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PhysicsBasedAnimationToolkit 0.0.10
Cross-platform C++20 library of algorithms and data structures commonly used in computer graphics research on physically-based simulation.
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PhysicsBasedAnimationToolkit 0.0.10
Cross-platform C++20 library of algorithms and data structures commonly used in computer graphics research on physically-based simulation.
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Moment fitting for polynomial quadrature rules. More...
#include "Concepts.h"#include "pbat/Aliases.h"#include "pbat/common/ArgSort.h"#include "pbat/common/Eigen.h"#include "pbat/common/Indexing.h"#include "pbat/math/polynomial/Basis.h"#include "pbat/math/polynomial/Concepts.h"#include <algorithm>#include <exception>#include <limits>#include <tbb/parallel_for.h>#include <tuple>#include <unsupported/Eigen/NNLS>#include <utility>Go to the source code of this file.
Classes | |
| struct | pbat::math::DynamicQuadrature< Dims, Order > |
| Quadrature rule with variable points and weights. More... | |
Namespaces | |
| namespace | pbat |
| The main namespace of the library. | |
| namespace | pbat::math |
| Math related functionality. | |
Functions | |
| template<polynomial::CBasis TBasis, CFixedPointPolynomialQuadratureRule TQuad> | |
| Matrix< TBasis::kSize, TQuad::kPoints > | pbat::math::ReferenceMomentFittingMatrix (TBasis const &Pb, TQuad const &Q) |
| Compute the moment fitting matrix in the reference simplex space. | |
| template<polynomial::CBasis TBasis, CPolynomialQuadratureRule TQuad> | |
| Matrix< TBasis::kSize, Eigen::Dynamic > | pbat::math::ReferenceMomentFittingMatrix (TBasis const &Pb, TQuad const &Q) |
| Compute the moment fitting matrix in the reference simplex space. | |
| template<polynomial::CBasis TBasis, class TDerivedXg> | |
| Matrix< TBasis::kSize, Eigen::Dynamic > | pbat::math::ReferenceMomentFittingMatrix (TBasis const &Pb, Eigen::MatrixBase< TDerivedXg > const &Xg) |
| Compute the moment fitting matrix in the reference simplex space. | |
| template<class TDerivedP, class TDerivedB> | |
| VectorX | pbat::math::MomentFittedWeights (Eigen::MatrixBase< TDerivedP > const &P, Eigen::DenseBase< TDerivedB > const &b, Index maxIterations=10, Scalar precision=std::numeric_limits< Scalar >::epsilon()) |
| Computes non-negative quadrature weights \( w \) by moment fitting. | |
| template<polynomial::CBasis Polynomial, class TDerivedXg, class TDerivedWg> | |
| Vector< Polynomial::kSize > | pbat::math::Integrate (Polynomial const &P, Eigen::MatrixBase< TDerivedXg > const &Xg, Eigen::DenseBase< TDerivedWg > const &wg) |
| Computes \( \int_{\Omega} P(x) \, d\Omega \) given an existing quadrature rule \((Xg,wg) \). | |
| template<polynomial::CBasis Polynomial, class TDerivedXg1, class TDerivedXg2, class TDerivedWg2> | |
| Vector< TDerivedXg1::ColsAtCompileTime > | pbat::math::TransferQuadrature (Polynomial const &P, Eigen::MatrixBase< TDerivedXg1 > const &Xg1, Eigen::MatrixBase< TDerivedXg2 > const &Xg2, Eigen::DenseBase< TDerivedWg2 > const &wg2, Index maxIterations=10, Scalar precision=std::numeric_limits< Scalar >::epsilon()) |
| Obtain weights \( w_g^1 \) by transferring an existing quadrature rule \( X_g^2, w_g^2
\) defined on a simplex onto a new quadrature rule \( X_g^1, w_g^1 \) defined on the same simplex. | |
| template<auto Order, class TDerivedS1, class TDerivedXi1, class TDerivedS2, class TDerivedXi2, class TDerivedWg2> | |
| std::pair< VectorX, VectorX > | pbat::math::TransferQuadrature (Eigen::DenseBase< TDerivedS1 > const &S1, Eigen::MatrixBase< TDerivedXi1 > const &Xi1, Eigen::DenseBase< TDerivedS2 > const &S2, Eigen::MatrixBase< TDerivedXi2 > const &Xi2, Eigen::DenseBase< TDerivedWg2 > const &wi2, Index nSimplices=-1, bool bEvaluateError=false, Index maxIterations=10, Scalar precision=std::numeric_limits< Scalar >::epsilon()) |
| Obtain weights \( w_g^1 \) by transferring an existing quadrature rule \( X_g^2, w_g^2
\) defined on a domain of simplices onto a new quadrature rule \( X_g^1, w_g^1 \) defined on the same domain. | |
| template<int Order, class TDerivedS1, class TDerivedX1, class TDerivedS2, class TDerivedX2, class TDerivedW2> | |
| std::tuple< MatrixX, MatrixX, IndexVectorX > | pbat::math::ReferenceMomentFittingSystems (Eigen::DenseBase< TDerivedS1 > const &S1, Eigen::MatrixBase< TDerivedX1 > const &X1, Eigen::DenseBase< TDerivedS2 > const &S2, Eigen::MatrixBase< TDerivedX2 > const &X2, Eigen::DenseBase< TDerivedW2 > const &w2, Index nSimplices=Index(-1)) |
| Computes reference moment fitting systems for all simplices \( S_1 \), given an existing quadrature rule \( (X_g^2, w_g^2) \) defined on a domain of simplices. The quadrature points of the new rule \( X_g^1 \) are given and fixed. | |
| template<class TDerivedM, class TDerivedP> | |
| CSRMatrix | pbat::math::BlockDiagonalReferenceMomentFittingSystem (Eigen::MatrixBase< TDerivedM > const &M, Eigen::DenseBase< TDerivedP > const &P) |
| Block diagonalizes the given reference moment fitting systems (see ReferenceMomentFittingSystems()) into a large sparse matrix. | |
Moment fitting for polynomial quadrature rules.
1.13.2