Cse 528 Project : Sweeping a 3-d Tetrahedral Complex

This report outlines the design and implementation of an algorithm to sweep a 3 dimensional tetrahedral complex in a particular direction. The problem is considered in its most generality, that is, the tetrahedral complex can be concave and have holes inside it which can themselves be concave. This algorithm can be used to e ciently perform ray-tracing of 3-D objects. The main idea in the algorithm comes from the observation that there are few number of boundary vertices than there are internal vertices in a arbitrary tetrahedral complex. Thus, by suitably initializing our possible set of next vertices that can be visited, we get an e cient algorithm to implement the sweep. Another advantage of using this to do ray-tracing is that it uses much less space. Chapter