer may produce a wide range of effects, from accurately simulating natural laws to purely artistic effects.
1.2
Overview of the Procedural Visualization Approach
We believe that using a procedural approach in volume graphics flexible, extensible, and powerful method for modeling, rendering, visualizing volumetric data. Our procedural visualization methodology procedural techniques for general volume modeling, improving
is a and uses the
effectiveness of volume rendering, and abstracting large datasets for interactive visualization on the desktop.
2.
PROCEDURAL VOLUME MODELING TECHNIQUES
Many advanced geometric modeling techniques, such as fractals [Peitgen92], implicit surfaces [Blinn82, Wyvill86, Nishimura85], grammarbased modeling [Smith84, Prusinkiewicz90], and volumetric procedural models/hypertextures [Perlin85, Ebert94] use procedural abstraction of detail to allow the designer to control and animate objects at a high level. When modeling complex volumetric phenomena, such as clouds, this abstraction of detail and data amplification are necessary to make the modeling and animation tractable. It would be impractical for an animator to specify and control the detailed three-dimensional density for most intricate volume models. As an example of the advantages of procedural volume modeling, we will describe our approach to volumetric cloud modeling. Volumetric procedural models are a natural choice for cloud modeling because they are the most flexible advanced modeling technique. Since a procedure is evaluated to determine the object’s density, any advanced modeling technique, simple physics simulation, mathematical function or artistic algorithm can be included in the model. Combining traditional volumetric procedural models with implicit functions creates a model that has the advantages of both techniques. Implicit functions have been used for many years as a modeling tool for creating solid objects and smoothly blended surfaces [Bloomenthal97]. However, only a few researchers have explored their potential for modeling volumetric density distributions of semi-transparent volumes (e.g., [Nishita96], [Stam91, Stam93, Stam95], [Ebert97a]). Ebert’s early work on using volume rendered implicit spheres to produce a fly-through of a volumetric cloud was described in [Ebert97a]. This work has been developed further to use implicits to provide a natural way of specifying and animating the global structure of the cloud, while using more traditional procedural techniques to model the detailed structure. More details on the implementation of these techniques can be found in [Ebert98]. The volumetric cloud model uses a two-level: the cloud macrostructure and the cloud microstructure. These are modeled by implicit functions and turbulent volume densities, respectively. The basic structure of the cloud model combines these two components to determine the final density of the cloud. The cloud's microstructure is created by using procedural turbulence and noise functions [Ebert98]. This allows the procedural simulation of natural
detail to the level needed. Simple mathematical functions are added to allow shaping of the density distributions and control over the sharpness of the density falloff. Implicit functions were chosen to model the cloud macrostructure because of their ease of specification and smoothly blending density distributions. The user simply specifies the location, type, and weight of the implicit primitives to create the overall cloud shape. Since these are volume rendered as a semi-transparent medium, the whole volumetric field function is being rendered, as compared to implicit surface rendering where only a small range of values of the field are used to create the objects. The implicit density functions are primitive-based density functions: they are defined by summed, weighted, parameterized, primitive implicit surfaces. The real power of implicit functions is the smooth blending of the density fields from separate primitive sources. Wyvill’s standard cubic function [Wyvill1986] is used as the density (blending) function for the implicit primitives. The final implicit density value is then the weighted sum of the density field values of each primitive. To create non-solid implicit primitives, the location of the point is procedurally altered before the evaluation of the blending functions. This alteration can be the product of the procedure and the implicit function and/or a warping of the implicit space. These techniques are combined into a simple cloud model as shown below: volumetric_procedural_implicit_function(pnt, blend%, pixel_size) perturbed_point = procedurally alter pnt using noise and turbulence density1 = implicit_function(perturbed_point) density2 = turbulence(pnt, pixel_size) blend = blend% * density1 +(1 - blend%) * density2 density = shape resulting density based on user controls for wispiness and denseness(e.g., use pow & exponential function) return(density)
The density from the implicit primitives is combined with a pure turbulence based density using a user specified blend% (60% to 80% gives good results). The blending of the two densities allows the creation of clouds that range from entirely determined by the implicit function density to entirely determined by the procedural turbulence function. When the clouds are completely determined by the implicit functions, they tend to look more like cotton balls. The addition of the procedural alteration and turbulence is
what gives them their naturalistic look. An example resulting cloud can be seen in Figure 1.
3.
