#include <NURBSShape_fwd.hpp>

Detailed Description

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

Class representing a shape made out of NURBS patches in an arbitrary dimensional space.

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

Usage example:

    int p = 3;
    auto knots = Range<double>{0, 0, 0, 0, 1, 1, 1, 1};
    Range<double> ws{1, 1, 1, 1};
 
    Range<Vec2d> cps1{{1, 1}, {2, 3}, {4, 4}, {6, 1}};
    Range<Vec2d> cps2{{1, 1}, {0, -3}, {8, -2}, {6, 1}};
 
    NURBSPatch<Vec2d, Vec1d> p1(cps1, {ws}, {knots}, {p});
    NURBSPatch<Vec2d, Vec1d> p2(cps2, {ws}, {knots}, {p});
 
    Range<NURBSPatch<Vec2d, Vec1d>> patches{p1, p2};
    NURBSShape<Vec2d, Vec1d> shape(patches);
    shape.seed(1337);
 
    double h = 0.01;
    DomainDiscretization<Vec2d> domain = shape.discretizeBoundaryWithStep(h);

Template Parameters

vec_t Vector type.

Definition at line 52 of file NURBSShape_fwd.hpp.

Inheritance diagram for mm::NURBSShape< vec_t, param_vec_t >:

Collaboration diagram for mm::NURBSShape< vec_t, param_vec_t >:

Public Member Functions
	NURBSShape (const Range< NURBSPatch< vec_t, param_vec_t >> &patches_in)
	Construct NURBSShape from a Range of patches. More...

	NURBSShape (Range< NURBSPatch< vec_t, param_vec_t >> &&patches_in)
	Move constructor for constructing NURBSShape from a Range of patches. More...

bool	contains (const vec_t &) const override
	Return true if `point` is not more than `margin()` outside the domain. More...

bool	hasContains () const override
	Return true if shape has `contains()` method implemented. More...

std::pair< vec_t, vec_t >	bbox () const override
	Return the bounding box of the domain. More...

DomainDiscretization< vec_t >	discretizeBoundaryWithDensity (const std::function< scalar_t(vec_t)> &, int) const override
	Discretizes boundary with given density and fill engine. More...

std::ostream &	print (std::ostream &ostream) const override
	Output information about this shape to given output stream `os`. More...

NURBSShape *	clone () const override
	Polymorphic clone pattern. More...

NURBSShape &	maxPoints (int max_points)
	Maximal number of points generated in surface fill. More...

NURBSShape &	seed (int seed)
	Set custom seed for the random number generator. More...

NURBSShape &	proximityTolerance (scalar_t zeta)
	Set proximity tolerance in surface fill. More...

NURBSShape &	numSamples (int n_samples)
	Controls the number of generated candidates from each point in surface fill. More...

NURBSShape &	boundaryProximity (scalar_t epsilon)
	Calculate boundary normals `epsilon` times the size of domain away from the boundary. More...

scalar_t	margin () const
	Returns current margin. More...

virtual void	setMargin (scalar_t margin)
	Sets domain margin to `margin`. More...

void	toggleMargin ()
	Toggles the margin from positive to negative. More...

ShapeUnion< vec_t >	add (const DomainShape &other) const
	Returns a shape representing a union of `*this` and `other`. More...

ShapeUnion< vec_t >	operator+ (const DomainShape &other) const
	Operator form of DomainShape::add. More...

ShapeDifference< vec_t >	subtract (const DomainShape &other) const
	Returns a shape representing a difference of `*this` and `other`. More...

ShapeDifference< vec_t >	operator- (const DomainShape &other) const
	Operator form of DomainShape::subtract. More...

virtual std::pair< bool, vec_t >	projectPointToBoundary (const vec_t &point, const vec_t &unit_normal) const
	Project point to boundary using bisection along the line define by `unit_normal`. More...

virtual DomainDiscretization< vec_t >	discretizeBoundaryWithStep (scalar_t step, int type) const
	Returns a discretization of the boundary of this shape with approximately uniform distance `step` between nodes. More...

DomainDiscretization< vec_t >	discretizeBoundaryWithStep (scalar_t step) const
	Returns a discretization of the boundary of this shape with approximately uniform distance `step` between nodes. More...

virtual DomainDiscretization< vec_t >	discretizeWithStep (scalar_t step, int internal_type, int boundary_type) const
	Returns a discretization of this shape with approximately uniform distance `step` between nodes. More...

