Reflections in Curved Surfaces (thesis)

Abstract:

Reflections add a new dimension to the realism of computer generated scenes. The only existing method for implementing reflections satisfactorily is ray-tracing. However, it has major drawbacks, the most obvious being its expensive CPU requirements. The objective of this dissertation is to gain an understanding of the nature of reflections, and to develop alternate methods for rendering them by exploiting their geometric coherence. We develop a disciplined science for characterizing reflections in curved surfaces. There is no hope for closed form solutions to rendering them since they are algebraically intractable.
However, we describe three techniques to handle the situation: contour tracing, special purpose numerical methods, and spline approximation. We extend four existing algorithms to include reflections, namely, the painter's algorithm, the z-buffer algorithm, the scan plane algorithm, and what we call the
curvilinear trapezoid method. Methods and scope for parallelizing these algorithms are also discussed. A comparative study of these algorithms is attempted to outline their suitability under various computing environments. The computing environment is thus a significant factor for the choice of an algorithm. Our efforts are focused on scenes composed of spheres but more general scenes are possible. (Note: paper has been copied with two pages per sheet.)