ptems::Polytope< DIM > Class Template Reference

Class for specifying indices of vertices for defining a DIM-dimensional polytope. More...

#include <ptems/polytope.hpp>

Public Member Functions
	Polytope ()
	Creates an empty polytope. More...
template<typename It >
	Polytope (It begin, It end)
	Creates a polytope from a list of (DIM-1)-dimensional polytopes denoting the faces of this polytope. More...
	Polytope (std::set< Polytope< DIM-1 >> &&faces)
	Creates a polytope from a list of DIM-1 dimensional polytopes denoting the faces of this polytope. More...
	Polytope (const std::initializer_list< Polytope< DIM-1 >> &faces)
	Creates a polytope from a list of DIM-1 dimensional polytopes denoting the faces of this polytope. More...
void	AddFace (Polytope< DIM-1 > &&face)
	Adds a face to the polytope. More...
void	AddFace (const Polytope< DIM-1 > &face)
	Adds a face to the polytope. More...
template<typename... ARGS>
void	AddFace (const ARGS &... face)
	Adds a face to the polytope by in-place construction. More...
const std::set< Polytope< DIM-1 > >	Faces () const
	Gets a list of the faces in the polytope. More...
template<typename V >
bool	Validate ([[maybe_unused]] const V &vertexList) const
	Checks if the polytope defines a valid polytope. More...
int	Compare (const Polytope &rhs) const
	Compares this polytope to the specified polytope with strict ordering. More...

Related Functions
(Note that these are not member functions.)
template<std::size_t DIM>
bool	operator== (const Polytope< DIM > &lhs, const Polytope< DIM > &rhs)
	Checks if the specified polytopes are equivalent (same faces) More...
template<std::size_t DIM>
bool	operator!= (const Polytope< DIM > &lhs, const Polytope< DIM > &rhs)
	Checks if the specified polytopes are not equivalent (different faces) More...
template<std::size_t DIM>
bool	operator< (const Polytope< DIM > &lhs, const Polytope< DIM > &rhs)
	Less than operator for strict ordering of polytopes. More...
template<std::size_t DIM>
bool	operator<= (const Polytope< DIM > &lhs, const Polytope< DIM > &rhs)
	Less than or equal operator for strict ordering of polytopes. More...
template<std::size_t DIM>
bool	operator> (const Polytope< DIM > &lhs, const Polytope< DIM > &rhs)
	Greater than operator for strict ordering of polytopes. More...
template<std::size_t DIM>
bool	operator>= (const Polytope< DIM > &lhs, const Polytope< DIM > &rhs)
	Greater than or equal operator for strict ordering of polytopes. More...
Polytope< 3 >	CreateTetrahedron (std::size_t p1, std::size_t p2, std::size_t p3, std::size_t apex)
	Creates a polytope for a tetrahedron element. More...
Polytope< 3 >	CreatePyramid (std::size_t p1, std::size_t p2, std::size_t p3, std::size_t p4, std::size_t apex)
	Creates a polytope for a pyramid element. More...
Polytope< 3 >	CreateHexahedron (std::size_t p1, std::size_t p2, std::size_t p3, std::size_t p4, std::size_t p5, std::size_t p6, std::size_t p7, std::size_t p8)
	Creates a polytope for a hexahedron element. More...
Polytope< 3 >	CreatePrism (std::size_t p1, std::size_t p2, std::size_t p3, std::size_t p4, std::size_t p5, std::size_t p6)
	Creates a polytope for a triangular prism element. More...
Polytope< 3 >	CreatePolygonalPrism (const std::initializer_list< std::size_t > &points)
	Creates a polytope for a polygon extruded as a prism. More...
template<typename... T>
Polytope< 3 >	CreatePolygonalPrism (std::size_t p1, T... pN)
	Creates a polytope for a polygon extruded as a prism. More...
Polytope< 3 >	CreatePolygonalPyramid (const std::initializer_list< std::size_t > &points)
	Creates a polytope for a pyramid by extending polygon to a point. More...
template<typename... T>
Polytope< 3 >	CreatePolygonalPyramid (std::size_t p1, T... pN)
	Creates a polytope for a pyramid by extending polygon to a point. More...

Detailed Description

template<std::size_t DIM>
class ptems::Polytope< DIM >

Class for specifying indices of vertices for defining a DIM-dimensional polytope.

Template Parameters

Dimension

of the polytope

Constructor & Destructor Documentation

Polytope() [1/4]

template<std::size_t DIM>

ptems::Polytope< DIM >::Polytope ( )

inline

Creates an empty polytope.

Polytope() [2/4]

template<std::size_t DIM>

template<typename It >

ptems::Polytope< DIM >::Polytope ( It  begin, It  end  )

inline

Creates a polytope from a list of (DIM-1)-dimensional polytopes denoting the faces of this polytope.

