A reformulated radiosity algorithm is presented that produces initial images in time linear to the number of patches. The enormous memory costs of the radiosity algorithm are also elim-inated by computing form-factors on-the-fly. The technique is based on the approach of rendering by progressive refinement. The algorithm provides a useful solution almost immediately which progresses gracefully and continuously to the complete radiosity solution. In this way the competing demands of real-ism and interactivity are accommodated. The technique brings the use of radiosity for interactive rendering within reach and has implications for the use and development of current and future graphics workstations.

Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of the visibility culling techniques developed in the last decade. The taxonomy we use distinguishes between point-based and from-region methods. Point-based methods are further subdivided into object and image-precision techniques, while from-region approaches can take advantage of the cell-and-portal structure of architectural environments or handle generic scenes.

A polygon hidden surface and hidden line removal algorithm is presented. The algorithm recursively subdivides the image into polygon shaped windows until the depth order within the window is found. Accuracy of the input data is preserved. The approach is based on a two-dimensional polygon clipper which is sufficiently general to clip a concave polygon with holes to the borders of a concave polygon with holes. A major advantage of the algorithm is that the polygon form of the output is the same as the polygon form of the input. This allows entering previously calculated images to the system for further processing. Shadow casting may then be performed by first producing a hidden surface removed view from the vantage point of the light source and then resubmitting these tagged polygons for hidden surface removal from the position of the observer. Planar surface detail also becomes easy to represent without increasing the complexity of the hidden surface problem. Translucency is also possible. Calculation times are primarily related to the visible complexity of the final image, but can range from a linear to an exponential relationship with the number of input polygons depending on the particular environment portrayed. To avoid excessive computation time, the implementation uses a screen area subdivision preprocessor to create several windows, each containing a specified number of polygons. The hidden surface algorithm is applied to each of these windows separately. This technique avoids the difficulties of subdividing by screen area down to the screen resolution level while maintaining the advantages of the polygon area sort method.

We introduce the notion of image-driven simplification, a framework that uses images to decide which portions of a model to simplify. This is a departure from approaches that make polygonal simplification decisions based on geometry. As with many methods, we use the edge collapse operator to make incremental changes to a model. Unique to our approach, however, is the use of comparisons between images of the original model against those of a simplified model to determine the cost of an edge collapse. We use common graphics rendering hardware to accelerate the creation of the required images. As expected, this method produces models that are close to the original model according to image differences. Perhaps more surprising, however, is that the method yields models that have high geometric fidelity as well. Our approach also solves the quandary of how to weight the geometric distance versus appearance properties such as normals, color and texture. All of these tradeoffs are ba...

(one pass per subpixel sample) through the hardware rendering pipeline. The resulting image is very high quality, but the performance degrades in proportion to the number of subpixel samples used by the filter function. This paper describes algorithms for accelerating antialiasing in 3D graphics through low-cost custom hardware. The rendering architecture employs a multiple-pass algorithm to perform front-to-back hidden surface removal and shading. Coverage mask evaluation is used to composite objects in 3D. The key advantage of this approach is that antialiasing requires no additional memory and decreases rendering performance by only 30-40% for typical images. The system is image partition based and is scalable to satisfy a wide range of performance and cost constraints. An A-buffer implementation does not require several passes of the object data, but does require sorting objects by depth before compositing them. The amount of memory required to store the sorted layers is limited to...

The conventional procedure for generating shaded images of curved surfaces is to approximate each surface element by a mosaic of polygons and to then apply one of several established polygon display algorithms. The method described here produces an excellent approximation of bi-cubic parametric surfaces in scan line order. Each surface patch is described in terms of edge curves which are intersected by successive scanning planes to form endpoints of scan line segments. Visibility is calculated for each segment by a hybrid priority/zbuffer scheme. Shading is computed using Phong's illumination model with interpolated surface normal values. CR Categories: 8.2.

Computer graphics is a defining application for computational geometry. The interaction between these fields is explored through two scenarios. Spatial subdivisions studied from the viewpoint of computational geometry are shown to have found application in computer graphics. Hidden surface removal problems of computer graphics have led to sweepline and area subdivision algorithms in computational geometry. The paper ends with two promising research areas with practical applications: precise computation and polyhedral decomposition. 1. Introduction Computational geometry and computer graphics both consider geometric phenomena as they relate to computing. Computational geometry provides a theoretical foundation involving the study of algorithms and data structures for doing geometric computations. Computer graphics concerns the practical development of the software, hardware and algorithms necessary to create graphics (i.e. to display geometry) on the computer screen. At the interface l...

A number of image analysis tasks can benefit from registration of the image with a model of the surface being imaged. Automatic navigation using visible light or radar images requires exact alignment of such images with digital terrain models. In addition, automatic classification of terrain, using satellite imagery, requires such alignment to deal correctly with the effects of varying sun angle and surface slope. Even inspection techniques for certain industrial parts may be improved by this means. We achieve the required alignment by matching the real image with a synthetic image obtained from a surface model and known positions of the light sources. The synthetic image intensity is calculated using the reflectance map, a convenient way of describing surface reflection as a function of surface gradient. We illustrate the technique using LANDSAT images and digital terrain models. Key Words and Phrases: image registration, synthetic images, surface models, automatic hill shading, digital terrain models, image transformation, image matching, shaded images

Data Type ............ 14 2.4 The Simple Graphics Package .............. 19 2.4.1 Two-Dimensional Windowing and Viewporting 19 2.5 Two-Dimensional Line Clipping ............. 23 2.5.1 Cohen-Sutherland Line Clipping ........ 25 2.5.2 The Clipping Divider .............. 27 2.6 Windowing and Viewporting Revisited ......... 28 CHAPTER 3. Coordinate-free Geometric Programming I 31 3.1 Problems with the Coordinate-based Approach .... 31 3.2 Aftinc Spaces ....................... 33 3.3 Euclidean Geometry ................... 42 3.3.1 The Inner Product ................ 43 3.4 Frames ........................... 44 3.5 *Matrix Representations of Points and Vectors .... 49 3.6 Aftinc Transformations .................. 51 3.7 *Matrix Representations of Aftinc Transformations . . 58 3.8 Ambiguity Revisited ................... 60 3.9 Coordinate-Free Line Clipping ............. 62 3.10 A Brief Review of Linear Algebra ............ 67 CHAPTER 4. Three-Dimensional Wireframe Viewing 69 4.1

. This paper describes a robust, hardware--accelerated algorithm to compute an approximate visibility map, which describes the visible scene from a particular viewpoint. The user can control the degree of approximation, choosing more accuracy at the cost of increased execution time. The algorithm exploits item buffer hardware to coarsely determine visibility, which is later refined. The paper also describes a conceptually simple algorithm to compute a subset of the discontinuity mesh using the visibility map. Key words: approximate visibility, visibility map, discontinuity meshing, hardware assisted, occlusion culling, form factor, item buffer 1 Introduction The visibility map is a data structure that describes the projection of the visible scene onto the image plane. It is a planar graph in which the vertices, edges, and faces are annotated with the corresponding vertices, edges, and faces of the scene. The visibility map provides more than just the set of visible surfaces...