Monte Carlo methods. Vol. 1: basics
Monte Carlo methods. Vol. 1: basics
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Algorithm 720: An algorithm for adaptive cubature over a collection of 3-dimensional simplices
ACM Transactions on Mathematical Software (TOMS)
Implementation of a lattice method for numerical multiple integration
ACM Transactions on Mathematical Software (TOMS)
An adaptive algorithm for the approximate calculation of multiple integrals
ACM Transactions on Mathematical Software (TOMS)
Algorithm 764: Cubpack++: a C++ package for automatic two-dimensional cubature
ACM Transactions on Mathematical Software (TOMS)
Computing moments of objects enclosed by piecewise polynomial surfaces
ACM Transactions on Graphics (TOG)
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines
Algorithm 824: CUBPACK: a package for automatic cubature; framework description
ACM Transactions on Mathematical Software (TOMS)
An adaptive numerical cubature algorithm for simplices
ACM Transactions on Mathematical Software (TOMS)
Topology preserving surface extraction using adaptive subdivision
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Real-time meshless deformation: Collision Detection and Deformable Objects
Computer Animation and Virtual Worlds - CASA 2005
Frontiers in Computer Graphics and Applications
IEEE Computer Graphics and Applications
Computation of Surface Areas In GMSolid
IEEE Computer Graphics and Applications
Field modeling with sampled distances
Computer-Aided Design
Finite element analysis in situ
Finite Elements in Analysis and Design
Engineering analysis in imprecise geometric models
Finite Elements in Analysis and Design
Geometric interoperability via queries
Computer-Aided Design
Meshfree natural vibration analysis of 2D structures
Computational Mechanics
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Numerical integration over solid domains often requires geometric adaptation to the solid's boundary. Traditional approaches employ hierarchical adaptive space decomposition, where the integration cells intersecting the boundary are either included or discarded based on their position with respect to the boundary and/or statistical measures. These techniques are inadequate when accurate integration near the boundary is particularly important. In boundary value problems, for instance, a small error in the boundary cells can lead to a large error in the computed field distribution. We propose a novel technique for exploiting the exact local geometry in boundary cells. A classification system similar to marching cubes is combined with a suitable parameterization of the boundary cell's geometry. We can then allocate integration points in boundary cells using the exact geometry instead of relying on statistical techniques. We show that the proposed geometrically adaptive integration technique yields greater accuracy with fewer integration points than previous techniques.