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Binary partitions with applications to hidden surface removal and solid modelling
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I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
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I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
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I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
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SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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VRST '97 Proceedings of the ACM symposium on Virtual reality software and technology
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VRST '97 Proceedings of the ACM symposium on Virtual reality software and technology
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I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
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PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
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VRAIS '96 Proceedings of the 1996 Virtual Reality Annual International Symposium (VRAIS 96)
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BSP trees have been shown to provide an effective representation of polyhedra through the use of spatial subdivision, and are an alternative to the topologically based b-reps. While bsp tree algorithms are known for a number of important operations, such as rendering, no previous work on bsp trees has provided the capability of performing boolean set operations between two objects represented by bsp trees, i.e. there has been no closed boolean algebra when using bsp trees. This paper presents the algorithms required to perform such operations. In doing so, a distinction is made between the semantics of polyhedra and the more fundamental mechanism of spatial partitioning. Given a partitioning of a space, a particular semantics is induced on the space by associating attributes required by the desired semantics with the cells of the partitioning. So, for example, polyhedra are obtained simply by associating a boolean attribute with each cell. Set operations on polyhedra are then constructed on top of the operation of merging spatial partitionings. We present then the algorithm for merging two bsp trees independent of any attributes/semantics, and then follow this by the additional algorithmic considerations needed to provide set operations on polyhedra. The result is a simple and numerically robust algorithm for set operations.