Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Calculus and Analytic Geometry
Calculus and Analytic Geometry
Nonconvex rigid bodies with stacking
ACM SIGGRAPH 2003 Papers
Visualization and 3D Data Processing in the David Restoration
IEEE Computer Graphics and Applications
Fast frictional dynamics for rigid bodies
ACM SIGGRAPH 2005 Papers
Particle-based simulation of granular materials
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Multi-material interface reconstruction on generalized polyhedral meshes
Journal of Computational Physics
Automatic generation of tourist maps
ACM SIGGRAPH 2008 papers
Adaptive moment-of-fluid method
Journal of Computational Physics
Simulating balance recovery responses to trips based on biomechanical principles
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Flexible simulation of deformable models using discontinuous Galerkin FEM
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Towards virtually cooking chinese food
ICME'09 Proceedings of the 2009 IEEE international conference on Multimedia and Expo
Journal of Computational Physics
Accurate moment computation using the GPU
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Haptic simulation of linear elastic media with fluid pockets
HAPTICS'04 Proceedings of the 12th international conference on Haptic interfaces for virtual environment and teleoperator systems
Interactive dynamics for large virtual reality applications
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
3D orientation of archaeological fragments coming from a Gothic spire
VAST'04 Proceedings of the 5th International conference on Virtual Reality, Archaeology and Intelligent Cultural Heritage
Software for exact integration of polynomials over polyhedra
Computational Geometry: Theory and Applications
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The location of a body's center of mass, and its moments and products of inertia about various axes are important physical quantities needed for any type of dynamic simulation or physical based modeling. We present an algorithm for automatically computing these quantities for a general class of rigid bodies: those composed of uniform density polyhedra. The mass integrals may be converted into volume integrals under these assumptions, and the bulk of the paper is devoted to the computation of these volume integrals. Our algorithm is based on a three-step reduction of the volume integrals to successively simpler integrals. The algorithm is designed to minimize the numerical errors that can result from poorly conditioned alignment of polyhedral faces. It is also designed for efficiency. All required volume integrals of a polyhedron are computed together during a single walk over the boundary of the polyhedron; exploiting common subexpressions reduces floating point operations. We present numerical results detailing the speed and accuracy of the algorithm, and also give a complete low level pseudocode description.