#include <NURBSPatch_fwd.hpp>

Detailed Description

template<typename vec_t, typename param_vec_t>
class mm::NURBSPatch< vec_t, param_vec_t >

Class representing a single NURBS patch in an arbitrary dimensional space, defined on an arbitrary dimensional domain and generated by a tensor product of NURBS curves.

Warning: Currently only supports NURBS surfaces (2D domain) and NURBS curves (1D domain).

Usage example:

    int p = 2;
    Range<double> w({1, sqrt(3) / 2, 1, sqrt(3) / 2, 1, sqrt(3) / 2, 1, sqrt(3) / 2, 1});
    Range<double> knots({0, 0, 0, PI / 2, PI / 2, PI, PI, 3 * PI / 2,
                         3 * PI / 2, 2 * PI, 2 * PI, 2 * PI});
    Range<Vec3d> cp({Vec3d(1, 0, 0), Vec3d(1, 1, 0), Vec3d(0, 1, 0), Vec3d(-1, 1, 0),
                     Vec3d(-1, 0, 0), Vec3d(-1, -1, 0), Vec3d(0, -1, 0), Vec3d(1, -1, 0),
                     Vec3d(1, 0, 0)});
 
    NURBSPatch<Vec3d, Vec1d> curve(cp, w, {knots}, {p});
 
    Vec3d pt = curve.evaluate({PI});

Template Parameters

param_vec_t	Vector type of the parametric space.
vec_t	Vector type of ambient space.

Definition at line 72 of file NURBSPatch_fwd.hpp.

Public Member Functions
	NURBSPatch (const NdRange< proj_vec_t > &wcp, const std::array< Range< scalar_t >, param_dim > &ks, const std::array< int, param_dim > &in_p)
	Construct NURBS patch with weighted control points. More...

	NURBSPatch (const NdRange< vec_t > &cp, const NdRange< double > &w, const std::array< Range< scalar_t >, param_dim > &ks, const std::array< int, param_dim > &in_p)
	Construct NURBS patch with control points and weights. More...

	NURBSPatch (const NURBSPatch< vec_t, param_vec_t > &patch) noexcept
	Copy constructor. More...

NURBSPatch< vec_t, param_vec_t > &	operator= (const NURBSPatch< vec_t, param_vec_t > &) noexcept
	Copy assignment. More...

	NURBSPatch (NURBSPatch< vec_t, param_vec_t > &&) noexcept=default
	Move constructor. More...

NURBSPatch< vec_t, param_vec_t > &	operator= (NURBSPatch< vec_t, param_vec_t > &&) noexcept=default
	Move assignment. More...

void	computeDerivativeStructure ()
	Calculate data needed for derivative evaluation. More...

vec_t	evaluate (const param_vec_t &t, scalar_t *w) const
	Evaluate NURBS patch in one point along the second dimension. More...

vec_t	evaluate (const param_vec_t &t) const
	Overload if weight is not required. More...

proj_vec_t	evaluateWeighted (const param_vec_t &t) const
	Evaluate NURBS patch in one point. More...

Eigen::Matrix< scalar_t, dim, param_dim >	jacobian (const param_vec_t &t, const vec_t &pt, const scalar_t &w) const
	Evaluate NURBS jacobian matrix in one point. More...

Eigen::Matrix< scalar_t, dim, param_dim >	jacobian (const param_vec_t &t) const
	Overload that calculates the point automatically. More...

std::pair< vec_t, Eigen::Matrix< scalar_t, dim, param_dim > >	evaluatePointAndJacobian (const param_vec_t &t) const
	Evaluate NURBS and its jacobian matrix in one parameter. More...

BoxShape< param_vec_t >	getDomain () const
	Get domain of the NURBS patch. More...

Range< NURBSPatch< vec_t, Vec< scalar_t, param_dim - 1 > > >	getBoundaries () const
	Get all boundaries of the NURBS patch as a Range of NURBS patches. More...

param_vec_t	getPatchParameterFromBoundaryParameter (const Vec< scalar_t, param_dim - 1 > &t, int i, scalar_t epsilon=0) const
	Get vector from the parametric domain of the NURBS patch from the parameter of the NURBS patch representing one of the boundaries of the NURBS. More...

Vec< scalar_t, param_dim - 1 >	getBoundaryParameterFromPatchParameter (const param_vec_t &t, int i) const
	Get parameter from the parametric domain of the NURBS patch representing the boundary of the NURBS patch corresponding to a parameter from the parametric domain of the NURBS surface. More...

