The Polygon class represents a polygon in a N-dimensional Euclidean space. More...

#include <vclib/space/core/polygon.h>

Public Types
using	ScalarType = PointT::ScalarType
	The scalar type of the points that define the polygon.

using	PointType = PointT
	The type of the points that define the polygon.

using	Iterator = typename std::vector< PointT >::iterator
	The iterator type of the polygon.

using	ConstIterator = typename std::vector< PointT >::const_iterator
	The const iterator type of the polygon.

Public Member Functions
	Polygon ()
	Construct a new empty Polygon object.

	Polygon (std::initializer_list< PointT > points)
	Construct a new Polygon object from an initializer list of points.

template<typename Iterator > requires (std::is_same_v<typename Iterator::value_type, PointT>)
	Polygon (Iterator begin, Iterator end)
	Construct a new Polygon object from a range of points.

template<Range R> requires (InputRange<R, PointT>)
	Polygon (R &&range)
	Construct a new Polygon object from a range of points.

uint	size () const
	Returns the number of points that define the polygon.

void	resize (uint n)
	Resizes the polygon to contain n points.

void	reserve (uint n)
	Reserves space for n points in the polygon.

void	clear ()
	Clears the polygon, removing all points.

void	pushBack (const PointT &point)
	Adds a point to the back of the polygon.

void	pushBack (PointT &&point)
	Adds a point to the back of the polygon.

PointT &	point (uint i)
	Returns the point at index i in the polygon.

const PointT &	point (uint i) const
	Returns the point at index i in the polygon.

ScalarType	sideLength (uint i) const
	Returns the side length of the i-th side of the polygon.

PointT	normal () const
	Computes the normal of the polygon.

PointT	barycenter () const
	Computes the barycenter of the polygon.

template<typename WIterator >
PointT	weightedBarycenter (WIterator wBegin) const
	Computes the weighted barycenter of the polygon.

ScalarType	perimeter () const
	Returns the perimeter of the polygon.

ScalarType	area () const
	Returns the area of the polygon.

PointType &	operator[] (uint i)
	Returns the i-th point of the polygon.

const PointType &	operator[] (uint i) const
	Returns the i-th point of the polygon.

Iterator	begin ()
	Returns an iterator pointing to the first point of the polygon.

Iterator	end ()
	Returns an iterator pointing past the last point of the polygon.

ConstIterator	begin () const
	Returns a const iterator pointing to the first point of the polygon.

ConstIterator	end () const
	Returns a const iterator pointing past the last point of the polygon.

Static Public Member Functions
template<typename Iterator > requires ( std::is_same_v<typename Iterator::value_type, PointT> && PointT::DIM == 3)
static PointT	normal (Iterator begin, Iterator end)
	Computes the normal of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

template<Range R>
static PointT	normal (R &&range)
	Computes the normal of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

template<typename Iterator > requires (std::is_same_v<typename Iterator::value_type, PointT>)
static PointT	barycenter (Iterator begin, Iterator end)
	Computes the barycenter of a container of points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

template<Range R>
static PointT	barycenter (R &&range)
	Computes the barycenter of a container of points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

template<typename Iterator , typename WIterator > requires (std::is_same_v<typename Iterator::value_type, PointT>)
static PointT	weightedBarycenter (Iterator begin, Iterator end, WIterator wBegin)
	Computes the weighted barycenter of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon. Weights are iterated by another iterator wBegin, which iterates to a container of the same size of the polygon container.

template<Range Rp, Range Rw>
static PointT	weightedBarycenter (Rp &&rPolygon, Rw &&rWeights)
	Computes the weighted barycenter of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon. Weights are iterated by another iterator wBegin, which iterates to a container of the same size of the polygon container.

template<typename Iterator > requires (std::is_same_v<typename Iterator::value_type, PointT>)
static ScalarType	perimeter (Iterator begin, Iterator end)
	Calculates the perimeter of a polygon defined by a range of points.

template<Range R>
static ScalarType	perimeter (R &&range)
	Calculates the perimeter of a polygon defined by a range of points.

template<typename Iterator > requires (std::is_same_v<typename Iterator::value_type, PointT>)
static ScalarType	area (Iterator begin, Iterator end)
	Calculates the area of a polygon. This function works also with simple triangles, but it is less efficient thant the function "Triangle<PointT>::area()".

template<Range R>
static ScalarType	area (R &&range)
	Calculates the area of a polygon. This function works also with simple triangles, but it is less efficient thant the function "Triangle<PointT>::area()".