PROCEDURALLY-ENHANCED VOLUME RENDERING
We have applied the procedural visualization approach to the problem of direct volume visualization, using procedural methods to generate illustrative enhancements to a typical raycast volume rendering pipeline. The typical direct volume renderer uses a transfer function to map the scalar voxel values to color and opacity. This mapping is essentially a very simple procedural method. Some methods have incorporated gradient along with the voxel value as parameters to the transfer functions. We generalize still further to use a variety of volume feature indicators as parameters for multivariate transfer functions, using these procedural methods to augment standard rendering process with non-photorealistic rendering (NPR) techniques to enhance the expressiveness of the visualization. NPR draws inspiration from such fields as art and technical illustration to develop automatic methods to synthesize images with an illustrated look from geometric surface models. Procedural methods can be used to develop a set of NPR techniques specifically for the visualization of volume data, including both the adaptation of existing NPR techniques to volume rendering and the development of new techniques specifically suited for volume models. We call this approach volume illustration.
3.1
Related Work
Traditional volume rendering spans a spectrum from the accurate to the ad hoc, using both realistic illumination models to simulate atmospheric attenuation and transfer functions to produce artificial views of the data to highlight regions of interest [Drebin88, Kindlmann98, Fujishiro99]. While transfer functions can be effective at bringing out the structure in the value distribution of a volume, they are generally limited by their dependence on voxel value as the sole transfer function domain. In contrast, there has been extensive research for illustrating surface shape using non-photorealistic rendering techniques. Techniques adapted from art and illustration include a tone-based illumination model [Gooch98], the extraction and rendering of silhouettes and other expressive lines [Salisbury94, Gooch99], and the use of expressive textures to convey surface shape [Rheingans96, Salisbury97, Interrante97]. A few researchers have applied NPR techniques to the display of data, drawing techniques from painting [Kirby99], pen-and-ink illustrations [Treavett00], and technical
illustration [Interrante98, Saito94]. With the exceptions of the work of Saito and Interrante, the use of NPR techniques has been confined to surface rendering.
3.2
Approach
We have used the procedural approach to develop a collection of volume illustration techniques that adapt and extend NPR techniques to volume objects. Most traditional volume enhancement has relied on functions of the volume sample values (e.g., opacity transfer functions), although some techniques have also used the volume gradient (e.g., [Levoy90]). In contrast, our volume illustration techniques are fully incorporated into the volume rendering process, utilizing viewing information, lighting information, and additional volumetric properties to provide a powerful, easily extensible framework for volumetric enhancement. Comparing Diagram 1, the traditional volume rendering system, and Diagram 2, our volume illustration rendering system, demonstrates the difference in our approach to volume enhancement. By procedurally enhancing the volume sample’s color, illumination, and opacity into the rendering system, we can implement a wide range of enhancement techniques. The properties that can be incorporated into the volume illustration procedures include the following: •
Volume sample location and value
•
Local volumetric properties, such as gradient and minimal change direction
•
View direction
•
Light information
The view direction and light information allows global orientation information to be used in enhancing local volumetric features. Combining this rendering information with user selected parameters provides a powerful framework for volumetric enhancement and modification for artistic effects. Traditional Volume Rendering Pipeline
Volume Illustration Rendering Pipeline volume values f1(xi)
Volume values f1(xi) shading
classification
voxel colors cλ(xi)
voxel opacities α(xi)
shaded, segmented volume [cλ(xi), α(xi)] resampling and compositing (raycasting, splatting, etc.) image pixels Cλ(ui)
Diagram 1. Pipeline.
Traditional Volume Rendering
Volume Rendering
Transfer function
Volume Illustration color modification
Volume Illustration opacity modification
Final volume sample [cλ(xi), α(xi)] image pixels Cλ (ui)
Diagram 2. Volume Rendering Pipeline.
Illustration
Volumetric illustration differs from surface-based NPR in several important ways. In NPR, the surfaces (features) are well defined, whereas with volumes, feature areas within the volume must be determined through analysis of local volumetric properties. The volumetric features vary continuously throughout three-dimensional space and are not as well defined as surface features. Once these volumetric feature volumes are identified, user selected parametric properties can be used to enhance and illustrate them. Figure 2 shows gaseous illumination of an abdominal CT volume of 256×256×128 voxels. In this image, as in others of this data set, the scene is illuminated by a single light above the volume and slightly toward the viewer. The structure of tissues and organs is difficult to understand. In Figure 3, a transfer function has been used to assign voxel colors which mimic those found in actual tissue. The volume is illuminated as before. Organization of tissues into organs is clear, but the interiors of structures are still unclear.
