Overview of Three-Dimensional Computer Graphics DONALD H

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Overview of Three-Dimensional Computer Graphics DONALD H. HOUSE Visualization Laboratory, College of Architecture, Texas A&M University

Three-dimensional computer graphics is by 4D homogeneous transformation ma- called three-dimensional for several trices, each specifying a transformation reasons. The graphics are generated by from the local system to its reference constructing a virtual 3D model which system. The 4D homogeneous form is then imaged, employing a physical allows the unification of the basic trans- simulation of illumination in three-di- formations of translation, scale, rotata- mensional space. Much of the research tion, and shear in a single representa- in the field is aimed at creating an tion. Complex affine transformations illusion of three-dimensionality. Devices are built up by matrix multiplication. such as perspective, physically realistic For geometric modeling, the simplest shading, focus, atmospherics, and 3D geometric primitives are points, orienta- motion for animation have been investi- tion vectors, lines, and polygons. These gated [Foley et al. 1990; Watt and Watt are arranged together to form more 1992; Glassner 1995]. complex objects. More sophisticated modelers provide ORGANIZATION OF A 3D GRAPHICS parametric surfaces and/or implicit sur- SYSTEM faces. Parametric surfaces are defined A three-dimensional graphics system via an underlying piecewise polynomial can be organized into three major com- formulation [Bartels et al. 1987; Rogers ponents: scene specification, rendering, and Adams 1990]. A typical formulation and image storage and display. Figure 1 is a biparametric surface, defined in gives a schematic view of the process Figure 3. An implicit surface is the set used in three-dimensional graphics and of points of satisfying a mathematical shows the role of each component. expression of the form F(x, y, z) ϭ 0. Scene Specification. Scene specifica- Implicit techniques can be generalized tion provides an internal 3D representa- to describe highly complex forms [Ebert tion of the virtual scene to be imaged. 1994]. Its interface may be interactive or pro- Volume data is geometric data in the grammable. Scene specification requires form of a set of scalar values distributed a concept of geometric coordinate sys- in a three-dimensional field. A typical tem and ways of describing geometry, example is data from medical scanners. virtual materials, and lighting. The material is the attribute of a geo- Each local coordinate system used to metric object that describes how its sur- describe the geometry of the scene is face reflects and refracts light. This is defined with respect to an external ref- usually specified by providing parame- erence system. These might themselves ters to a generalized function. A mate- be specified relative to other external rial specification also usually includes systems, allowing models to be de- provision for a set of maps that modify scribed in a hierarchical fashion,as basic color or geometry information as shown in Figure 2. a function of parametric position on a Coordinate systems are often defined surface.

ACM Computing Surveys, Vol. 28, No. 1, March 1996 146 • Donald H. House

Fig. 1. The 3D graphics process.

and accurately, is the essence of the traditional rendering problem. The renderer is the engine driving the image-making process. Simple renderers consider only the direct interaction of lights with surfaces. More sophisticated renderers attempt to solve the global illumination problem, taking into account interreflections among objects. The key steps in rendering, not neces- sarily completed in this order, are the Fig. 2. A clown described by a hierarchy of local following: coordinate frames. (1) Orienting the 3D scene to the camera’s position. (2) Projecting points in the 3D scene into their images on a 2D virtual image plane. (3) Deciding which of the surfaces pro- jected onto the image plane are Fig. 3. A biparametric surface. visible. (4) Fixing a set of sample points on the 3D geometry. Lights provide the illumination source (5) Determining the shade or color re- for simulated shading calculations. flected or transmitted to the screen Some rendering algorithms work with for the visible sample points. light sources with geometric properties (6) Constructing the image using the such as shape and area, but most sys- calculated sample shades. tems work with variants of infinite and The virtual camera provides both a point lights. These and some of their point of view from which to render an variants are illustrated in Figure 4. image and the basic parameters of the Rendering. Rendering is the process mathematical projection used to form of transforming a 3D scene description the virtual image. into a 2D image. Making this process The shader is the algorithm that uses both physically realistic and algorith- the information collected by the ren- mic, so that it can be done efficiently derer about a point sample on the scene

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Fig. 4. Infinite and point light sources and variants. geometry, its material attributes, and tronics providing controls to draw the the available lighting to calculate a image frame as a raster on the CRT. color for the sample. Image file storage efficiency is an im- A digital image is constructed from a portant issue due to the very large num- set of shaded samples by some form of ber of pixels in an image. Fortunately, low-pass filtering and resampling [Wol- various forms of internal image coher- berg 1990]. In simplest terms, the digi- ency lend themselves to exploitation in tal image pixel grid is superimposed the development of file-compression over the virtual screen, then each pixel is techniques. For these and also for com- colored with a weighted average of the mercial reasons, the number of image shaded samples in the pixel’s vicinity. file formats in common use is quite large [Murray and vanRyper 1994]. Image Storage and Display. Ren- dered results must be turned into tangi- RESEARCH ISSUES ble images that can be viewed, stored, and transmitted. Thus, a three-dimen- Several research areas are timely and sional graphic system is organized important to the development of the around digital image data structures, a field. In rendering, they are improving model of display technology, and file global illumination techniques and de- formats. veloping nonphotorealistic techniques. In The pixmap is the basic data struc- modeling, they are exploring volume ture for the storage of digital images. It methods, improving interactive tech- is simply a 2D array of pixel values, niques, and effectivly modeling natural each stored in units of one or more bits. forms. In computer animation, impor- The number of bits per pixel determines tant research areas are physically based how many distinct colors or other at- modeling, applications of AI and ALife, tributes an image may have. and interactive techniques. Finally, there The most frequently used display de- is the related field of virtual reality. vice is the color cathode ray tube (CRT), interfaced to the pixmap data structure REFERENCES via a hardware framebuffer. The framebuffer is simply an array of computer BARTELS, R., BEATTY, J., AND BARSKY, B. 1987. An memory that holds the pixmap and elec- Introduction to Splines for Use in Computer

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Graphics and Geometric Modeling. Morgan MURRAY,J.AND VANRYPER, W. 1994. Encyclope- Kaufmann, Los Altos, CA. dia of Graphics File Formats. O’Reilly, Sebas- EBERT, D. S., ED. 1994. Texturing and Modeling: topol, CA. A Procedural Approach. AP Professional, Bos- ROGERS,D.AND ADAMS, J. 1990. Mathematical ton, MA. Elements for Computer Graphics. McGraw- FOLEY, J., VAN DAM, A., FEINER, S., AND HUGHES,J. Hill, New York. 1990. Computer Graphics Principles and WATT,A.AND WATT, M. 1992. Advanced Anima- Practice. Addison-Wesley, Reading, MA. tion and Rendering Techniques. Addison-Wes- GLASSNER, A. 1995. Principles of Digital Image ley, Reading, MA. Synthesis. Morgan Kaufmann, Los Altos, WOLBERG, G. 1990. Digital Image Warping. CA. IEEE Press, Los Alamitos, CA.

ACM Computing Surveys, Vol. 28, No. 1, March 1996