#include <vtkDGOperatorEntry.h>

Detailed Description

A record for a basis in a function space that is specific to one cell shape.

OperatorName → vtkCellAttribute::CellTypeInfo (FS, Basis, Order) → CellShape → vtkDGOperatorEntry.

OperatorName: one of "Basis"_token, "BasisGradient"_token, "Curl"_token, "Div"_token, etc. FunctionSpace: one of "constant"_token, "HGRAD"_token, "HCURL"_token, "HDIV"_token. Basis: one of "I"_token, "C"_token, "F"_token, "A"_token. "I", "C", and "F" are the incomplete, complete, and full bases of a fixed order; "A" is a basis registered for an arbitrary order, which numbers its degrees of freedom lexicographically rather than corner-first the way "C" does at a fixed order (see vtkDGLagrangePoints). Order: a non-negative integer, or -1 to register an operator that accepts any order. CellShape: one of "vtkDGHex"_token, "vtkDGQuad"_token, etc. but may also include "vtkDeRhamCell"_token, or "vtkDGCell"_token. In this way, if a cell does not have its own operator it can see whether a more generic version exists. This accommodates the "constant" function space where all shapes produce the same function.

Arbitrary-order operators

Most operators implement a single polynomial order and are registered under that order. Some, those whose basis functions are written for an arbitrary order, are instead registered under the order -1, which vtkDGCell treats as a wildcard matching any order for which no exact registration exists.

Such an operator cannot be evaluated until it is bound to a concrete polynomial order with SetOrder(); until then its NumberOfFunctions is unknown. vtkDGCell::GetOperatorEntry() performs this binding for you, returning a copy of the registered entry that carries the order requested by the cell-attribute. Every entry handed out by that method is therefore ready to evaluate and reports a concrete NumberOfFunctions, whether or not its order is fixed.

The order is a vector holding one polynomial order per parametric axis of the cell, so that anisotropic bases (higher order along one axis than another) are expressible. It is fixed for all cells sharing a vtkCellAttribute::CellTypeInfo; order that varies from cell to cell is not supported.

Definition at line 55 of file vtkDGOperatorEntry.h.

Public Types
using	OperatorFunction
	The signature of the functions that evaluate an operator.
using	FunctionCounter = std::function<int(const std::vector<int>&)>
	The signature of functions reporting how many basis functions an arbitrary-order operator provides at a given order.

Public Member Functions
	vtkDGOperatorEntry ()=default
	vtkDGOperatorEntry (const vtkDGOperatorEntry &)=default
vtkDGOperatorEntry &	operator= (const vtkDGOperatorEntry &)=default
	vtkDGOperatorEntry (int numFunc, int opSize, OperatorFunction op, const std::string &shader)
	Construct an entry for an operator implementing a single polynomial order.
	vtkDGOperatorEntry (FunctionCounter counter, int opSize, OperatorFunction op, const std::string &shader)
	Construct an entry for an operator implementing an arbitrary polynomial order.
	operator bool () const
	Entries may be implicitly converted to booleans.
bool	IsOrderDependent () const
	Return whether this operator implements an arbitrary polynomial order.
bool	SetOrder (const std::vector< int > &order)
	Bind an order-dependent operator to a concrete polynomial order.
void	Evaluate (const std::array< double, 3 > &rst, std::vector< double > &values) const
	Evaluate this operator at the parametric coordinates rst.
std::string	GetShaderString (const std::string &functionName, const std::string &parameterName, int order) const
	Return a glsl string that defines this operator.

Static Public Member Functions

static int	TensorProductFunctionCount (const std::vector< int > &order)
	A tensor product with an independent order along each parametric axis: (n0 + 1)(n1 + 1)… functions, and 1 for a shape with no parametric axes.
static int	SimplexFunctionCount (const std::vector< int > &order)
	A simplex, whose axes share a single total degree: (n+1)(n+2)…(n+d)/d!
static int	WedgeFunctionCount (const std::vector< int > &order)
	A wedge: a triangle (the r- and s-axes) crossed with an edge (the t-axis), so the two counts multiply.