Static Public Attributes
static const uint	DIM = PointT::DIM
	The dimension of the points that define the polygon.

Private Attributes
std::vector< PointT >	mPoints

Detailed Description

template<PointConcept PointT>
class vcl::Polygon< PointT >

The Polygon class represents a polygon in a N-dimensional Euclidean space.

The class allows to store a sequence of points that define a polygon, and provides a set of member functions to compute properties of the polygon, such as the normal, the barycenter, the perimeter, the area... The class also provides a series of static member functions to compute these properties for a polygon defined by a range of points.

Template Parameters

PointT The type of the points that define the polygon.

Constructor & Destructor Documentation

◆ Polygon() [1/3]

template<PointConcept PointT>

vcl::Polygon< PointT >::Polygon ( std::initializer_list< PointT > points )

inline

Construct a new Polygon object from an initializer list of points.

Parameters

[in] points the list of points that define the polygon.

◆ Polygon() [2/3]

template<PointConcept PointT>

template<typename Iterator >
requires (std::is_same_v<typename Iterator::value_type, PointT>)

vcl::Polygon< PointT >::Polygon	(	Iterator	begin,
		Iterator	end
	)

inline

Construct a new Polygon object from a range of points.

Template Parameters

Iterator an iterator which points to a type that satisfies the PointConcept.

Parameters

[in]	begin	iterator pointing to the first point of the polygon.
[in]	end	end iterator.

◆ Polygon() [3/3]

template<PointConcept PointT>

template<Range R>
requires (InputRange<R, PointT>)

vcl::Polygon< PointT >::Polygon ( R && range )

inline

Construct a new Polygon object from a range of points.

Template Parameters

R	a range of points that satisfy the PointConcept.

Parameters

[in] range the range of points that define the polygon.

Member Function Documentation

◆ area() [1/3]

template<PointConcept PointT>

ScalarType vcl::Polygon< PointT >::area ( ) const

inline

Returns the area of the polygon.

Returns: The area of the polygon.

◆ area() [2/3]

template<PointConcept PointT>

template<typename Iterator >
requires (std::is_same_v<typename Iterator::value_type, PointT>)

static ScalarType vcl::Polygon< PointT >::area	(	Iterator	begin,
		Iterator	end
	)

inlinestatic

Calculates the area of a polygon. This function works also with simple triangles, but it is less efficient thant the function "Triangle<PointT>::area()".

Template Parameters

Iterator an iterator which points to a type that satisfies the PointConcept.

Parameters

[in]	begin	an iterator pointing to the first point in the polygon
[in]	end	an iterator pointing past the last point in the polygon

Returns: the area of the polygon

Note: The points in the polygon must have a scalar type, and must satisfy the PointConcept concept.; The polygon must be simple, i.e., it cannot intersect itself.

◆ area() [3/3]

template<PointConcept PointT>

template<Range R>

static ScalarType vcl::Polygon< PointT >::area ( R && range )

inlinestatic

Calculates the area of a polygon. This function works also with simple triangles, but it is less efficient thant the function "Triangle<PointT>::area()".

Template Parameters

R	a range of points that satisfy the PointConcept.

Parameters

[in] range the range of points that define the polygon.

Returns: The area of the polygon.

◆ barycenter() [1/3]

template<PointConcept PointT>

PointT vcl::Polygon< PointT >::barycenter ( ) const

inline

Computes the barycenter of the polygon.

The barycenter is computed as the average of the points that define the polygon.

Returns: The barycenter of the polygon.

◆ barycenter() [2/3]

template<PointConcept PointT>

template<typename Iterator >
requires (std::is_same_v<typename Iterator::value_type, PointT>)

static PointT vcl::Polygon< PointT >::barycenter	(	Iterator	begin,
		Iterator	end
	)

inlinestatic

Computes the barycenter of a container of points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

Template Parameters

Iterator an iterator which points to a type that satisfies the PointConcept.

Parameters

[in]	begin	iterator pointing to the first point of the polygon.
[in]	end	end iterator

Returns: The barycenter of the polygon.

