Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A model for n-dimensional boundary topology
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Variable independence and aggregation closure
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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Computation of the union, intersection, and difference of n-dimensional objects plays a central role in several computer-aided geometric design problems. An algorithm for computing these operations that uses a boundary classification technique is presented here. The algorithm is recursive in structure, with the recursion being on the dimensions of objects dealt with at each stage. The representation treats all entities as objects, making no distinction between faces, edges, or vertices. The objects produced are "regularized"; that is, there are no degenerate boundaries such as dangling edges. The sample application given involves hidden-surface removal.