Parallelising ray tracing with a data parallel approach allows rendering of arbitrarily large models, but the inherent load imbalances may lead to severe inefficiencies. To compensate for the uneven load distribution, demand-driven tasks may be split off and scheduled to processors that are less busy. We propose a hybrid scheduling algorithm which brings tasks and data together according to coherence between rays. Coherent tasks are scheduled demand driven and the remainder is executed data parallel. This method removes the worst hot-spots from the data parallel component and reschedules those as demand driven tasks, thereby evening out the workload. Processing power, communication and memory are three resources which should be evenly used. Our current implementation is assessed against these requirements. Related issues, such as the distribution of the workload over space and the resulting requirements for the distribution objects over the processors, are investigated as well. Final...

. We consider the use of bounding boxes to detect collisions among a set of convex objects in R d . We derive tight bounds on the ratio between the number of box intersections and the number of object intersections. Conrming intuition, we show that the performance of bounding boxes improves signicantly when the underlying objects are all convex. In particular, the ratio is ( 1 1=d 1=2 box ) if each object has aspect ratio at most and the set has scale factor box . More signicantly, the bounding box performance ratio is 2(1 1=d) 3 1=d avg 1 3 1=d box n 1 1=d 3 1=d if only the average aspect ratio avg of the n objects is known. These bounds are the best possible as we show matching lower bound constructions. The case of convex objects is interesting for several reasons: rst, in many applications, the objects are either naturally convex or are approximated by their convex hulls for convenience; second, in some applications, the penetration of convex hul...

: We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling Additional Key Words and Phrases: hierarchical data structure, collision detection, shape approximation, contac...

The result of a scene manipulation is usually displayed by rerendering the entire image even if the change has affected only a small portion of it. This paper presents a system that efficiently detects and recomputes the exact portion of the image that has changed after an arbitrary manipulation of a scene viewed from a fixed camera. The incremental rendering allows for all visual effects produced by ray tracing, including shadows, reflections, refractions, textures, and bump maps. Two structures are maintained to achieve this. A ray tree is associated with each pixel and is used to detect and rebuild only the modified rays after an optical or geometrical change. A color tree represents the complete color expression of a pixel. All changes affecting the color of a pixel without changing the corresponding ray tree require only re-evaluation of the affected portions of the color tree. Optimizations are presented to efficiently detect the modified structures by the use of strategies such as grouping similar information and building hierarchies. Pruning and weighted re-evaluation of information are also considered to manage the memory requirements. The incremental rendering is done efficiently and accurately and is suitable in an interactive context.

Ray tracing is a powerful technique to generate realistic images of 3D scenes. A drawback is its high demand for processing power. Multiprocessing is one way to meet this demand. However, when the models are very large, special attention must be paid to the way the algorithm is parallelised. Combining demand driven and data parallel techniques provides good opportunities to arrive at an efficient scalable algorithm. Which tasks to process demand driven and which data driven, is decided by the data intensity of the task and the amount of data locality (coherence) that will be present in the task. Rays with the same origin and similar directions, such as primary rays and light rays, exhibit much coherence. These rays are therefore traced in demand driven fashion, a bundle at a time. Non-coherent rays are traced data parallel. By combining demand driven and data driven tasks, a good load balance may be achieved, while at the same time spreading the communication evenly across the network. This leads to a scalable and efficient parallel implementation of the ray tracing algorithm.

The main focus of this thesis is on the analysis, via simplification, estimation and clas-sification, of discrete geometric objects using methods from discrete and combinatorial geometry. Geometric objects are ubiquitous in computing today, with uses in areas from GIS to structural molecular biology to graphics and visualization. Usually computation on geometric objects involves several different aspects of their shapes. A first issue is compact and effective shape representation: given a geometric object, how to store it so as to enable efficient manipulation and querying. For example, while the inherently discrete nature of computers allow for only an approximate representation, one would further like to simplify objects (such as polygonal curves) for reducing storage and fast processing. Once we have an efficient representation of objects, it becomes possible to define and compute various geometric attributes, shape descriptors, over them. For example, possible descriptors of point sets are their diameter, depth distribution, spread and so on. Using these shape de-scriptors, it is natural to compare the various qualities of two different geometric objects, via shape matching and shape clustering, for classifying these objects. In this thesis, I will