◆ barycenter() [3/3]

template<PointConcept PointT>

template<Range R>

static PointT vcl::Polygon< PointT >::barycenter ( R && range )

inlinestatic

Computes the barycenter of a container of points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

Template Parameters

R	a range of points that satisfy the PointConcept.

Parameters

[in] range the range of points that define the polygon.

Returns: The barycenter of the polygon.

◆ normal() [1/3]

template<PointConcept PointT>

PointT vcl::Polygon< PointT >::normal ( ) const

inline

Computes the normal of the polygon.

The normal is computed as the normalized sum of the cross products of each triplet of consecutive points.

Note: This function requires that the dimension of the points that define the polygon is 3.

Returns: The normal of the polygon.

◆ normal() [2/3]

template<PointConcept PointT>

template<typename Iterator >
requires ( std::is_same_v<typename Iterator::value_type, PointT> && PointT::DIM == 3)

static PointT vcl::Polygon< PointT >::normal	(	Iterator	begin,
		Iterator	end
	)

inlinestatic

Computes the normal of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

The normal is computed as the normalized sum of the cross products of each triplet of consecutive points.

Template Parameters

Iterator an iterator which points to a type that satisfies the PointConcept.

Parameters

[in]	begin	iterator pointing to the first point of the polygon.
[in]	end	end iterator

Returns: The normal of the polygon.

◆ normal() [3/3]

template<PointConcept PointT>

template<Range R>

static PointT vcl::Polygon< PointT >::normal ( R && range )

inlinestatic

Computes the normal of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon.

Template Parameters

R	a range of points that satisfy the PointConcept.

Parameters

[in] range the range of points that define the polygon.

Returns: The normal of the polygon.

◆ operator[]() [1/2]

template<PointConcept PointT>

PointType & vcl::Polygon< PointT >::operator[] ( uint i )

inline

Returns the i-th point of the polygon.

Parameters

i	the index of the point to return.

Returns: The i-th point of the polygon.

◆ operator[]() [2/2]

template<PointConcept PointT>

const PointType & vcl::Polygon< PointT >::operator[] ( uint i ) const

inline

Returns the i-th point of the polygon.

Parameters

i	the index of the point to return.

Returns: The i-th point of the polygon.

◆ perimeter() [1/3]

template<PointConcept PointT>

ScalarType vcl::Polygon< PointT >::perimeter ( ) const

inline

Returns the perimeter of the polygon.

Returns: The perimeter of the polygon.

◆ perimeter() [2/3]

template<PointConcept PointT>

template<typename Iterator >
requires (std::is_same_v<typename Iterator::value_type, PointT>)

static ScalarType vcl::Polygon< PointT >::perimeter	(	Iterator	begin,
		Iterator	end
	)

inlinestatic

Calculates the perimeter of a polygon defined by a range of points.

The function calculates the perimeter of a polygon defined by a range of points. The function takes two iterators as input, representing the beginning and end of the range of points. The points in the range must satisfy the PointConcept, which is a concept that requires the point type to have a ScalarType and a dist() function that calculates the distance between two points.

Template Parameters

Iterator an iterator which points to a type that satisfies the PointConcept.

Parameters

[in]	begin	An iterator pointing to the first point in the range.
[in]	end	An iterator pointing to one past the last point in the range.

Returns: The perimeter of the polygon defined by the range of points.

◆ perimeter() [3/3]

template<PointConcept PointT>

template<Range R>

static ScalarType vcl::Polygon< PointT >::perimeter ( R && range )

inlinestatic

Calculates the perimeter of a polygon defined by a range of points.

Template Parameters

R	a range of points that satisfy the PointConcept.

Parameters

[in] range the range of points that define the polygon.

Returns: The perimeter of the polygon.

◆ point() [1/2]

template<PointConcept PointT>

PointT & vcl::Polygon< PointT >::point ( uint i )

inline

Returns the point at index i in the polygon.

Parameters

[in] i the index of the point to return.

◆ point() [2/2]

template<PointConcept PointT>

const PointT & vcl::Polygon< PointT >::point ( uint i ) const

inline

Returns the point at index i in the polygon.

Parameters

[in] i the index of the point to return.

◆ pushBack() [1/2]

template<PointConcept PointT>

void vcl::Polygon< PointT >::pushBack ( const PointT & point )

inline

Adds a point to the back of the polygon.

Parameters

[in] point the point to add to the polygon.

