Real-Time Algorithms and Intersection Test Methods for Computer Graphics

Doctoral thesis, 1998

In real-time computer graphics applications, at least three major forces are in conflict, namely, rendering speed, the level of realism, and interactivity. Therefore this thesis focuses on real-time algorithms that enhance the realism while maintaining high rendering speed, and on fast intersection test methods in order to speed up, for example, collision detection, picking processes and ray tracing. The first part on real-time algorithms consists of five papers, where the first introduces a new algorithm for enlarging and diminishing images. It can be used in, for example, real-time three dimensional games and interactive image processing programs. The remaining four papers use radiosity, soft shadows, planar reflections and environment mapping, respectively, in order to increase the level of realism in real-time computer graphics applications. The radiosity paper describes how to compute textures containing illumination, and how these together with hardware texture mapping can reconstruct the radiosity function, and thereby achieving real-time performance. Besides improving the realism of a rendered scene, shadows and reflections are used (by the viewer) as cues to determine spatial relationships between objects. Some techniques for gaining performance are described for an existing soft shadow algorithm, which is followed by a short note on how to implement real-time planar reflections. The first part is then ended with a report on a new environment mapping method, which provides a better approximation of reflections in curved surfaces. The second part on intersection test methods starts with a paper that derives a new method for speeding up the primary ray intersections in a ray tracing program. The second paper presents a fast method for computing the intersection between a ray and a triangle, which is followed by a paper on determining whether two triangles overlap. The methods of the last two papers have applications in ray tracing, global illumination, picking processes, and in collision detection. The majority of the algorithms and methods presented in this thesis have been implemented and used in commercial software. Categories and Subject Descriptors (as by ACM CR): I.3[Computer Graphics]: Three-Dimensional Graphics and Realism - color, shading, shadowing, and texture; Computational Geometry and Object Modeling - Geometric algorithms, languages, and systems. General Terms: Algorithms. Additional Key Words and Phrases: ray tracing, radiosity, virtual reality.