#include <PolygonShape_fwd.hpp>

Detailed Description

template<typename vec_t>
class mm::PolygonShape< vec_t >

Shape representing a simple (i.e. non self intersecting) nonempty polygon in 2D, which is given as a sequence of points.

Template Parameters

vec_t This shape class is used only for 2D domains.

Usage example:

    PolygonShape<Vec2d> poly({{0.0, -2.0}, {1.0, -1.0}, {2.0, 0.0}, {1.0, 1.0}, {0.0, 2.0},
                              {-1.0, 1.0}, {-2.0, 0.0}, {-1.0, -1.0}});
    if (poly.contains({2.3, 4.5})) {
        // do something
    }
    std::cout << poly << std::endl;
    auto d = poly.discretizeBoundaryWithStep(0.1);

Definition at line 27 of file PolygonShape_fwd.hpp.

Inheritance diagram for mm::PolygonShape< vec_t >:

Collaboration diagram for mm::PolygonShape< vec_t >:

Public Member Functions
	PolygonShape (const std::vector< vec_t > &points)
	Create polygon given a sequence of points. More...

const std::vector< vec_t > &	points () const
	Get points representing the polygon. More...

void	setMargin (scalar_t margin) override
	Computes the polygon extended by margin as well. More...

bool	contains (const vec_t &point) const override
	Winding number test for point in a polygon inclusion (paying respect to margin). More...

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

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

DomainDiscretization< vec_t >	discretizeBoundaryWithDensity (const std::function< scalar_t(vec_t)> &dr, int type) const override
	Returns a discretization of the boundary of this shape with approximately uniform distance `step` between nodes. More...

PolygonShape< vec_t > *	clone () const override
	Polymorphic clone pattern. More...

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

virtual DomainDiscretization< vec_t >	discretizeBoundaryWithDensity (const std::function< scalar_t(vec_t)> &dr, int type) const=0
	Discretizes boundary with given density and fill engine. More...

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

scalar_t	margin () const
	Returns current 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 bool	hasContains () const
	Return true if shape has `contains()` method implemented. 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
typedef vec_t::Scalar	scalar_t
	Scalar data type used in computation. More...

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

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

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

Private Types
using	base_t = DomainShape< vec_t >
	Base class type. More...

Private Member Functions
void	extendByMargin ()
	Save a version of points extended by margin_ for later contains checks. More...

Static Private Member Functions
static scalar_t	isLeft (const vec_t &P0, const vec_t &P1, const vec_t &P2)
	Tests if a point is left, on, or right of an infinite line. More...

Private Attributes
std::vector< vec_t >	points_
	The points that define the polygon, stored in CCW order. More...

std::vector< vec_t >	points_with_margin_
	Polygon extended by margin_, for contains checks. 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.

Constructor & Destructor Documentation

◆ PolygonShape()

template<typename vec_t >

mm::PolygonShape< vec_t >::PolygonShape ( const std::vector< vec_t > & points )

explicit

Create polygon given a sequence of points.

The points are stored in CCW order. It is the user's responsibility to ensure the polygon is non self intersecting. Polygon area is computed to ensure that polygon is nonempty and to possibly reverse the point ordering, so that points are stored in counter clockwise (CCW) order.

Definition at line 17 of file PolygonShape.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 >

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

overridevirtual

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 76 of file PolygonShape.hpp.

◆ clone()

template<typename vec_t >

PolygonShape<vec_t>* mm::PolygonShape< vec_t >::clone ( ) const

inlineoverridevirtual

Polymorphic clone pattern.

Implements mm::DomainShape< vec_t >.

Definition at line 81 of file PolygonShape_fwd.hpp.

◆ contains()

template<typename vec_t >

bool mm::PolygonShape< vec_t >::contains ( const vec_t & point ) const

overridevirtual

Winding number test for point in a polygon inclusion (paying respect to margin).

Loosely based on: http://geomalgorithms.com/a03-_inclusion.html

Implements mm::DomainShape< vec_t >.

Definition at line 54 of file PolygonShape.hpp.

◆ discretizeBoundaryWithDensity() [1/4]

template<typename vec_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithDensity

inline

Overload with default type.

Definition at line 189 of file DomainShape_fwd.hpp.

◆ discretizeBoundaryWithDensity() [2/4]

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.

◆ discretizeBoundaryWithDensity() [3/4]

template<typename vec_t >

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

overridevirtual

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.

The boundary points are guaranteed to be added in counter clock-wise order.

Implements mm::DomainShape< vec_t >.

Definition at line 118 of file PolygonShape.hpp.

◆ discretizeBoundaryWithDensity() [4/4]

template<typename vec_t >

virtual DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithDensity

Discretizes boundary with given density and fill engine.

