Out of core Polyhedral Union and its Application to Interactive Shadow Rendering

Abstract

Four methods for storing a set of points using a computer are currently known: Boundary representations, Constructive Solid Geometry, Binary Space Partitioning trees, and Nef polyhedra. We describe a time and spaceefficient BSP-based algorithm for computing the union of a set of solids and compare it with the other solid representations. The algorithm does not require that the entire tree fit in memory; it only needs to maintain the path from the root to one node in the tree at a time. We show that the algorithm is practical by providing time and space statistics. We also show the benefit of using the resulting union solid for computing interactive shadows.