A Confinement-Based Hierarchy for Convex Differences Aggregates

Constructive Solid Geometry (CSG) is a solid representation that is appealing for interactive design of models through Boolean operations. Unfortunately, there is a lack of efficient algorithms that render CSG models at interactive rates using conventional computer graphics hardware. The Convex Differences Aggregate (CDA) representation was introduced to solve this problem. CDAs are defined as lists of cells that represent the set theoretic difference of convex polyhedra, which can be manipulated and rendered very efficiently during interactive Boolean operations. Still, due to the linearity of the CDA structure, the CDA algorithms do not scale well and are limited to the conceptual design of relatively small models. This paper extends the CDA representation through a confinement-based hierarchy. The Hierarchical CDA (HCDA) is organized as a tree of cells that has the advantage of a built-in spatial acceleration scheme and a level-ofdetail (LOD) representation. We show how these mechanisms are exploited for scalability during interactive Boolean operations.