DomainDiscretization< vec_t >	discretizeWithStep (scalar_t step) const
	discretizeWithStep but with default types as assigned by the shape. More...

virtual DomainDiscretization< vec_t >	discretizeWithDensity (const std::function< scalar_t(vec_t)> &dr, int internal_type, int boundary_type) const
	Returns a discretization of the domain with spatially variable step. More...

template<typename func_t , typename fill_t >
DomainDiscretization< vec_t >	discretizeWithDensity (const func_t &dr, const fill_t &fill, int internal_type, int boundary_type) const
	Overload for fill engine. More...

DomainDiscretization< vec_t >	discretizeWithDensity (const std::function< scalar_t(vec_t)> &dr) const
	Overload with default types. More...

template<typename func_t , typename fill_t >
DomainDiscretization< vec_t >	discretizeWithDensity (const func_t &dr, const fill_t &fill) const
	Overload for fill engine with default types. More...

DomainDiscretization< vec_t >	discretizeBoundaryWithDensity (const std::function< scalar_t(vec_t)> &dr) const
	Overload with default type. More...

TranslatedShape< vec_t >	translate (const vec_t &a)
	Translate the shape by given vector `a`. More...

RotatedShape< vec_t >	rotate (const Eigen::Matrix< scalar_t, dim, dim > &Q)
	Transform the shape by given orthogonal matrix `Q`. More...

RotatedShape< vec_t >	rotate (scalar_t angle)
	2D version of rotate accepting an angle. 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...

enum	{ dim = vec_t::dim }
	Store dimension of the domain. More...

typedef vec_t	vector_t
	Vector data type used in computations. More...

Friends
struct	nurbs_shape_internal::NURBSShapeHelper< vec_t, param_vec_t >

Protected Attributes
scalar_t	margin_
	Tolerance for the geometric operation of the domain. More...

Private Attributes
Range< NURBSPatch< vec_t, param_vec_t > >	patches
	Range of NURBS patches. More...

int	max_points = 5000000
	Maximal number of points generated in surface fill. More...

int	seed_
	Seed for the random number generator. More...

int	n_samples = 15
	Number of samples in surface fill. More...

scalar_t	zeta = 1 - 1e-10
	Proximity tolerance in surface fill. More...

scalar_t	epsilon = 0
	Evaluate normals slightly away from the boundary. More...

Member Enumeration Documentation

◆ anonymous enum

template<typename vec_t >

anonymous enum

inherited

Store dimension of the domain.

Enumerator
dim	Dimensionality of the domain.

Definition at line 57 of file DomainShape_fwd.hpp.

◆ 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 58 of file NURBSShape_fwd.hpp.

Constructor & Destructor Documentation

◆ NURBSShape() [1/2]

template<typename vec_t , typename param_vec_t >

mm::NURBSShape< vec_t, param_vec_t >::NURBSShape ( const Range< NURBSPatch< vec_t, param_vec_t >> & patches_in )

Construct NURBSShape from a Range of patches.

Definition at line 22 of file NURBSShape.hpp.

◆ NURBSShape() [2/2]

template<typename vec_t , typename param_vec_t >

mm::NURBSShape< vec_t, param_vec_t >::NURBSShape ( Range< NURBSPatch< vec_t, param_vec_t >> && patches_in )

Move constructor for constructing NURBSShape from a Range of patches.

Definition at line 33 of file NURBSShape.hpp.

Member Function Documentation

◆ add()

template<typename vec_t >

ShapeUnion< vec_t > mm::DomainShape< vec_t >::add ( const DomainShape< vec_t > & other ) const

inherited

Returns a shape representing a union of *this and other.

Definition at line 66 of file DomainShape.hpp.

◆ bbox()

template<typename vec_t , typename param_vec_t >

std::pair<vec_t, vec_t> mm::NURBSShape< vec_t, param_vec_t >::bbox ( ) const

inlineoverridevirtual

Return the bounding box of the domain.

Bounding box is returned in format bbox() == {{mx, my, ...}, {MX, MY, ...}}, such that mx <= Mx and my <= My etc.\ and that the whole domain is contained in the cuboid [mx, my, ...] x [Mx, My, ...].

Implements mm::DomainShape< vec_t >.

Definition at line 82 of file NURBSShape_fwd.hpp.

◆ boundaryProximity()

template<typename vec_t , typename param_vec_t >

NURBSShape< vec_t, param_vec_t > & mm::NURBSShape< vec_t, param_vec_t >::boundaryProximity ( scalar_t epsilon )

Calculate boundary normals epsilon times the size of domain away from the boundary.

By default epsilon = 0. This can be useful if normals are undefined on the boundary. It should hold that 0 < epsilon < 1.

Definition at line 59 of file NURBSShape.hpp.