3.3
Enhancement Techniques
In a surface model, the essential feature is the surface itself. The surface is explicitly and discretely defined by a surface model, making “surfaceness” a boolean quality. Many other features, such as silhouettes or regions of high curvature, are simply interesting parts of the surface. Such features can be identified by analysis of regions of the surface. In a volume model, there are no such discretely defined features. Volume characteristics and the features that they indicate exist continuously throughout the volume. However, the boundaries between regions are still one feature of interest. The local gradient magnitude at a volume sample can be used to indicate the degree to which the sample is a boundary between disparate regions. The direction of the gradient is analogous to the surface normal. Regions of high gradient are similar to surfaces, but now “surfaceness” is a continuous, volumetric quality, rather than a boolean quality. Few of the usual depth cues are present in traditional rendering of translucent volumes. Obscuration cues are largely missing since there are no opaque objects to show a clear depth ordering. Perspective cues from converging lines and texture compression are also lacking, since few volume models contain straight lines or uniform textures. The dearth of clear depth cues makes understanding spatial relationships of features in the volume difficult. Similarly, information about the orientation of features within the volume is also largely missing. As a result, the shape of individual structures within even illuminated volumes is difficult to perceive. We have developed several techniques for the procedural enhancement of volume features based on gradient, as well as depth and orientation cues in volume models, inspired by shading concepts in art and technical illustration.
3.3.1
Silhouettes
Surface orientation is an important visual cue that has been successfully conveyed by artists for centuries through numerous techniques, including silhouette lines and orientation-determined saturation effects. Silhouette lines are particularly important in the perception of surface shape, and have been utilized in surface illustration and surface visualization rendering [Salisbury94, Interrante95]. Similarly, silhouette volumes increase the perception of volumetric features. In order to strengthen the cues provided by silhouette volumes, we increase the opacity of volume samples where the gradient nears perpendicular to the view direction, indicated by a dot product between gradient and view direction which nears zero. Figure 4 shows the result of both boundary and silhouette enhancement in the medical volume. The fine honeycomb structure of the liver interior is clearly apparent, as well as additional internal structure of the kidneys. 3.3.2
Feature halos
Illustrators sometimes use null halos around foreground features to reinforce the perception of depth relationships within a scene. The effect is to leave the areas just outside surfaces empty, even if an accurate depiction would show a background object in that place. Interrante [Interrante98] used a similar idea to show depth relationships in 3D flow data using Line Integral Convolution (LIC). The resulting halos achieved the desired effect, but the method depended on having flow data suitable for processing with LIC. We use a more general method for creating halo effects during the illumination process using the local spatial properties of the volume. Halos are created primarily in planes orthogonal to the view vector by making regions just outside features darker and more opaque, obscuring background elements which would otherwise be visible. The strongest halos are created in empty regions just outside (in the plane perpendicular to the view direction) of a strong feature. Figure 5 shows the effectiveness of adding halos to the medical volume. Structures in the foreground, such as the liver and kidneys, stand out more clearly. 3.3.3
Tone shading
Another illustrative technique used by painters is to modify the tone of an object based on the orientation of that object relative to the light. This technique can be used to give surfaces facing the light a warm cast while surfaces not facing the light get a cool cast, giving effects suggestive of illumination by a warm light source, such as sunlight. Gooch et al. proposed
an illumination model based on this technique [Gooch98], defining a parameterized model for effects from pure tone shading to pure illuminated object color. The parameters define a warm color by combining yellow and the scaled fully illuminated object color. Similarly, a cool color combines blue and the scaled ambient illuminated object color. The final surface color is formed by interpolation between the warm and cool color based on the signed dot product between the surface normal and light vector. We implemented an illumination model similar to Gooch tone shading for use with volume models. The color at a voxel is a weighted sum of the illuminated gaseous color (including any traditional transfer function calculations) and the total tone and directed shading from all directed light sources. The tone contribution from a single light source is interpolated from the warm and cool colors, depending on the angle between the light vector and the sample gradient. Samples oriented toward the light become more like the warm color while samples oriented away from the light become more like the cool color. Figure 6 shows tone shading applied together with colors from a transfer function. The tone effects are subtle, but still improve shape perception. The basic tissue colors are preserved, but the banded structure of the aorta is more apparent than in a simple illuminated and color-mapped image (Figure 3).