◆ pushBack() [2/2]

template<PointConcept PointT>

void vcl::Polygon< PointT >::pushBack ( PointT && point )

inline

Adds a point to the back of the polygon.

Parameters

[in] point the point to add to the polygon.

◆ reserve()

template<PointConcept PointT>

void vcl::Polygon< PointT >::reserve ( uint n )

inline

Reserves space for n points in the polygon.

Parameters

[in] n the number of points for which to reserve space.

◆ resize()

template<PointConcept PointT>

void vcl::Polygon< PointT >::resize ( uint n )

inline

Resizes the polygon to contain n points.

Parameters

[in] n the number of points that the polygon should contain.

◆ sideLength()

template<PointConcept PointT>

ScalarType vcl::Polygon< PointT >::sideLength ( uint i ) const

inline

Returns the side length of the i-th side of the polygon.

The i-th side is the side that connects the i-th point with the (i+1)-th point, where the indices are taken modulo the number of points in the polygon.

Parameters

[in] i the index of the side for which to compute the length.

◆ size()

template<PointConcept PointT>

uint vcl::Polygon< PointT >::size ( ) const

inline

Returns the number of points that define the polygon.

Returns: The number of points that define the polygon.

◆ weightedBarycenter() [1/3]

template<PointConcept PointT>

template<typename Iterator , typename WIterator >
requires (std::is_same_v<typename Iterator::value_type, PointT>)

static PointT vcl::Polygon< PointT >::weightedBarycenter	(	Iterator	begin,
		Iterator	end,
		WIterator	wBegin
	)

inlinestatic

Computes the weighted barycenter of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon. Weights are iterated by another iterator wBegin, which iterates to a container of the same size of the polygon container.

Template Parameters

Iterator	an iterator which points to a type that satisfies the PointConcept.
WIterator	an iterator which points to a scalar type.

Parameters

[in]	begin	iterator pointing to the first point of the polygon.
[in]	end	end iterator of the polygon container.
[in]	wBegin	iterator pointing to the first weight associated to the fist polygon point.

Returns: The weighted barycenter of the polygon.

◆ weightedBarycenter() [2/3]

template<PointConcept PointT>

template<Range Rp, Range Rw>

static PointT vcl::Polygon< PointT >::weightedBarycenter	(	Rp &&	rPolygon,
		Rw &&	rWeights
	)

inlinestatic

Computes the weighted barycenter of a container of 3D points iterated between the iterators begin and end, listed in counterclockwise order, representing a polygon. Weights are iterated by another iterator wBegin, which iterates to a container of the same size of the polygon container.

Template Parameters

Rp	a range of points that satisfy the PointConcept.
Rw	a range of weights.

Parameters

[in]	rPolygon	the range of points that define the polygon.
[in]	rWeights	the range of weights associated to the points.

Returns: The weighted barycenter of the polygon.

◆ weightedBarycenter() [3/3]

template<PointConcept PointT>

template<typename WIterator >

PointT vcl::Polygon< PointT >::weightedBarycenter ( WIterator wBegin ) const

inline

Computes the weighted barycenter of the polygon.

The weighted barycenter is computed as the weighted average of the points that define the polygon. The weights are provided by a container of the same size as the polygon, iterated by the iterator wBegin.

Template Parameters

WIterator an iterator which points to a scalar type.

Parameters

[in] wBegin iterator pointing to the first weight associated to the fist polygon point.

Returns: The weighted barycenter of the polygon.

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

vclib/core/include/vclib/space/core/polygon.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Polygon() [1/3]

◆ Polygon() [2/3]

◆ Polygon() [3/3]

Member Function Documentation

◆ area() [1/3]

◆ area() [2/3]

◆ area() [3/3]

◆ barycenter() [1/3]

◆ barycenter() [2/3]

◆ barycenter() [3/3]

◆ normal() [1/3]

◆ normal() [2/3]

◆ normal() [3/3]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ perimeter() [1/3]

◆ perimeter() [2/3]

◆ perimeter() [3/3]

◆ point() [1/2]

◆ point() [2/2]

◆ pushBack() [1/2]

◆ pushBack() [2/2]

◆ reserve()

◆ resize()

◆ sideLength()

◆ size()

◆ weightedBarycenter() [1/3]

◆ weightedBarycenter() [2/3]

◆ weightedBarycenter() [3/3]