Binary space partitioning trees as an alternative representation of polytopes
Computer-Aided Design
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Geometric programming: a programming approach to geometric design
ACM Transactions on Graphics (TOG)
Splitting a complex of convex polytopes in any dimension
Proceedings of the twelfth annual symposium on Computational geometry
Interactive Boolean operations for conceptual design of 3-D solids
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A volumetic approach to interactive CSG modeling and rendering
Proceedings of the fifth ACM symposium on Solid modeling and applications
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Fast volumetric CSG modeling using standard graphics system
Proceedings of the seventh ACM symposium on Solid modeling and applications
Geometric Programming for Computer Aided Design
Geometric Programming for Computer Aided Design
Interactive boolean operations on surfel-bounded solids
ACM SIGGRAPH 2003 Papers
Solid and physical modeling with chain complexes
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A codimension-zero approach to discretizing and solving field problems
Advanced Engineering Informatics
Improved Binary Space Partition merging
Computer-Aided Design
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This paper introduces a new progressive multi-resolution approach for representating and processing polyhedral objects of any dimension. Our representation, a variant of BSP trees [Nay90] combined with the Split scheme introduced in [BP96], allows progressive streaming and rendering of solid models at multiple levels of detail (LOD). Boolean set operations are computed progressively by reading in input a stream of incremental refinements of the operands. Each refinement of the input is mapped immediately to a refinement of the output so that the result is also represented as a stream of progressive refinements. The computation of complex models results in a tree of pipelined processes that make continuous progress concurrently, so that coarse approximations of the final results are obtained nearly instantly, long before the input operands are fully processed. We demonstrate the practical effectiveness of this approach with models constructed with our prototype system.