3.4
Enhancement Examples
We have also applied the techniques in the previous sections to several other scientific data sets. Figure 7 shows a 512x512x128 element flow data set from the time series simulation of unsteady flow emanating from a 2D rectangular slot jet. The 2D jet source is located at the left of the image and the flow is to the right. Flow researchers notice that both Figures 7 and 8 resemble Schlieren photographs that are traditionally used to analyze flow. Figure 8 shows the effectiveness of boundary enhancement, silhouette enhancement, and tone shading on this data set. The overall flow structure, vortex shedding, and helical structure are much easier to perceive in Figure 8 than in Figure 7. Figures 9 and 10 are volume renderings of a 64x64x64 high-potential iron protein data set. Figure 9 is a traditional gas-based rendering of the data. Figure 10 has our tone shading volume illustration techniques applied. The relationship of structure features and the three-dimensional location of the features is much clearer with the tone-based shading enhancements applied.
4.
PROCEDURAL ABSTRACTION OF LARGE DATASETS
The idea of functionally representing volumetric data has been inherent in visualization for the past 10 years. Most isosurface visualization algorithms assume that a continuous function describes the field being visualized and use the sampled data points and implied characteristics of the function (e.g., gradient) to create smooth surfaces representing isovalues of the field [Gallagher89]. Similarly, a procedural approach to data abstraction extends this inherent nature to capitalize on the compact representation capability of functions for characterizing data. A collection of procedural basis functions (implicit field functions, fractals, fractal interpolation functions) can be used to describe large data sets at multiple scales of resolution, capitalizing on the power of procedural modeling techniques and parametric representation to provide a flexible, extensible system that features data amplification and inherent multi-resolution models.
4.1
Characterization of data by functional description
A data set can be prepreprocessed in order to create a compact functional representation of each data variable. This functional representation can allow viewers to quickly transfer a compact representation of the potentially multigigabyte database to their workstation for visualization, interaction, and exploration, which will be processed on the local workstation for visualization. Within the procedural model, statistically appropriate procedural detail can be generated to quickly simulate data detail during interaction and exploration. While the viewer performs an initial exploration of the data, more detailed data can be retrieved from the database to replace the procedural detail. Implicit function techniques provide a compact, flexible method for describing three-dimensional fields [Bloomenthal97]. Figure 1 shows the detailed volumetric models of clouds that can be represented with as few as nine implicit functions (each with four parameters, totaling less than 200 bytes of storage). This use of implicits is different from traditional implicit modeling techniques: in that it uses implicits to characterize volume distributions of data and not to model surfaces. A collection of implicit and fractal basis functions, skeletal primitives, and blending functions can be used to functionally represent and visualize general multivariate volumetric data. Additionally, specialized functional representations can take advantage of domain-specific knowledge, allowing more sophisticated procedural simulations (e.g., simplified Navier-Stokes simulations, diffusion simulations) to be incorporated into the functional representation to provide more accurate characterization of the data, more
compact representation of the data, and the ability to generate appropriate detail and missing data. One key challenge in this research is the development of automatic and semi-automatic techniques for generating compact implicit, multi-fractal, and FIF representations of large volumetric data sets. Implicits are a natural choice for multi-resolution volumetric data representation because of their C2 continuous blending, well-defined spatial extent of each implicit (local control), and the ability to both add and subtract detail from the volumetric approximation through the use of positive and negative weighting of primitives. A small number of implicits can be used to represent the main characteristics of the volumetric data set. The addition of more implicits with finer spatial extents will add detail on demand. In general, implicits provide a smoothly varying volumetric field representation, which is appropriate for large-scale volumetric features and, in some applications, fine resolution features. In contrast, multi-fractals provide sharp detail and more discontinuous volumetric functions through the addition of detail at varying frequency scales. FIFs and multi-fractals are a natural choice for representing data with large abrupt changes in values, discontinuous functions, and substantial noise. FIFs provide primitives that can represent detailed data that is smooth, rough, and even transitions from smooth to rough. The combination of these three types of primitives provides a powerful system for representing volumetric data with a wide variety of characteristics.
4.2
Visualization from functional descriptions
Two basic approaches for are available for the visualization of functionally represented data: voxelize, then visualize, and visualize directly from the functional representation. To voxelize the functional representation, all that is needed is to evaluate the appropriate functions at the centers of a fixed volume grid. Direct visualization of the functional representation can include statistically appropriate procedural pseudo-detail to provide a better representation of the underlying data set. This pseudo-detail can be tagged internally and replaced with better approximations as computational time allows.
