Two Algorithms for Determining Volumes of Convex Polyhedra
Journal of the ACM (JACM)
Algorithm 550: Solid Polyhedron Measures [Z]
ACM Transactions on Mathematical Software (TOMS)
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Construction and Use of Geometric Models
Computer Aided Design: Modelling, Systems Engineering, CAD-Systems - CREST Advanced Course
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
Boundary evaluation of non-convex primitives to produce parametric trimmed surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Analysis of Quadric-Surface-Based Solid Models
IEEE Computer Graphics and Applications
Partitioning Polyhedral Objects into Nonintersecting Parts
IEEE Computer Graphics and Applications
ACM Transactions on Graphics (TOG)
A volumetic approach to interactive CSG modeling and rendering
Proceedings of the fifth ACM symposium on Solid modeling and applications
Constraints in constructive solid geometry
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Fast CSG voxelization by frame buffer pixel mapping
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
Fast volumetric CSG modeling using standard graphics system
Proceedings of the seventh ACM symposium on Solid modeling and applications
Computer
Self-intersection avoidance and integral properties of generalized cylinders
Computer Aided Geometric Design
Fast and accurate computation of polyhedral mass properties
Journal of Graphics Tools
VIS '91 Proceedings of the 2nd conference on Visualization '91
Mesh Simplification with Hierarchical Shape Analysis and Iterative Edge Contraction
IEEE Transactions on Visualization and Computer Graphics
Efficient volume measurement using voxelization
SCCG '03 Proceedings of the 19th spring conference on Computer graphics
B-rep SE: simplicially enhanced boundary representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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
Single-pass GPU solid voxelization for real-time applications
GI '08 Proceedings of graphics interface 2008
Shape sensitivity of constructively represented geometric models
Computer Aided Geometric Design
GPU-accelerated multi-valued solid voxelization by slice functions in real time
VRCAI '08 Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
Fast computation of inertia through affinely extended Euler tensor
Computer-Aided Design
A quasi-Monte Carlo method for computing areas of point-sampled surfaces
Computer-Aided Design
Assessment of Ulcer Wounds Size Using 3D Skin Surface Imaging
IVIC '09 Proceedings of the 1st International Visual Informatics Conference on Visual Informatics: Bridging Research and Practice
Accurate moment computation using the GPU
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Approximating shapes with hierarchies and topologies
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
GPU-accelerated multi-valued solid voxelization by slice functions in real time
Proceedings of the 24th Spring Conference on Computer Graphics
GPU-based fast volumetric terrain modeling for volumetric GIS
Proceedings of the 2nd International Conference on Computing for Geospatial Research & Applications
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
| Hi-index | 48.24 |
The volume, moments of inertia, and similar properties of solids are defined by triple (volumetric) integrals over subsets of three-dimensional Euclidean space. The automatic computation of such integral properties for geometrically complex solids is important in CAD/CAM, robotics, and other fields and raises interesting mathematical and computational problems that have received little attention from numerical analysts and computer scientists. This paper summarizes the known methods for calculating integral properties of solids that may be geometrically complex and identifies some significant gaps in our current knowledge.