Public Attributes
int	NumberOfFunctions { 0 }
	The number of functions in the basis.
int	OperatorSize { 1 }
	The number of coordinates each operator-function evaluates to.
OperatorFunction	Op
	A function you may call to evaluate the operator.
std::string	ShaderOp
	A string holding the source code to evaluate all the basis functions.
std::vector< int >	Order
	The polynomial order along each parametric axis of the cell.
FunctionCounter	FunctionCount
	For order-dependent operators, computes NumberOfFunctions from an Order.

Member Typedef Documentation

◆ OperatorFunction

using vtkDGOperatorEntry::OperatorFunction

Initial value:

std::function<void(

const std::array<double, 3>&, std::vector<double>&, const std::vector<int>&)>

The signature of the functions that evaluate an operator.

Operators take

the parametric coordinates (always an (r, s, t) 3-tuple) at which to evaluate;
a vector in which to store the operator's values; and
the polynomial order along each parametric axis of the cell.

The order is empty for operators registered at a fixed order (they ignore it).

Definition at line 66 of file vtkDGOperatorEntry.h.

◆ FunctionCounter

using vtkDGOperatorEntry::FunctionCounter = std::function<int(const std::vector<int>&)>

The signature of functions reporting how many basis functions an arbitrary-order operator provides at a given order.

Definition at line 71 of file vtkDGOperatorEntry.h.

Constructor & Destructor Documentation

◆ vtkDGOperatorEntry() [1/4]

vtkDGOperatorEntry::vtkDGOperatorEntry ( )

default

◆ vtkDGOperatorEntry() [2/4]

vtkDGOperatorEntry::vtkDGOperatorEntry ( const vtkDGOperatorEntry & )

default

◆ vtkDGOperatorEntry() [3/4]

vtkDGOperatorEntry::vtkDGOperatorEntry	(	int	numFunc,
		int	opSize,
		OperatorFunction	op,
		const std::string &	shader )

inline

Construct an entry for an operator implementing a single polynomial order.

Definition at line 78 of file vtkDGOperatorEntry.h.

◆ vtkDGOperatorEntry() [4/4]

vtkDGOperatorEntry::vtkDGOperatorEntry	(	FunctionCounter	counter,
		int	opSize,
		OperatorFunction	op,
		const std::string &	shader )

inline

Construct an entry for an operator implementing an arbitrary polynomial order.

The entry must be bound to an order with SetOrder() before it can be evaluated.

Definition at line 89 of file vtkDGOperatorEntry.h.

Member Function Documentation

◆ operator=()

vtkDGOperatorEntry & vtkDGOperatorEntry::operator= ( const vtkDGOperatorEntry & )

default

◆ operator bool()

vtkDGOperatorEntry::operator bool ( ) const

inline

Entries may be implicitly converted to booleans.

The conversion returns false when the function used to invoke the operation is null or when the operation accepts an arbitrary polynomial order but has not been bound to one. Otherwise it returns true.

Definition at line 103 of file vtkDGOperatorEntry.h.

◆ IsOrderDependent()

bool vtkDGOperatorEntry::IsOrderDependent ( ) const

inline

Return whether this operator implements an arbitrary polynomial order.

Definition at line 106 of file vtkDGOperatorEntry.h.

◆ SetOrder()

bool vtkDGOperatorEntry::SetOrder ( const std::vector< int > & order )

Bind an order-dependent operator to a concrete polynomial order.

The order holds one entry per parametric axis of the cell. This computes NumberOfFunctions for the given order and returns whether it is positive.

Calling this on an operator that implements a single fixed order is a no-op that returns true; such operators always know their own size.

◆ Evaluate()

void vtkDGOperatorEntry::Evaluate	(	const std::array< double, 3 > &	rst,
		std::vector< double > &	values ) const

inline

Evaluate this operator at the parametric coordinates rst.