5.
CONCLUSIONS
We have described a procedural visualization framework that is a powerful, flexible, and extensible approach to visualization challenges today and over the next decade. Using procedural techniques allow the abstraction of volumetric models and datasets to a compact, higher-level for ease in specification and interactive viewing on desktop computers. Extending this
visualization approach to volume illustration provide procedural control of visualization enhancement and a powerful technique for expressively conveying important features within data volumes.
6.
ACKNOWLEDGMENTS
The authors would like to thank Dr. Elliott Fishman of Johns Hopkins Medical Institutions for the abdominal CT dataset. The iron protein dataset came from the vtk website (www.kitware.com/vtk.html). Christopher Morris generated some of the pictures included in this paper. This material is based on work supported by the National Science Foundation under Grants No. 0081581, 9996043, and 9978032.
7.
REFERENCES
[Blinn82] Blinn, J., "Light Reflection Functions for Simulation of Clouds and Dusty Surfaces," Computer Graphics (SIGGRAPH ’82 Proceedings), 16(3)21:29, July 1982. [Bloomenthal97] Bloomenthal, J., Bajaj, C., Blinn, J., Cani-Gascuel, M.P., Rockwood, A., Wyvill, B., Wyvill, G., Introduction to Implicit Surfaces, Morgan Kaufman Publishers, 1997. . [Drebin88] Robert A. Drebin and Loren Carpenter and Pat Hanrahan. Volume Rendering, Computer Graphics (Proceedings of SIGGRAPH 88), 22(4), pp. 65-74 (August 1988, Atlanta, Georgia). Edited by John Dill. [Ebert94] Ebert, D., Carlson, W., Parent, R., "Solid Spaces and Inverse Particle Systems for Controlling the Animation of Gases and Fluids," The Visual Computer, 10(4):179-190, 1994. [Ebert97a] Ebert, D., "Volumetric Modeling with Implicit Functions: A Cloud is Born," SIGGRAPH 97 Visual Proceedings (Technical Sketch), 147, ACM SIGGRAPH 1997. [Ebert98] Ebert, D., Musgrave, F., Peachey, D., Perlin, K., Worley, S., Texturing and Modeling: A Procedural Approach, Second Edition, AP Professional, July 1998. [Fujishiro99] Issei Fujishiro and Taeko Azuma and Yuriko Takeshima. Automating Transfer Function Design for Comprehensible Volume Rendering Based on 3D Field Topology Analysis, IEEE Visualization ’99, pp. 467-470 (October 1999, San Francisco, California). IEEE. Edited by David Ebert and Markus Gross and Bernd Hamann. [Gallgher89] R. Gallagher and J. Nagtegaal, "An Efficient 3-D Visualization Technique for Finite Element Models and Other Coarse Volumes," Computer Graphics (SIGGRAPH ’89 Proceedings), 23 (3), pp. 185-194 (July 1989). Edited by Jeffrey Lane. [Gooch98] Amy Gooch, Bruce Gooch, Peter Shirley, and Elaine Cohen. A Non-photorealistic Lighting Model for Automatic Technical Illustration. In Proceedings of SIGGRAPH ’98 (Orlando, FL, July 1998), Computer Graphics Proceedings, Annual Conference Series, pp. 447-452, ACM SIGGRAPH, ACM Press, July 1998. [Gooch99] Bruce Gooch and Peter-Pike J. Sloan and Amy Gooch and Peter Shirley and Rich Riesenfeld. Interactive Technical Illustration, 1999 ACM Symposium on Interactive 3D Graphics, pp. 31-38 (April 1999). ACM SIGGRAPH. Edited by Jessica Hodgins and James D. Foley. ISBN 1-58113-082-1 . [Interrante97] Victoria Interrante and Henry Fuchs and Stephen M. Pizer. Conveying the 3D Shape of Smoothly Curving Transparent Surfaces via Texture, IEEE Transactions on Visualization and Computer Graphics, 3(2), (April - June 1997). ISSN 1077-2626.
