vtk::basis::hgrad Namespace Reference

A function space for basis functions defined on corner vertices of cells. More...

Functions
bool VTKFILTERSCELLGRID_EXPORT	RegisterOperators ()
	Register basis-function operators for the "HGRAD" function space with vtkDGCell.
bool VTKFILTERSCELLGRID_EXPORT	FixedOrderLagrangePoints (vtkDGCell::Shape shape, vtkStringToken basis, int nominalOrder, std::vector< std::vector< double > > &points)
	Fetch parametric coordinates where Lagrange basis functions exactly interpolate a value.
bool VTKFILTERSCELLGRID_EXPORT	FixedOrderGaussPoints (vtkDGCell::Shape shape, int nominalOrder, std::vector< std::vector< double > > &points)
	Fetch parametric coordinates where the "G" (Gauss-point) basis functions interpolate.

Detailed Description

A function space for basis functions defined on corner vertices of cells.

This function space is analogous to the traditional Lagrange shape functions.

Function Documentation

RegisterOperators()

bool VTKFILTERSCELLGRID_EXPORT vtk::basis::hgrad::RegisterOperators

(

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Register basis-function operators for the "HGRAD" function space with vtkDGCell.

FixedOrderLagrangePoints()

bool VTKFILTERSCELLGRID_EXPORT vtk::basis::hgrad::FixedOrderLagrangePoints	(	vtkDGCell::Shape	shape,
		vtkStringToken	basis,
		int	nominalOrder,
		std::vector< std::vector< double > > &	points )

Fetch parametric coordinates where Lagrange basis functions exactly interpolate a value.

This only returns true when the shape, basis, and nominalOrder match a fixed-order basis function. You should prefer using the vtkLagrangePoints calculator as that class calls this method when appropriate but also handles arbitrary-order basis functions.

This function exists because programmatically generating parametric coordinates for serendipity and other finite elements would be difficult.

FixedOrderGaussPoints()

bool VTKFILTERSCELLGRID_EXPORT vtk::basis::hgrad::FixedOrderGaussPoints	(	vtkDGCell::Shape	shape,
		int	nominalOrder,
		std::vector< std::vector< double > > &	points )

Fetch parametric coordinates where the "G" (Gauss-point) basis functions interpolate.

The G bases are nodal on the Gauss points rather than on a uniform lattice, so they need their own point set. Returns true and fills points for the shapes whose G basis is nodal; returns false for the tetrahedron and pyramid, whose G bases are modal and so interpolate nowhere (see TestCellGridLagrangePoints).

Prefer the vtkLagrangePoints calculator, which calls this when appropriate.