This namespace contains implementation of B-spline related algorithms. More...

Functions
template<class T , typename KnotIterator , typename MatrixType >
void	allDersBasis ()

template<class T , typename KnotIterator , typename MatrixType >
void	allDersSingle ()

template<short_t d>
void	buildCoeffsStrides (const gsVector< index_t, d > &size_of_coefs, gsVector< index_t, d > &strides)

template<typename T , typename KnotVectorType >
void	computeAlpha (std::vector< std::vector< T > > &alpha, const KnotVectorType &knots, T value, int r, int k, int p, int s)

template<typename T , typename KnotVectorType , typename ValIt , typename newKnotsType >
void	computeTensorAlpha (std::vector< std::vector< T > > &alpha, newKnotsType &nknots, const KnotVectorType &knots, ValIt valBegin, ValIt valEnd, bool sparse=false)

void	correctNewStride (gsVector< unsigned > &new_str, const gsVector< unsigned > &str, const int direction, const int r)

template<class T , typename KnotIterator >
void	deBoorTriangle (T u, KnotIterator knot, int deg, T N[])

template<class Basis_t >
void	degreeElevateBSpline (Basis_t &basis, gsMatrix< typename Basis_t::Scalar_t > &coefs, short_t m)
	Increase the degree of a 1D B-spline from degree p to degree p + m.

template<class T , typename KnotIterator , typename MatrixType >
void	derivBasis ()

template<class T , typename KnotIterator , typename MatrixType >
void	derivBasisSingle ()

template<class T , typename KnotIterator , typename Derived >
void	evalBasis (T u, KnotIterator knot, int deg, gsEigen::MatrixBase< Derived > const &result)

template<class T , typename KnotIterator , typename MatrixType >
void	evalBasis2 (const T &u, const KnotIterator &knot, int deg, MatrixType &result)

template<class T , typename KnotIterator , typename MatrixType >
void	evalBasisSingle ()

template<class T , typename KnotIterator , typename Derived >
void	evalDeg1Basis (const T &u, const KnotIterator knot, gsEigen::MatrixBase< Derived > const &result)
	Evaluation for degree 1 B-spline basis.

template<class T , typename KnotIterator , typename Derived >
void	evalDeg2Basis (const T &u, const KnotIterator knot, gsEigen::MatrixBase< Derived > const &result)
	Evaluation for degree 2 B-spline basis.

template<class T , typename KnotIterator , typename MatrixType >
void	evalDeg3Basis (const T &u, const KnotIterator knot, MatrixType &result)
	Evaluation for degree 3 B-spline basis.

template<class T , typename KnotIterator , typename MatrixType >
void	evalGeo (const T &u, const KnotIterator &knot, int deg, MatrixType coefs, MatrixType &result)

int	getIndex (const gsVector< unsigned > &stride, const gsVector< int > &position)

void	getLastIndex (const gsVector< unsigned > &stride, const unsigned number_of_points, gsVector< int > &last_point)

template<short_t d>
void	getLastIndexLocal (const gsVector< index_t, d > &size_of_coef, gsVector< index_t, d > &last_point)

unsigned	numberOfIterations (const gsVector< index_t > &nmb_of_coefs, const unsigned direction)

Detailed Description

This namespace contains implementation of B-spline related algorithms.

Function Documentation

void gismo::bspline::allDersBasis ( )

Input: a sequence of 2*p+1 knots, evaluation point, output the value of all derivatives up to order k supported on those knots

void gismo::bspline::allDersSingle ( )

Input: a sequence of p+2 knots, evaluation point, output the value of all derivatives up to order k supported on those knots

void gismo::bspline::buildCoeffsStrides	(	const gsVector< index_t, d > &	size_of_coefs,
		gsVector< index_t, d > &	strides
	)

Function builds strides from given sizes of the coefficients. We can use computed strides for calculating indices corresponding to the size of the coefficients

Parameters

size_of_coefs	size of the coefficients
strides	we compute strides into this variable

void gismo::bspline::computeAlpha	(	std::vector< std::vector< T > > &	alpha,
		const KnotVectorType &	knots,
		T	value,
		int	r,
		int	k,
		int	p,
		int	s
	)

Computes 2D vector of alpha values.

Parameters

alpha	- to be computed
knots	- knot vector
value	- knot we want to insert
r	- how many times we want to insert knot value
k	- value in [knots[k], knots[k + 1])
p	- degree corresponding B-splines
s	- multiplicity of knot value

Returns: void (note "returns" value through alpha)

void gismo::bspline::computeTensorAlpha	(	std::vector< std::vector< T > > &	alpha,
		newKnotsType &	nknots,
		const KnotVectorType &	knots,
		ValIt	valBegin,
		ValIt	valEnd,
		bool	sparse = `false`
	)

Computes 2D vector of alpha values, and also computes new knot values and saves them into nknots.