[Interrante98] Victoria Interrante and Chester Grosch. Visualizing 3D Flow, IEEE Computer Graphics & Applications, 18(4), pp. 49-53 (July - August 1998). ISSN 0272-1716. [Kajiya84] James T. Kajiya and Brian P. Von Herzen. Ray Tracing Volume Densities, Computer Graphics (Proceedings of SIGGRAPH 84), 18(3), pp. 165-174 (July 1984, Minneapolis, Minnesota). Edited by Hank Christiansen. [Kindlmann98] Gordon Kindlmann and James Durkin. Semi-Automatic Generation of Transfer Functions for Direct Volume Rendering, In Proceedings of 1998 IEEE Symposium on Volume Visualization, pp. 79-86. [Kirby99] R.M. Kirby, H. Marmanis, and D.H. Laidlaw. Visualizing Multivalued Data from 2D Incompressible Flows Using Concepts from Painting, IEEE Visualization ’99, pp. 333-340 (October 1999, San Francisco, California). IEEE. Edited by David Ebert and Markus Gross and Bernd Hamann. ISBN 0-7803-5897-X. [Levoy90] Marc Levoy. Efficient Ray Tracing of Volume Data, ACM Transactions on Graphics, 9 (3), pp. 245-261 (July 1990). ISSN 0730-0301. [Nishimura85] Nishimura, H., Hirai, A., Kawai, T., Kawata, T., Shirakawa, I., Omura, K., "Object Modeling by Distribution Function and a Method of Image Generation," Journal of Papers Given at the Electronics Communication Conference ’85, J68-D(4), 1985. [Nishita87] Nishita, T., Miyawaki, Y., Nakamae, E., "A shading model for atmospheric scattering considering luminous intensity distribution of light sources," Computer Graphics (SIGGRAPH ’87Proceedings), 21, pages 303-310, July 1987. [Nishita96] Nishita, T., Nakamae, E., Dobashi, Y., "Display Of Clouds And Snow Taking Into Account Multiple Anisotropic Scattering And Sky Light," SIGGRAPH 96 Conference Proceedings, pages 379-386. ACM SIGGRAPH, August 1996. [Nishita98] Tomoyuki Nishita. Light Scattering Models for the Realistic Rendering of Natural Scenes, Eurographics Rendering Workshop 1998, pp. 1-10 (June 1998, Vienna, Austria). Eurographics. Edited by George Drettakis and Nelson Max. ISBN3-211-83213-0. [Rheingans96] Penny Rheingans. Opacity-modulating Triangular Textures for Irregular Surfaces, Proceedings of IEEE Visualization ’96, pp. 219-225 (October 1996, San Francisco CA). IEEE. Edited by Roni Yagel and Gregory Nielson. ISBN 0-89791-864-9. [Rheingans01] Penny Rheingans and David Ebert. Volume Illustration: Nonphotorealistic Rendering of Volume Models, IEEE Transactions on Visualization and Computer Graphics, vol. 7, no.3, pp. 253-264, July-September 2001. [Saito94] Takafumi Saito. Real-time Previewing for Volume Visualization. In Proceedings of 1994 IEEE Symposium on Volume Visualization, pp. 99-106. [Salisbury94] Michael P. Salisbury and Sean E. Anderson and Ronen Barzel and David H. Salesin. Interactive Pen-And-Ink Illustration, Proceedings of SIGGRAPH 94, Computer Graphics Proceedings, Annual Conference Series, pp. 101-108 (July 1994, Orlando, Florida). ACM Press. Edited by Andrew Glassner. ISBN 0-89791-667-0. [Salisbury97] Michael P. Salisbury and Michael T. Wong and John F. Hughes and David H. Salesin. Orientable Textures for Image-Based Pen-and-Ink Illustration, Proceedings of SIGGRAPH 97, Computer Graphics Proceedings, Annual Conference Series, pp. 401406 (August 1997, Los Angeles, California). Addison Wesley. Edited by Turner Whitted. ISBN 0-89791-896-7. [Treavett00] S.M.F. Treavett and M. Chen. Pen-and-Ink Rendering in Volume Visualisation, Proceedings of IEEE Visualization 20000, October 2000, ACM SIGGRAPH Press.
Figure 1: Closeup of a procedural cloud created with nine volumetric implicits.
Figure 2. Gaseous illumination of medical CT volume. Voxels are a constant color.
Figure 4. Silhouette and enhancement of CT volume.
boundary
Figure 3. Gaseous illumination of colormapped CT volume.
Figure 5. Distance color blending and halos around features of CT volume.
Figure 6. Tone shading in colored volume. Surfaces toward light receive warm color.
Figure 7. Atmospheric volume rendering of square jet. No illustration enhancements.
Figure 8. Square jet with boundary and silhouette enhancement, and tone shading.
Figure 9. protein.
Figure 10. Tone shaded iron protein.
Atmospheric rendering of iron