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

◆ discretizeBoundaryWithStep() [1/4]

template<typename vec_t >

DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithStep

inline

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() [2/4]

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() [3/4]

template<typename vec_t >

virtual DomainDiscretization<vec_t> mm::DomainShape< vec_t >::discretizeBoundaryWithStep

inline

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.

Definition at line 118 of file DomainShape_fwd.hpp.

◆ discretizeBoundaryWithStep() [4/4]

template<typename vec_t >

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

overridevirtual

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.

The boundary points are guaranteed to be added in counter clock-wise order.

Reimplemented from mm::DomainShape< vec_t >.

Definition at line 89 of file PolygonShape.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.

◆ extendByMargin()

template<typename vec_t >

void mm::PolygonShape< vec_t >::extendByMargin

private

Save a version of points extended by margin_ for later contains checks.

Definition at line 39 of file PolygonShape.hpp.

◆ hasContains()

template<typename vec_t >

virtual bool mm::DomainShape< vec_t >::hasContains ( ) const

inlinevirtualinherited

Return true if shape has contains() method implemented.

Reimplemented in mm::NURBSShape< vec_t, param_vec_t >, mm::RotatedShape< vec_t >, mm::ShapeDifference< vec_t >, mm::ShapeUnion< vec_t >, mm::STLShape< vec_t >, mm::TranslatedShape< vec_t >, and mm::UnknownShape< vec_t >.

Definition at line 96 of file DomainShape_fwd.hpp.

◆ isLeft()

template<typename vec_t >

static scalar_t mm::PolygonShape< vec_t >::isLeft	(	const vec_t &	P0,
		const vec_t &	P1,
		const vec_t &	P2
	)

inlinestaticprivate

Tests if a point is left, on, or right of an infinite line.

Input: three points P0, P1, and P2

Returns: a number > 0 if P2 is left of the line through P0 and P1 (looking from P0 to P1), 0 for P2 on the line P0P1 or a number < 0 for P2 right of the line P0P1.

Definition at line 94 of file PolygonShape_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.

◆ 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.

◆ points()

template<typename vec_t >

const std::vector<vec_t>& mm::PolygonShape< vec_t >::points ( ) const

inline

Get points representing the polygon.

Definition at line 53 of file PolygonShape_fwd.hpp.

◆ print()

template<typename vec_t >

std::ostream& mm::PolygonShape< 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 83 of file PolygonShape_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.

◆ 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.

◆ setMargin()

template<typename vec_t >

void mm::PolygonShape< vec_t >::setMargin ( scalar_t margin )

overridevirtual

Computes the polygon extended by margin as well.

Reimplemented from mm::DomainShape< vec_t >.

Definition at line 33 of file PolygonShape.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

◆ 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.

◆ points_

template<typename vec_t >

std::vector<vec_t> mm::PolygonShape< vec_t >::points_

private

The points that define the polygon, stored in CCW order.

Definition at line 31 of file PolygonShape_fwd.hpp.

◆ points_with_margin_

template<typename vec_t >

std::vector<vec_t> mm::PolygonShape< vec_t >::points_with_margin_

private

Polygon extended by margin_, for contains checks.

It updates along with margin and has the first point repeated at the end.

Definition at line 34 of file PolygonShape_fwd.hpp.

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

include/medusa/bits/domains/PolygonShape_fwd.hpp
include/medusa/bits/domains/PolygonShape.hpp

Detailed Description

template<typename vec_t> class mm::PolygonShape< vec_t >

Public Member Functions

Public Types

Protected Attributes

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ PolygonShape()

Member Function Documentation

◆ add()

◆ bbox()

◆ clone()

◆ contains()

◆ discretizeBoundaryWithDensity() [1/4]

◆ discretizeBoundaryWithDensity() [2/4]

◆ discretizeBoundaryWithDensity() [3/4]

◆ discretizeBoundaryWithDensity() [4/4]

◆ discretizeBoundaryWithStep() [1/4]

◆ discretizeBoundaryWithStep() [2/4]

◆ discretizeBoundaryWithStep() [3/4]

◆ discretizeBoundaryWithStep() [4/4]

◆ discretizeWithDensity() [1/4]

◆ discretizeWithDensity() [2/4]

◆ discretizeWithDensity() [3/4]

◆ discretizeWithDensity() [4/4]

◆ discretizeWithStep() [1/2]

◆ discretizeWithStep() [2/2]

◆ extendByMargin()

◆ hasContains()

◆ isLeft()

◆ margin()

◆ operator+()

◆ operator-()

◆ points()

◆ print()

◆ projectPointToBoundary()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ setMargin()

◆ subtract()

◆ toggleMargin()

◆ translate()

Member Data Documentation

◆ margin_

◆ points_

◆ points_with_margin_

template<typename vec_t>
class mm::PolygonShape< vec_t >