◆ clone()

template<typename vec_t , typename param_vec_t >

NURBSShape* mm::NURBSShape< vec_t, param_vec_t >::clone ( ) const

inlineoverridevirtual

Polymorphic clone pattern.

Implements mm::DomainShape< vec_t >.

Definition at line 95 of file NURBSShape_fwd.hpp.

◆ contains()

template<typename vec_t , typename param_vec_t >

bool mm::NURBSShape< vec_t, param_vec_t >::contains ( const vec_t & point ) const

inlineoverridevirtual

Return true if point is not more than margin() outside the domain.

Implements mm::DomainShape< vec_t >.

Definition at line 78 of file NURBSShape_fwd.hpp.

◆ discretizeBoundaryWithDensity() [1/2]

template<typename vec_t , typename param_vec_t >

DomainDiscretization< vec_t > mm::NURBSShape< vec_t, param_vec_t >::discretizeBoundaryWithDensity	(	const std::function< scalar_t(vec_t)> &	dr,
		int	type
	)		const

overridevirtual

Discretizes boundary with given density and fill engine.

If type is 0, the underlying shape provides the default.

Implements mm::DomainShape< vec_t >.

Definition at line 44 of file NURBSShape.hpp.

◆ discretizeBoundaryWithDensity() [2/2]

template<typename vec_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithDensity ( const std::function< scalar_t(vec_t)> & dr ) const

inlineinherited

Overload with default type.

Definition at line 189 of file DomainShape_fwd.hpp.

◆ discretizeBoundaryWithStep() [1/2]

template<typename vec_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithStep ( scalar_t step ) const

inlineinherited

Returns a discretization of the boundary of this shape with approximately uniform distance step between nodes.

Node type are decided by the underlying shape.

Definition at line 126 of file DomainShape_fwd.hpp.

◆ discretizeBoundaryWithStep() [2/2]

template<typename vec_t >

virtual DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithStep	(	scalar_t	step,
		int	type
	)		const

inlinevirtualinherited

Returns a discretization of the boundary of this shape with approximately uniform distance step between nodes.

step must be positive. Added nodes are of type type, which must be non-positive. Value 0 indicates that types are dependant on the implementation of concrete shape.

Reimplemented in mm::PolygonShape< vec_t >, mm::TranslatedShape< vec_t >, mm::ShapeUnion< vec_t >, mm::BoxShape< vec_t >, mm::ShapeDifference< vec_t >, and mm::BallShape< vec_t >.

Definition at line 118 of file DomainShape_fwd.hpp.

◆ discretizeWithDensity() [1/4]

template<typename vec_t >

template<typename func_t , typename fill_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeWithDensity	(	const func_t &	dr,
		const fill_t &	fill
	)		const

inlineinherited

Overload for fill engine with default types.

Definition at line 177 of file DomainShape_fwd.hpp.

◆ discretizeWithDensity() [2/4]

template<typename vec_t >

template<typename func_t , typename fill_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeWithDensity	(	const func_t &	dr,
		const fill_t &	fill,
		int	internal_type,
		int	boundary_type
	)		const

inlineinherited

Overload for fill engine.

Definition at line 162 of file DomainShape_fwd.hpp.

◆ discretizeWithDensity() [3/4]

template<typename vec_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeWithDensity ( const std::function< scalar_t(vec_t)> & dr ) const

inlineinherited

Overload with default types.

Definition at line 170 of file DomainShape_fwd.hpp.

◆ discretizeWithDensity() [4/4]

template<typename vec_t >

DomainDiscretization< vec_t > mm::DomainShape< vec_t >::discretizeWithDensity	(	const std::function< scalar_t(vec_t)> &	dr,
		int	internal_type,
		int	boundary_type
	)		const

virtualinherited

Returns a discretization of the domain with spatially variable step.

Parameters

dr	Function giving desired internodal distance at each point.
internal_type	User supplied type of internal nodes. Must be non-negative.
boundary_type	User supplied type of boundary nodes. Must be non-positive. If any of the types is 0, the underlying shape provides the default.

Returns: Discretization with nodes distributed according to dr.

Reimplemented in mm::TranslatedShape< vec_t >, mm::ShapeUnion< vec_t >, and mm::ShapeDifference< vec_t >.

Definition at line 77 of file DomainShape.hpp.

◆ discretizeWithStep() [1/2]

template<typename vec_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeWithStep ( scalar_t step ) const

inlineinherited

discretizeWithStep but with default types as assigned by the shape.

Definition at line 144 of file DomainShape_fwd.hpp.

◆ discretizeWithStep() [2/2]

template<typename vec_t >

virtual DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeWithStep	(	scalar_t	step,
		int	internal_type,
		int	boundary_type
	)		const

inlinevirtualinherited

Returns a discretization of this shape with approximately uniform distance step between nodes.

step must be positive.

