Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Boundary integration over linear polyhedra
Computer-Aided Design
Robust and efficient evaluation of functionals on parametric surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing moments of objects enclosed by piecewise polynomial surfaces
ACM Transactions on Graphics (TOG)
Algorithm 550: Solid Polyhedron Measures [Z]
ACM Transactions on Mathematical Software (TOMS)
Fast and accurate computation of polyhedral mass properties
Journal of Graphics Tools
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
UberFlow: a GPU-based particle engine
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Hardware-based simulation and collision detection for large particle systems
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
The Visual Computer: International Journal of Computer Graphics
Performing efficient NURBS modeling operations on the GPU
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Performing Efficient NURBS Modeling Operations on the GPU
IEEE Transactions on Visualization and Computer Graphics
Accelerating geometric queries using the GPU
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces
Computer-Aided Design
CAD-integrated analysis of 3-D beams: a surface-integration approach
Engineering with Computers
Spline surface intersections optimized for GPUs
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
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We present algorithms for computing accurate moments of solid models that are represented using multiple trimmed NURBS surfaces. Our algorithms make use of programmable Graphics Processing Units (GPUs) to accelerate the computations. We evaluate the surface coordinates and normals accurately, with theoretical bounds, using our GPU NURBS evaluator. We have developed a framework that makes use of this data to evaluate surface integrals of trimmed NURBS surfaces in real time. With our framework, we can compute volume and moments of solid models with theoretical guarantees. The framework also supports local geometry changes, which is useful for providing interactive feedback to the designer while the solid model is being designed. We can compute the center of mass and check for stability of the solid model interactively. Applications of such real-time moment computation include deformation modeling, animation, and physically based simulations.