Parameters

alpha	- 2D vector; to be computed
nknots	- new knot vector, to be computed
knots	- knot vector
valBegin	- iterator pointing to the begining of the vector of the knots we want to insert
valEnd	- iterator pointing to the end of the vector of the knots we want to insert
sparse

Returns: void (note "returns" values through alpha and nknots)

void gismo::bspline::correctNewStride	(	gsVector< unsigned > &	new_str,
		const gsVector< unsigned > &	str,
		const int	direction,
		const int	r
	)

inline

Corrects values of a new stride according to the old stride with respect to direction of knot refinment and number of knots we want to insert.

Parameters

new_str	- vector of new strides (will be modified)
str	- vector of old strides
direction	- direction of the refinement
r	- number of knots we will insert

Returns: void (note it modifies "new_str")

void gismo::bspline::deBoorTriangle	(	T	u,
		KnotIterator	knot,
		int	deg,
		T	N[]
	)

Input: parameter position u, KnotIterator knot identifying the active interval, degree deg, Output: table N. Computes deBoor table used in Algorithm A2.5 in NURBS book. Used by evalDerSingle_into(...), evalAllDerSingle_into(...) and evalSingle_into(...).

void gismo::bspline::derivBasis ( )

Input: a sequence of 2*p+1 knots, evaluation point, output the derivatives evaluated at all functions supported on those knots

void gismo::bspline::derivBasisSingle ( )

Input: a sequence of p+2 knots, evaluation point. Output: the value of the derivative of basis function supported on those knots

void gismo::bspline::evalBasis	(	T	u,
		KnotIterator	knot,
		int	deg,
		gsEigen::MatrixBase< Derived > const &	result
	)

Input: an iterator pointing to the the biggest knot less than u, evaluation point u, output the value of all basis functions which are active at u. Uses B-spline recursion for evaluation

void gismo::bspline::evalBasis2	(	const T &	u,
		const KnotIterator &	knot,
		int	deg,
		MatrixType &	result
	)

Input: a sequence of 2*p+1 knots starting at iterator position knot, evaluation point u, output the value of all basis functions which are active on u. Uses DeBoor's algorithm for evaluation

void gismo::bspline::evalBasisSingle ( )

Input: a sequence of p+2 knots, evaluation point. Output: the value of the basis function supported on those knots

void gismo::bspline::evalGeo	(	const T &	u,
		const KnotIterator &	knot,
		int	deg,
		MatrixType	coefs,
		MatrixType &	result
	)

Input: a sequence of 2*p+1 knots starting at iterator position knot, evaluation point u, output the value of the B-spline defined by coefs Uses DeBoor's algorithm for evaluation

Todo:: add an overload with stride parameter for coefs

int gismo::bspline::getIndex	(	const gsVector< unsigned > &	stride,
		const gsVector< int > &	position
	)

inline

From strides and current position computes index (row) used in global presentation of the coefficients

Parameters

stride	- vector of strides
position	- current position [x0, x1, x2, x3, ...]

Returns: global index (row)

void gismo::bspline::getLastIndex	(	const gsVector< unsigned > &	stride,
		const unsigned	number_of_points,
		gsVector< int > &	last_point
	)

inline

Computes last point of the cube, so that can be passed to nextCubePoint function

Parameters

stride	- vector of strides
number_of_points	- total number of coefficients (coef.rows())
last_point	- throght this parameter function sets last point of the cube

Returns: void (note: "returns" value throught last_point)

void gismo::bspline::getLastIndexLocal	(	const gsVector< index_t, d > &	size_of_coef,
		gsVector< index_t, d > &	last_point
	)

Computes last point of a cube. We can pass the point to nextCubePoint function. Function computes last point for local algorithm.

Parameters

size_of_coef	size of the coefficients
last_point	we compute last point into this variable

unsigned gismo::bspline::numberOfIterations	(	const gsVector< index_t > &	nmb_of_coefs,
		const unsigned	direction
	)

inline

Function computes necessary number of iterations for given number of the coefficients. We will iterate through cube (its size is nmb_of_coefs) in given direction.

Parameters

nmb_of_coefs	number of the coefficients
direction	direction in which we iterate

Returns: number of iterations

Functions

Detailed Description

Function Documentation