Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Boundary integration over linear polyhedra
Computer-Aided Design
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
A survey of moment-based techniques for unoccluded object representation and recognition
CVGIP: Graphical Models and Image Processing
An implementation of triangular B-spline surfaces over arbitrary triangulations
Selected papers of the international symposium on Free-form curves and free-form surfaces
SIAM Journal on Numerical Analysis
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Graphical Models and Image Processing
Robust and efficient evaluation of functionals on parametric surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Algorithm 783: Pcp2Nurb—smooth free-form surfacing with linearly trimmed bicubic B-splines
ACM Transactions on Mathematical Software (TOMS)
Algorithm 550: Solid Polyhedron Measures [Z]
ACM Transactions on Mathematical Software (TOMS)
Fast volume-preserving free form deformation using multi-level optimization
Proceedings of the fifth ACM symposium on Solid modeling and applications
Multiresolution curve editing with linear constraints
Proceedings of the sixth ACM symposium on Solid modeling and applications
Localized volume preservation for simulation and animation
ACM SIGGRAPH 2006 Research posters
B-rep SE: simplicially enhanced boundary representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Detail preserving deformation of B-spline surfaces with volume constraint
Computer Aided Geometric Design
Exact volume preserving skinning with shape control
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Fast computation of inertia through affinely extended Euler tensor
Computer-Aided Design
Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors
Pattern Recognition Letters
Accurate moment computation using the GPU
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Global curve analysis via a dimensionality lifting scheme
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
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Combining a polynomial free-form surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of the enclosed objects. For example, for an cubic representation, volume, center of mass, and the inertia tensor can be computed in seconds even for complex objects with serval thousand patches while change due to local modification of the surface geometry can be computed in real-time as feedback for animation or design. Speed and simplicity of the approach allow solving the inverse problem of modeling to match prescribed moments.