Public Types
enum	{ dim = vec_t::dim, proj_dim = dim + 1, param_dim = param_vec_t::dim }
	Store dimensionality. More...

typedef vec_t::scalar_t	scalar_t
	Scalar type. More...

typedef Vec< scalar_t, proj_dim >	proj_vec_t
	Vector type before projection. More...

template<typename T >
using	NdRange = typename nurbs_patch_internal::NestedRange< param_dim, T >::type
	Range of param_dim dimensions. More...

Friends
struct	nurbs_patch_internal::NURBSPatchHelper< vec_t, param_vec_t >

Private Attributes
std::array< int, param_dim >	p
	Underlying B-spline orders. More...

NdRange< proj_vec_t >	weighted_control_points
	Multidimensional Range of control points. More...

std::array< Range< scalar_t >, param_dim >	knots
	Array of Ranges of knots (knot vector). More...

std::unique_ptr< std::array< NURBSPatch< vec_t, param_vec_t >, param_dim > >	der_structure
	NURBS surfaces needed for derivative calculation. More...

Member Enumeration Documentation

◆ anonymous enum

template<typename vec_t , typename param_vec_t >

anonymous enum

Store dimensionality.

Enumerator
dim	Dimensionality of space after projection.
proj_dim	Dimensionality of space before projection.
param_dim	Dimensionality of parametric space.

Definition at line 78 of file NURBSPatch_fwd.hpp.

Constructor & Destructor Documentation

◆ NURBSPatch() [1/4]

template<typename vec_t , typename param_vec_t >

mm::NURBSPatch< vec_t, param_vec_t >::NURBSPatch	(	const NdRange< proj_vec_t > &	wcp,
		const std::array< Range< scalar_t >, param_dim > &	ks,
		const std::array< int, param_dim > &	in_p
	)

Construct NURBS patch with weighted control points.

Parameters

wcp	Multidimensional Range of weighted control points, e. g. `Vec<double, 4>(w * x, w * y, w * z, w)`.
ks	Array of Ranges of knots (pair of knot vectors).
in_p	Array of underlying B-spline orders (starting from order 0).

Definition at line 17 of file NURBSPatch.hpp.

◆ NURBSPatch() [2/4]

template<typename vec_t , typename param_vec_t >

mm::NURBSPatch< vec_t, param_vec_t >::NURBSPatch	(	const NdRange< vec_t > &	cp,
		const NdRange< double > &	w,
		const std::array< Range< scalar_t >, param_dim > &	ks,
		const std::array< int, param_dim > &	in_p
	)

Construct NURBS patch with control points and weights.

Parameters

cp	Multidimensional Range of control points.
w	Multidimensional Range of weights.
ks	Array of Ranges of knots (pair of knot vectors).
in_p	Array of underlying B-spline orders (starting from order 0).

Definition at line 26 of file NURBSPatch.hpp.

◆ NURBSPatch() [3/4]

template<typename vec_t , typename param_vec_t >

mm::NURBSPatch< vec_t, param_vec_t >::NURBSPatch ( const NURBSPatch< vec_t, param_vec_t > & patch )

noexcept

Copy constructor.

Definition at line 37 of file NURBSPatch.hpp.

◆ NURBSPatch() [4/4]

template<typename vec_t , typename param_vec_t >

mm::NURBSPatch< vec_t, param_vec_t >::NURBSPatch ( NURBSPatch< vec_t, param_vec_t > && )

defaultnoexcept

Move constructor.

Member Function Documentation

◆ computeDerivativeStructure()

template<typename vec_t , typename param_vec_t >

void mm::NURBSPatch< vec_t, param_vec_t >::computeDerivativeStructure

Calculate data needed for derivative evaluation.

Definition at line 64 of file NURBSPatch.hpp.

◆ evaluate() [1/2]

template<typename vec_t , typename param_vec_t >

vec_t mm::NURBSPatch< vec_t, param_vec_t >::evaluate ( const param_vec_t & t ) const

Overload if weight is not required.

Parameters

t	Point of evaluation.

Returns: Vector to the point on the NURBS surface corresponding to parameter t.

Definition at line 81 of file NURBSPatch.hpp.

