Construction of fully symmetric cubature formulae of degree 4k-3 for fully symmetric planar regions
Journal of Computational and Applied Mathematics - Numerical Quadrature
Error estimation in automatic quadrature routines
ACM Transactions on Mathematical Software (TOMS)
Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles
ACM Transactions on Mathematical Software (TOMS)
Monomial cubature rules since “Stroud”: a compilation
Journal of Computational and Applied Mathematics
Null rules and orthogonal expansions
Proceedings of the conference on Approximation and computation : a fetschrift in honor of Walter Gautschi: a fetschrift in honor of Walter Gautschi
Algorithm 584: CUBTRI: Automatic Cubature over a Triangle
ACM Transactions on Mathematical Software (TOMS)
Applying appearance standards to light reflection models
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Algorithm 816: r2d2lri: an algorithm for automatic two-dimensional cubature
ACM Transactions on Mathematical Software (TOMS)
Research Frontiers in Object Technology
Information Systems Frontiers
A multivariate view of random bucket digital search trees
Journal of Algorithms - Analysis of algorithms
Algorithm 824: CUBPACK: a package for automatic cubature; framework description
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Bivariate Product Cubature Using Peano Kernels for Local Error Estimates
Journal of Scientific Computing
Gauss-Green cubature and moment computation over arbitrary geometries
Journal of Computational and Applied Mathematics
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In this article, software for the numerical approximation ofdouble integrals over a variety of regions is described. Thesoftware was written in C++. Classes for a large number of shapesare provided. A global adaptive integration algorithm is used basedon transformations and subdivisions of regions.