Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Interference detection among solids and surfaces
Communications of the ACM
The PADL-1.0/2 system for defining and displaying solid objects
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Computational geometry.
Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Eliminating Redundant Primitives from Set-Theoretic Solid Models by a Consideration of Constituents
IEEE Computer Graphics and Applications
Systems semantics: principles, applications, and implementation
ACM Transactions on Programming Languages and Systems (TOPLAS)
ACM Transactions on Graphics (TOG)
Generalized sweep methods for parallel computational geometry
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
An efficient algorithm for CSG to b-rep conversion
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
An efficient intersection algorithm for polyhedral cellular decompositions
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Approximation hierarchies and S-bounds
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
The n-dimensional extended convex differences tree (ECDT) for representing polyhedra
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Refinement methods for geometric bounds in constructive solid geometry
ACM Transactions on Graphics (TOG)
Interactive inspection of solids: cross-sections and interferences
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Efficient parallel evaluation of CSG tree using fixed number of processors
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Obtaining robust Boolean set operations for manifold solids by avoiding and eliminating redundancy.
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Computing CSG tree boundaries as algebraic expressions
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Applying parallel processing techniques to classification problems in constructive solid geometry
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Boundary Evaluation Using Inner and Outer Sets: the ISOS Method
IEEE Computer Graphics and Applications
Efficient Bounds in Constructive Solid Geometry
IEEE Computer Graphics and Applications
Blister: GPU-based rendering of Boolean combinations of free-form triangulated shapes
ACM SIGGRAPH 2005 Papers
Improved Binary Space Partition merging
Computer-Aided Design
Efficient editing of solid models by exploiting structural and spatial locality
Computer Aided Geometric Design
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Constructive solid geometry (CSG) is the primary scheme used for representing solid objects in many contemporary solid modeling systems. A CSG representation is a binary tree whose nonterminal nodes represent Boolean operations and whose terminal nodes represent primitive solids. This paper deals with algorithms that operate directly on CSG representations to solve two computationally difficult geometric problems—null-object detection (NOD) and same-object detection (SOD). The paper also shows that CSG trees representing null objects may be reduced to null trees through the use of a new concept called primitive redundancy, and that, on average, tree reduction can be done efficiently by a new technique called spatial localization. Primitive redundancy and spatial localization enable a single complex instance of NOD to be converted into a number of simpler subproblems and lead to more efficient algorithms than those previously known.