◆ evaluate() [2/2]

template<typename vec_t , typename param_vec_t >

vec_t mm::NURBSPatch< vec_t, param_vec_t >::evaluate	(	const param_vec_t &	t,
		scalar_t *	w
	)		const

Evaluate NURBS patch in one point along the second dimension.

Parameters

t	Point of evaluation.
w	Variable in which the weight is stored.

Returns: Vector to the point on the NURBS surface corresponding to parameter t.

Definition at line 69 of file NURBSPatch.hpp.

◆ evaluatePointAndJacobian()

template<typename vec_t , typename param_vec_t >

std::pair< vec_t, Eigen::Matrix< typename NURBSPatch< vec_t, param_vec_t >::scalar_t, NURBSPatch< vec_t, param_vec_t >::dim, NURBSPatch< vec_t, param_vec_t >::param_dim > > mm::NURBSPatch< vec_t, param_vec_t >::evaluatePointAndJacobian ( const param_vec_t & t ) const

Evaluate NURBS and its jacobian matrix in one parameter.

Parameters

t	Parameter of evaluation.

Returns: Pair of point on the NURBS and jacobian matrix of the NURBS at parameter t.

Definition at line 114 of file NURBSPatch.hpp.

◆ evaluateWeighted()

template<typename vec_t , typename param_vec_t >

NURBSPatch< vec_t, param_vec_t >::proj_vec_t mm::NURBSPatch< vec_t, param_vec_t >::evaluateWeighted ( const param_vec_t & t ) const

Evaluate NURBS patch in one point.

Parameters

t	Point of evaluation.

Returns: Vector to the weighted point on the NURBS patch corresponding to parameter t.

Definition at line 88 of file NURBSPatch.hpp.

◆ getBoundaries()

template<typename vec_t , typename param_vec_t >

Range< NURBSPatch< vec_t, Vec< typename NURBSPatch< vec_t, param_vec_t >::scalar_t, NURBSPatch< vec_t, param_vec_t >::param_dim - 1 > > > mm::NURBSPatch< vec_t, param_vec_t >::getBoundaries

Get all boundaries of the NURBS patch as a Range of NURBS patches.

Returns: An array of NURBS curves representing the boundaries.

Definition at line 135 of file NURBSPatch.hpp.

◆ getBoundaryParameterFromPatchParameter()

template<typename vec_t , typename param_vec_t >

Vec< typename NURBSPatch< vec_t, param_vec_t >::scalar_t, NURBSPatch< vec_t, param_vec_t >::param_dim - 1 > mm::NURBSPatch< vec_t, param_vec_t >::getBoundaryParameterFromPatchParameter	(	const param_vec_t &	t,
		int	i
	)		const

Get parameter from the parametric domain of the NURBS patch representing the boundary of the NURBS patch corresponding to a parameter from the parametric domain of the NURBS surface.

Parameters

t	Parameter of the NURBS patch.
i	Index of the boundary.

Returns: Parameter from the parametric domain of the NURBS boundary curve corresponding to the input parameter.

Definition at line 149 of file NURBSPatch.hpp.

◆ getDomain()

template<typename vec_t , typename param_vec_t >

BoxShape< param_vec_t > mm::NURBSPatch< vec_t, param_vec_t >::getDomain

Get domain of the NURBS patch.

Returns: Domain of the NURBS in the form of a BoxShape.

Definition at line 122 of file NURBSPatch.hpp.

◆ getPatchParameterFromBoundaryParameter()

template<typename vec_t , typename param_vec_t >

param_vec_t mm::NURBSPatch< vec_t, param_vec_t >::getPatchParameterFromBoundaryParameter	(	const Vec< scalar_t, param_dim - 1 > &	t,
		int	i,
		scalar_t	epsilon = `0`
	)		const

Get vector from the parametric domain of the NURBS patch from the parameter of the NURBS patch representing one of the boundaries of the NURBS.

Patch parameter can be generated epsilon times the length of the domain away from the boundary. This is useful when normals are not defined at the boundary of the patch.

Parameters

t	Parameter of the NURBS patch representing the boundary.
i	Index of the boundary.
epsilon	Epsilon.

Returns: Vector from the parametric domain of the NURBS patch corresponding to the input parameter.

Definition at line 140 of file NURBSPatch.hpp.

