An object centered hierarchical representation for 3D objects: The prism tree

Efficient computation of surfaces and/or solids intersections is a cornerstone of many algorithms in geometric modelling and computer graphics, for example, set operations between solids, or ray casting display of surfaces. We represent an object centered, information preserving, hierarchical representation for polyhedra called prism tree, establish its fundamental properties, and give a neighbor-finding algorithm. The representation is then used to decompose the intersection algorithms in two steps: the localization of intersections, and their processing. When dealing with polyhedra with many faces (typically more than one thousand), the first step is by far the most expensive. The prism tree structure is used to compute efficiently this localization step. A preliminary implementation of the set operations and ray casting algorithms has been constructed.

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