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Bembel
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Bembel
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The Spline module provides basic routines related to spline function and local polynomials. More...
Classes | |
| class | Bembel::Basis::PSpecificBasisHandler< P, Scalar > |
| The functions above have a fixed compile time polynomial degree. The PSpecificBasis handler is used to convert this to a runtime p through template recursion. More... | |
| struct | Bembel::static_assertKlessseqN< condition > |
| Here we hardcode the binomial coefficients through template recursion and perform bounds checking, just in case... More... | |
| class | Bembel::Basis::PSpecificShapeFunctionHandler< P > |
| These routines implement a template recursion that allows to choose a compile time instantiation of a basis-evaluation routine with a runtime p. To replace the underlying basis, only these routines should be changed. More... | |
Functions | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::phi_ (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *c, Scalar w, double x) |
| evaluates the 1D basis at x weighted with a quadrature weight w | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::phi_dx_ (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *c, Scalar w, double x) |
| evaluates the derivative of phi | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::phiphi_ (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *c, Scalar w, Eigen::Vector2d a) |
| evaluates the 2D tensor product basis at a point a in [0,1]^2 | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::phiphi_dx_ (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *c, Scalar w, Eigen::Vector2d a) |
| evaluates the x-derivative of the 2D tensor product basis at a point a in [0,1]^2 | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::phiphi_dy_ (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *c, Scalar w, Eigen::Vector2d a) |
| evaluates the y-derivative of the 2D tensor product basis at a point a in [0,1]^2 | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::Phi_times_Phi_ (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *c, Scalar w, Eigen::Vector2d xi, Eigen::Vector2d eta) |
| evaluates the interaction of two phiphis, one at xi and one at eta. Used for e.g. gram matrices. | |
| template<int P, typename Scalar > | |
| void | Bembel::Basis::Div_Phi_times_Div_Phi_ (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *c, Scalar weight, Eigen::Vector2d xi, Eigen::Vector2d eta) |
| same as above, just using the divergence | |
| template<int N> | |
| constexpr double | Bembel::Basis::BernsteinX (double evaluation_point) noexcept |
| Template recursion to produce Bernstein polynomials. This is only limited by the binomial coefficient, see Pascal.hpp. | |
| template<typename T > | |
| Eigen::SparseMatrix< T > | Bembel::Spl::MakeProjection (const std::vector< T > &x_knots, const std::vector< T > &y_knots, const std::vector< T > &x_unique_knots, const std::vector< T > &y_unique_knots, const int polynomial_degree_x, const int polynomial_degree_y) noexcept |
| implements Bezier extraction via the solution of an interpolation problem. More... | |
| template<typename T > | |
| Eigen::Matrix< T, -1, -1 > | Bembel::Spl::DeBoor (Eigen::Matrix< T, -1, -1 > const &control_points, const std::vector< double > &knot_vector, const std::vector< double > &evaluation_points) noexcept |
| "By the book" implementations of the Cox-DeBoor formula. Inefficient, do not use at bottlenecks. More... | |
| template<typename T > | |
| Eigen::Matrix< T, -1, -1 > | Bembel::Spl::DeBoorDer (Eigen::Matrix< T, -1, -1 > const &control_points, std::vector< double > const &knot, std::vector< double > const &evaluation_points) noexcept |
| A "by the book" implementation of the derivatives and TP-algos based on the DeBoor Recursion. | |
| std::vector< double > | Bembel::Spl::MakeBezierKnotVector (int polynomial_degree) noexcept |
| Here, routines for the creation and processing of knot vectors are defined. | |
| template<typename T > | |
| std::vector< T > | Bembel::Spl::MakeInterpolationPoints (const std::vector< T > &uniq, const std::vector< T > &mask) noexcept |
| Creates a T-vector of equidistant itnerpolation points for a given knot vector without any repetitions. | |
| Eigen::Matrix< double, -1, -1 > | Bembel::Spl::GetInterpolationMatrix (int polynomial_degree, const std::vector< double > &mask) |
| returns the coefficients to represent a function in the Bernstein basis on [0,1]. | |
| template<typename T > | |
| void | Bembel::Spl::GetCoefficients (const int incr, const std::vector< double > &mask, const std::vector< T > &values, T *coefs) |
| this solves a generic interpolation problem. | |
| template<typename T > | |
| std::vector< T > | Bembel::Spl::GetCoefficients (const int increments, const std::vector< double > &mask, const std::vector< T > &values) |
| this solves a generic interpolation problem. | |
The Spline module provides basic routines related to spline function and local polynomials.
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noexcept |
"By the book" implementations of the Cox-DeBoor formula. Inefficient, do not use at bottlenecks.
ISO C++ forbids variable length array
Definition at line 22 of file DeBoor.hpp.
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noexcept |
implements Bezier extraction via the solution of an interpolation problem.
The inverse matrix, for the solition of the linear system to come.
For each basisfunction phi_j solves for the right coeef such that \Sum
Definition at line 23 of file Bezierextraction.hpp.
1.9.1