Parameters

step	Desired internodal distance.
internal_type	User supplied type of internal nodes. Must be non-negative.
boundary_type	User supplied type of boundary nodes. Must be non-positive. If any of the types is 0, the underlying shape provides the default.

Reimplemented in mm::TranslatedShape< vec_t >, mm::ShapeUnion< vec_t >, mm::BoxShape< vec_t >, mm::ShapeDifference< vec_t >, and mm::BallShape< vec_t >.

Definition at line 137 of file DomainShape_fwd.hpp.

◆ hasContains()

template<typename vec_t , typename param_vec_t >

bool mm::NURBSShape< vec_t, param_vec_t >::hasContains ( ) const

inlineoverridevirtual

Return true if shape has contains() method implemented.

Reimplemented from mm::DomainShape< vec_t >.

Definition at line 80 of file NURBSShape_fwd.hpp.

◆ margin()

template<typename vec_t >

scalar_t mm::DomainShape< vec_t >::margin ( ) const

inlineinherited

Returns current margin.

Definition at line 72 of file DomainShape_fwd.hpp.

◆ maxPoints()

template<typename vec_t , typename param_vec_t >

NURBSShape& mm::NURBSShape< vec_t, param_vec_t >::maxPoints ( int max_points )

inline

Maximal number of points generated in surface fill.

Warning: The actual upper bound for number of points generated is maxPoints \(\pm\) numSamples.

Definition at line 103 of file NURBSShape_fwd.hpp.

◆ numSamples()

template<typename vec_t , typename param_vec_t >

NURBSShape& mm::NURBSShape< vec_t, param_vec_t >::numSamples ( int n_samples )

inline

Controls the number of generated candidates from each point in surface fill.

For 2-D it is the actual number of candidates, for 3-D it is the number of candidates on the great circle. Its value is ignored in 1-D.

Definition at line 119 of file NURBSShape_fwd.hpp.

◆ operator+()

template<typename vec_t >

ShapeUnion<vec_t> mm::DomainShape< vec_t >::operator+ ( const DomainShape< vec_t > & other ) const

inlineinherited

Operator form of DomainShape::add.

See also: add

Definition at line 81 of file DomainShape_fwd.hpp.

◆ operator-()

template<typename vec_t >

ShapeDifference<vec_t> mm::DomainShape< vec_t >::operator- ( const DomainShape< vec_t > & other ) const

inlineinherited

Operator form of DomainShape::subtract.

See also: subtract

Definition at line 86 of file DomainShape_fwd.hpp.

◆ print()

template<typename vec_t , typename param_vec_t >

std::ostream& mm::NURBSShape< vec_t, param_vec_t >::print ( std::ostream & os ) const

inlineoverridevirtual

Output information about this shape to given output stream os.

Implements mm::DomainShape< vec_t >.

Definition at line 91 of file NURBSShape_fwd.hpp.

◆ projectPointToBoundary()

template<typename vec_t >

std::pair< bool, vec_t > mm::DomainShape< vec_t >::projectPointToBoundary	(	const vec_t &	point,
		const vec_t &	unit_normal
	)		const

virtualinherited

Project point to boundary using bisection along the line define by unit_normal.

Definition at line 21 of file DomainShape.hpp.

◆ proximityTolerance()

template<typename vec_t , typename param_vec_t >

NURBSShape< vec_t, param_vec_t > & mm::NURBSShape< vec_t, param_vec_t >::proximityTolerance ( scalar_t zeta )

Set proximity tolerance in surface fill.

A new candidate mush be at least zeta*h(p) away. It should hold that 0 < zeta < 1.

Definition at line 51 of file NURBSShape.hpp.

◆ rotate() [1/2]

template<typename vec_t >

RotatedShape< vec_t > mm::DomainShape< vec_t >::rotate ( const Eigen::Matrix< scalar_t, dim, dim > & Q )

inherited

Transform the shape by given orthogonal matrix Q.

Note: It is usually faster to first discretize the domain and than transform the whole discretization using DomainDiscretization::rotate.

Definition at line 98 of file DomainShape.hpp.

◆ rotate() [2/2]

template<typename vec_t >

RotatedShape< vec_t > mm::DomainShape< vec_t >::rotate ( scalar_t angle )

inherited

2D version of rotate accepting an angle.

Definition at line 89 of file DomainShape.hpp.

◆ seed()

template<typename vec_t , typename param_vec_t >

NURBSShape& mm::NURBSShape< vec_t, param_vec_t >::seed ( int seed )

inline

Set custom seed for the random number generator.