The values you pass must be resized to hold at least nn = NumberOfFunctions * OperatorSize entries before you call this method. The first nn entries will have new values written to them.

Definition at line 122 of file vtkDGOperatorEntry.h.

◆ TensorProductFunctionCount()

int vtkDGOperatorEntry::TensorProductFunctionCount ( const std::vector< int > & order )

static

A tensor product with an independent order along each parametric axis: (n0 + 1)(n1 + 1)… functions, and 1 for a shape with no parametric axes.

Ready-made FunctionCounter implementations, shared by the function spaces.

These report how many basis functions a shape admits at a given order. A shape whose parameter space cannot express the requested order returns zero, which makes SetOrder() fail rather than silently misinterpret it.

◆ SimplexFunctionCount()

int vtkDGOperatorEntry::SimplexFunctionCount ( const std::vector< int > & order )

static

A simplex, whose axes share a single total degree: (n+1)(n+2)…(n+d)/d!

functions. An anisotropic order is rejected.

◆ WedgeFunctionCount()

int vtkDGOperatorEntry::WedgeFunctionCount ( const std::vector< int > & order )

static

A wedge: a triangle (the r- and s-axes) crossed with an edge (the t-axis), so the two counts multiply.

The triangular axes must share an order.

◆ GetShaderString()

std::string vtkDGOperatorEntry::GetShaderString	(	const std::string &	functionName,
		const std::string &	parameterName,
		int	order ) const

Return a glsl string that defines this operator.

Member Data Documentation

◆ NumberOfFunctions

int vtkDGOperatorEntry::NumberOfFunctions { 0 }

The number of functions in the basis.

Note that each basis function may evaluate to a scalar or a vector. See OperatorSize for more information.

For order-dependent operators this is zero until SetOrder() is called.

Definition at line 157 of file vtkDGOperatorEntry.h.

◆ OperatorSize

int vtkDGOperatorEntry::OperatorSize { 1 }

The number of coordinates each operator-function evaluates to.

For H(grad) and constant function spaces, this is 1. For H(curl) and H(div), this is 3.

Definition at line 163 of file vtkDGOperatorEntry.h.

◆ Op

OperatorFunction vtkDGOperatorEntry::Op

A function you may call to evaluate the operator.

Prefer Evaluate(), which passes this entry's Order for you.

Definition at line 168 of file vtkDGOperatorEntry.h.

◆ ShaderOp

std::string vtkDGOperatorEntry::ShaderOp

A string holding the source code to evaluate all the basis functions.

Definition at line 171 of file vtkDGOperatorEntry.h.

◆ Order

std::vector<int> vtkDGOperatorEntry::Order

The polynomial order along each parametric axis of the cell.

This is empty for operators that implement a single fixed order and is otherwise assigned by SetOrder().

Definition at line 177 of file vtkDGOperatorEntry.h.

◆ FunctionCount

FunctionCounter vtkDGOperatorEntry::FunctionCount

For order-dependent operators, computes NumberOfFunctions from an Order.

This is null for operators that implement a single fixed order.

Definition at line 182 of file vtkDGOperatorEntry.h.

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

Filters/CellGrid/vtkDGOperatorEntry.h

Detailed Description

Arbitrary-order operators

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Member Typedef Documentation

◆ OperatorFunction

◆ FunctionCounter

Constructor & Destructor Documentation

◆ vtkDGOperatorEntry() [1/4]

◆ vtkDGOperatorEntry() [2/4]

◆ vtkDGOperatorEntry() [3/4]

◆ vtkDGOperatorEntry() [4/4]

Member Function Documentation

◆ operator=()

◆ operator bool()

◆ IsOrderDependent()

◆ SetOrder()

◆ Evaluate()

◆ TensorProductFunctionCount()

◆ SimplexFunctionCount()

◆ WedgeFunctionCount()

◆ GetShaderString()

Member Data Documentation

◆ NumberOfFunctions

◆ OperatorSize

◆ Op

◆ ShaderOp

◆ Order

◆ FunctionCount