LRSplineField Class Reference

Utility class for LR spline-based finite element fields. More...

#include <LRSplineField.h>

Static Public Member Functions
static bool	evalMapping (const LR::LRSplineSurface &surf, const ItgPoint &x, const LR::Element *&elm, Matrix &Xnod, Matrix &Jac, Matrix &dNdX, bool is_rational, Matrix3D *d2NdX2=nullptr, Matrix3D *Hess=nullptr)
	Evaluate the jacobian (and hessian) of the geometry mapping. More...
static bool	evalBasis (const LR::LRSplineSurface &surf, const ItgPoint &x, const LR::Element *&elm, const Matrix &Xnod, const Matrix &Jac, Matrix &dNdX, bool is_rational, Matrix3D *d2NdX2=nullptr, Matrix3D *Hess=nullptr)
	Evaluate a basis. More...
static bool	evalMapping (const LR::LRSplineVolume &vol, const ItgPoint &x, const LR::Element *&elm, Matrix &Xnod, Matrix &Jac, Matrix &dNdX, Matrix3D *d2NdX2=nullptr, Matrix3D *Hess=nullptr)
	Evaluate the jacobian (and hessian) of the geometry mapping. More...
static bool	evalBasis (const LR::LRSplineVolume &vol, const ItgPoint &x, const LR::Element *&elm, const Matrix &Xnod, const Matrix &Jac, Matrix &dNdX, Matrix3D *d2NdX2=nullptr, Matrix3D *Hess=nullptr)
	Evaluate a basis. More...

Detailed Description

Utility class for LR spline-based finite element fields.

This class implements the method to extract the geometry mapping and evaluate a basis.

Member Function Documentation

evalBasis() [1/2]

bool LRSplineField::evalBasis ( const LR::LRSplineSurface &  surf, const ItgPoint &  x, const LR::Element *&  elm, const Matrix &  Xnod, const Matrix &  Jac, Matrix &  dNdX, bool  is_rational, Matrix3D *  d2NdX2 = nullptr, Matrix3D *  Hess = nullptr  )

static

Evaluate a basis.

Parameters

surf	Surface to evaluate
x	Point to evaluate in
elm	Element info for point
Xnod	Geometry coefficients in point
Jac	Jacobian of geometry mapping in point
dNdX	Derivatives of basis functions in point
is_rational	True if surface is rational
d2NdX2	Second derivatives of basis functions in point
Hess	Hessian of geometry mapping in point

References ASMu2D::computeBasisNurbs(), SplineUtils::extractBasis(), utl::Hessian(), utl::matrix< T >::multiply(), ItgPoint::u, and ItgPoint::v.

Referenced by LRSplineFields2D::gradFE(), LRSplineFields2Dmx::gradFE(), LRSplineFields3D::gradFE(), LRSplineFields3Dmx::gradFE(), LRSplineField2D::gradFE(), LRSplineField3D::gradFE(), LRSplineField2D::hessianFE(), LRSplineField3D::hessianFE(), LRSplineFields2D::hessianFE(), LRSplineFields2Dmx::hessianFE(), LRSplineFields3D::hessianFE(), and LRSplineFields3Dmx::hessianFE().

evalBasis() [2/2]

bool LRSplineField::evalBasis ( const LR::LRSplineVolume &  vol, const ItgPoint &  x, const LR::Element *&  elm, const Matrix &  Xnod, const Matrix &  Jac, Matrix &  dNdX, Matrix3D *  d2NdX2 = nullptr, Matrix3D *  Hess = nullptr  )

static

Evaluate a basis.

Parameters

vol	Volume to evaluate
x	Point to evaluate in
elm	Element info for point
Xnod	Geometry coefficients in point
Jac	Jacobian of geometry mapping in point
dNdX	Derivatives of basis functions in point
d2NdX2	Second derivatives of basis functions in point
Hess	Hessian of geometry mapping in point

References SplineUtils::extractBasis(), utl::Hessian(), utl::matrix< T >::multiply(), ItgPoint::u, ItgPoint::v, and ItgPoint::w.

evalMapping() [1/2]

bool LRSplineField::evalMapping ( const LR::LRSplineSurface &  surf, const ItgPoint &  x, const LR::Element *&  elm, Matrix &  Xnod, Matrix &  Jac, Matrix &  dNdX, bool  is_rational, Matrix3D *  d2NdX2 = nullptr, Matrix3D *  Hess = nullptr  )

static

Evaluate the jacobian (and hessian) of the geometry mapping.

Parameters

surf	Surface to evaluate
x	Point to evaluate in
elm	Element info for point
Xnod	Geometry coefficients in point
Jac	Jacobian of geometry mapping in point
dNdX	Derivatives of basis functions in point
is_rational	True if surface is rational
d2NdX2	Second derivatives of basis functions in point
Hess	Hessian of geometry mapping in point

References ASMu2D::computeBasisNurbs(), SplineUtils::extractBasis(), ASMu2D::getCoordinates(), utl::Hessian(), utl::Jacobian(), ItgPoint::u, and ItgPoint::v.

Referenced by LRSplineFields2D::gradFE(), LRSplineFields2Dmx::gradFE(), LRSplineFields3D::gradFE(), LRSplineFields3Dmx::gradFE(), LRSplineField2D::gradFE(), LRSplineField3D::gradFE(), LRSplineField2D::hessianFE(), LRSplineField3D::hessianFE(), LRSplineFields2D::hessianFE(), LRSplineFields2Dmx::hessianFE(), LRSplineFields3D::hessianFE(), and LRSplineFields3Dmx::hessianFE().

evalMapping() [2/2]

bool LRSplineField::evalMapping ( const LR::LRSplineVolume &  vol, const ItgPoint &  x, const LR::Element *&  elm, Matrix &  Xnod, Matrix &  Jac, Matrix &  dNdX, Matrix3D *  d2NdX2 = nullptr, Matrix3D *  Hess = nullptr  )

static

Evaluate the jacobian (and hessian) of the geometry mapping.

Parameters

vol	Volume to evaluate
x	Point to evaluate in
elm	Element info for point
Xnod	Geometry coefficients in point
Jac	Jacobian of geometry mapping in point
dNdX	Derivatives of basis functions in point
d2NdX2	Second derivatives of basis functions in point
Hess	Hessian of geometry mapping in point

References SplineUtils::extractBasis(), utl::Hessian(), utl::Jacobian(), utl::matrix< T >::resize(), ItgPoint::u, ItgPoint::v, and ItgPoint::w.

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The documentation for this class was generated from the following files:

• src/ASM/LR/LRSplineField.h
• src/ASM/LR/LRSplineField.C