Definition at line 106 of file NURBSShape_fwd.hpp.

◆ setMargin()

template<typename vec_t >

virtual void mm::DomainShape< vec_t >::setMargin ( scalar_t margin )

inlinevirtualinherited

Sets domain margin to margin.

Reimplemented in mm::PolygonShape< vec_t >.

Definition at line 75 of file DomainShape_fwd.hpp.

◆ subtract()

template<typename vec_t >

ShapeDifference< vec_t > mm::DomainShape< vec_t >::subtract ( const DomainShape< vec_t > & other ) const

inherited

Returns a shape representing a difference of *this and other.

Definition at line 71 of file DomainShape.hpp.

◆ toggleMargin()

template<typename vec_t >

void mm::DomainShape< vec_t >::toggleMargin ( )

inlineinherited

Toggles the margin from positive to negative.

Definition at line 77 of file DomainShape_fwd.hpp.

◆ translate()

template<typename vec_t >

TranslatedShape< vec_t > mm::DomainShape< vec_t >::translate ( const vec_t & a )

inherited

Translate the shape by given vector a.

Note: It is usually faster to first discretize the domain and than translate the whole discretization using DomainDiscretization::translate.

Definition at line 84 of file DomainShape.hpp.

Member Data Documentation

◆ epsilon

template<typename vec_t , typename param_vec_t >

scalar_t mm::NURBSShape< vec_t, param_vec_t >::epsilon = 0

private

Evaluate normals slightly away from the boundary.

Definition at line 69 of file NURBSShape_fwd.hpp.

◆ margin_

template<typename vec_t >

scalar_t mm::DomainShape< vec_t >::margin_

protectedinherited

Tolerance for the geometric operation of the domain.

The domain should behave as if it was margin_ thicker. Default margin is 1e-10.

Definition at line 64 of file DomainShape_fwd.hpp.

◆ max_points

template<typename vec_t , typename param_vec_t >

int mm::NURBSShape< vec_t, param_vec_t >::max_points = 5000000

private

Maximal number of points generated in surface fill.

Definition at line 65 of file NURBSShape_fwd.hpp.

◆ n_samples

template<typename vec_t , typename param_vec_t >

int mm::NURBSShape< vec_t, param_vec_t >::n_samples = 15

private

Number of samples in surface fill.

Definition at line 67 of file NURBSShape_fwd.hpp.

◆ patches

template<typename vec_t , typename param_vec_t >

Range<NURBSPatch<vec_t, param_vec_t> > mm::NURBSShape< vec_t, param_vec_t >::patches

private

Range of NURBS patches.

Definition at line 64 of file NURBSShape_fwd.hpp.

◆ seed_

template<typename vec_t , typename param_vec_t >

int mm::NURBSShape< vec_t, param_vec_t >::seed_

private

Seed for the random number generator.

Definition at line 66 of file NURBSShape_fwd.hpp.

◆ zeta

template<typename vec_t , typename param_vec_t >

scalar_t mm::NURBSShape< vec_t, param_vec_t >::zeta = 1 - 1e-10

private

Proximity tolerance in surface fill.

Definition at line 68 of file NURBSShape_fwd.hpp.

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

include/medusa/bits/domains/NURBSShape_fwd.hpp
include/medusa/bits/domains/NURBSShape.hpp

Detailed Description

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

Public Member Functions

Public Types

Friends

Protected Attributes

Private Attributes

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ NURBSShape() [1/2]

◆ NURBSShape() [2/2]

Member Function Documentation

◆ add()

◆ bbox()

◆ boundaryProximity()

◆ clone()

◆ contains()

◆ discretizeBoundaryWithDensity() [1/2]

◆ discretizeBoundaryWithDensity() [2/2]

◆ discretizeBoundaryWithStep() [1/2]

◆ discretizeBoundaryWithStep() [2/2]

◆ discretizeWithDensity() [1/4]

◆ discretizeWithDensity() [2/4]

◆ discretizeWithDensity() [3/4]

◆ discretizeWithDensity() [4/4]

◆ discretizeWithStep() [1/2]

◆ discretizeWithStep() [2/2]

◆ hasContains()

◆ margin()

◆ maxPoints()

◆ numSamples()

◆ operator+()

◆ operator-()

◆ print()

◆ projectPointToBoundary()

◆ proximityTolerance()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ seed()

◆ setMargin()

◆ subtract()

◆ toggleMargin()

◆ translate()

Member Data Documentation

◆ epsilon

◆ margin_

◆ max_points

◆ n_samples

◆ patches

◆ seed_

◆ zeta

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