Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Two Algorithms for Determining Volumes of Convex Polyhedra
Journal of the ACM (JACM)
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
An algorithm for planning collision-free paths among polyhedral obstacles
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
Depth-order point classification techniques for CSG display algorithms
ACM Transactions on Graphics (TOG)
Octree detection of closed compartments
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Determination of mass properties of polygonal CSG objects in parallel
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Computing moments of objects enclosed by piecewise polynomial surfaces
ACM Transactions on Graphics (TOG)
Efficient octree conversion by connectivity labeling
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Shape sensitivity of constructive representations
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Shape sensitivity of constructively represented geometric models
Computer Aided Geometric Design
A quasi-Monte Carlo method for computing areas of point-sampled surfaces
Computer-Aided Design
Shape-based searching for product lifecycle applications
Computer-Aided Design
Accurate moment computation using the GPU
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
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This paper discusses a family of algorithms for computing the volume, moments of inertia, and other integral properties of geometrically complex solids, e.g. typical mechanical parts. The algorithms produce approximate decompositions of solids into cuboid cells whose integral properties are easy to compute.The paper focuses on versions of the algorithms which operate on solids represented by Constructive Solid Geometry (CSG), i.e., as set-theoretical combinations of primitive solid “building blocks.” Two known algorithms are summarized and a new algorithm is presented. The efficiencies and accuracies of the three algorithms are analyzed theoretically and compared experimentally.The new algorithm uses recursive subdivision to convert CSG representations of complex solids into approximate cellular decompositions based on variably sized blocks. Experimental data show that the new algorithm is efficient and has predictable accuracy. It also has other potential applications, e.g., in producing approximate octree representations of complex solids and in robot navigation.