◆ jacobian() [1/2]

template<typename vec_t , typename param_vec_t >

Eigen::Matrix< typename NURBSPatch< vec_t, param_vec_t >::scalar_t, NURBSPatch< vec_t, param_vec_t >::dim, NURBSPatch< vec_t, param_vec_t >::param_dim > mm::NURBSPatch< vec_t, param_vec_t >::jacobian ( const param_vec_t & t ) const

Overload that calculates the point automatically.

Warning: Less efficient.

Parameters

t	Point of evaluation.

Returns: Jacobian matrix of the NURBS patch at point t.

Warning: computeDerivativeStructure() must be called on the object before calling this function.

Definition at line 103 of file NURBSPatch.hpp.

◆ jacobian() [2/2]

template<typename vec_t , typename param_vec_t >

Eigen::Matrix< typename NURBSPatch< vec_t, param_vec_t >::scalar_t, NURBSPatch< vec_t, param_vec_t >::dim, NURBSPatch< vec_t, param_vec_t >::param_dim > mm::NURBSPatch< vec_t, param_vec_t >::jacobian	(	const param_vec_t &	t,
		const vec_t &	pt,
		const scalar_t &	w
	)		const

Evaluate NURBS jacobian matrix in one point.

Parameters

t	Point of evaluation.
pt	Point on the NURBS patch corresponding to `t`.
w	Weight of `pt`.

Returns: Jacobian matrix of the NURBS patch at point t.

Warning: computeDerivativeStructure() must be called on the object before calling this function.

Definition at line 95 of file NURBSPatch.hpp.

◆ operator=() [1/2]

template<typename vec_t , typename param_vec_t >

NURBSPatch< vec_t, param_vec_t > & mm::NURBSPatch< vec_t, param_vec_t >::operator= ( const NURBSPatch< vec_t, param_vec_t > & other )

noexcept

Copy assignment.

Definition at line 47 of file NURBSPatch.hpp.

◆ operator=() [2/2]

template<typename vec_t , typename param_vec_t >

NURBSPatch<vec_t, param_vec_t>& mm::NURBSPatch< vec_t, param_vec_t >::operator= ( NURBSPatch< vec_t, param_vec_t > && )

defaultnoexcept

Move assignment.

Member Data Documentation

◆ der_structure

template<typename vec_t , typename param_vec_t >

std::unique_ptr<std::array<NURBSPatch<vec_t, param_vec_t>, param_dim> > mm::NURBSPatch< vec_t, param_vec_t >::der_structure

private

NURBS surfaces needed for derivative calculation.

Definition at line 93 of file NURBSPatch_fwd.hpp.

◆ knots

template<typename vec_t , typename param_vec_t >

std::array<Range<scalar_t>, param_dim> mm::NURBSPatch< vec_t, param_vec_t >::knots

private

Array of Ranges of knots (knot vector).

Definition at line 90 of file NURBSPatch_fwd.hpp.

◆ p

template<typename vec_t , typename param_vec_t >

std::array<int, param_dim> mm::NURBSPatch< vec_t, param_vec_t >::p

private

Underlying B-spline orders.

Definition at line 88 of file NURBSPatch_fwd.hpp.

◆ weighted_control_points

template<typename vec_t , typename param_vec_t >

NdRange<proj_vec_t> mm::NURBSPatch< vec_t, param_vec_t >::weighted_control_points

private

Multidimensional Range of control points.

Definition at line 89 of file NURBSPatch_fwd.hpp.

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

include/medusa/bits/domains/NURBSPatch_fwd.hpp
include/medusa/bits/domains/NURBSPatch.hpp

Detailed Description

template<typename vec_t, typename param_vec_t> class mm::NURBSPatch< vec_t, param_vec_t >

Public Member Functions

Public Types

Friends

Private Attributes

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ NURBSPatch() [1/4]

◆ NURBSPatch() [2/4]

◆ NURBSPatch() [3/4]

◆ NURBSPatch() [4/4]

Member Function Documentation

◆ computeDerivativeStructure()

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ evaluatePointAndJacobian()

◆ evaluateWeighted()

◆ getBoundaries()

◆ getBoundaryParameterFromPatchParameter()

◆ getDomain()

◆ getPatchParameterFromBoundaryParameter()

◆ jacobian() [1/2]

◆ jacobian() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

Member Data Documentation

◆ der_structure

◆ knots

◆ p

◆ weighted_control_points

template<typename vec_t, typename param_vec_t>
class mm::NURBSPatch< vec_t, param_vec_t >