Template Parameters

It	The type of the iterator over the list of faces

Parameters

begin	The begin iterator to the list of faces
end	The end iterator to the list of faces

Polytope() [3/4]

template<std::size_t DIM>

ptems::Polytope< DIM >::Polytope ( std::set< Polytope< DIM-1 >> &&  faces )

inline

Creates a polytope from a list of DIM-1 dimensional polytopes denoting the faces of this polytope.

Parameters

faces

List (set) of faces

Polytope() [4/4]

template<std::size_t DIM>

ptems::Polytope< DIM >::Polytope ( const std::initializer_list< Polytope< DIM-1 >> &  faces )

inline

Creates a polytope from a list of DIM-1 dimensional polytopes denoting the faces of this polytope.

Parameters

faces

List of faces

Member Function Documentation

AddFace() [1/3]

template<std::size_t DIM>

template<typename... ARGS>

void ptems::Polytope< DIM >::AddFace ( const ARGS &...  face )

inline

Adds a face to the polytope by in-place construction.

Parameters

face	List of arguments to Polytope<DIM-1> constructor for the polytope defining the face

AddFace() [2/3]

template<std::size_t DIM>

void ptems::Polytope< DIM >::AddFace ( const Polytope< DIM-1 > &  face )

inline

Adds a face to the polytope.

Parameters

face	The face to add to the polytope

AddFace() [3/3]

template<std::size_t DIM>

void ptems::Polytope< DIM >::AddFace ( Polytope< DIM-1 > &&  face )

inline

Adds a face to the polytope.

Parameters

face	The face to add to the polytope

Compare()

template<std::size_t DIM>

int ptems::Polytope< DIM >::Compare ( const Polytope< DIM > &  rhs ) const

inline

Compares this polytope to the specified polytope with strict ordering.

Parameters

rhs	The right hand polytope to compare to

Returns

0 if this polytope is equal to rhs; -1 if in the ordered list of subfaces the first "different" subface polytope for this is less than the rhs (or this has less subfaces than rhs but all faces are equal upto that point); 1 this polytope is greater than rhs (opposite to -1).

Faces()

template<std::size_t DIM>

const std::set<Polytope<DIM-1> > ptems::Polytope< DIM >::Faces ( ) const

inline

Gets a list of the faces in the polytope.

Validate()

template<std::size_t DIM>

template<typename V >

bool ptems::Polytope< DIM >::Validate ( [[maybe_unused] ] const V &  vertexList ) const

inline

Checks if the polytope defines a valid polytope.

This check does not need to be complete (returning true does not guarantee a valid polytope), but at least the following conditions should be met:

• At least DIM+1 faces
• Each face of a face of this polytope appears exactly twice (shared between exactly two faces).
• Each face also returns true for Validate(vertexList)
• Two dimensional (sub)faces are planar

This SHOULD guarantee a closed polytope, but no guarantee about simplicity

Template Parameters

V	Type of vertex list - must be indexable

Parameters

vertexList

List of vertices to look up the polytope vertices in

Returns

true if valid; false otherwise

Friends And Related Function Documentation

CreateHexahedron()

template<std::size_t DIM>

Polytope< 3 > CreateHexahedron ( std::size_t  p1, std::size_t  p2, std::size_t  p3, std::size_t  p4, std::size_t  p5, std::size_t  p6, std::size_t  p7, std::size_t  p8  )

related

Creates a polytope for a hexahedron element.

Parameters

p1,p2,p3,p4	The points of base of the hexahedron in CCW order (viewed from the top)
p5,p6,p7,p8	The points of top of the hexahedron in CCW order (viewed from the top)

<3>

CreatePolygonalPrism() [1/2]

template<std::size_t DIM>

Polytope< 3 > CreatePolygonalPrism ( const std::initializer_list< std::size_t > &  points )

related

Creates a polytope for a polygon extruded as a prism.

Exceptions

std::invalid_argument

If number of points is odd or less than 6

Parameters

points

List of points defining the prism. The first half of the points define the base polygon of the prism and the second half of the points define the top polygon of the prism, both in CCW order (viewed from the top)

<3>

CreatePolygonalPrism() [2/2]

template<typename... T>

Polytope< 3 > CreatePolygonalPrism ( std::size_t  p1, T...  pN  )

related

Creates a polytope for a polygon extruded as a prism.

Template Parameters

T	Should be convertible to std::size_t

Parameters

p1,pN

List of points defining the prism. The first half of the points define the base polygon of the prism and the second half of the points define the top polygon of the prism, both in CCW order (viewed from the top)

<3>

CreatePolygonalPyramid() [1/2]

template<std::size_t DIM>

Polytope< 3 > CreatePolygonalPyramid ( const std::initializer_list< std::size_t > &  points )

related

Creates a polytope for a pyramid by extending polygon to a point.

Exceptions

std::invalid_argument

If number of points is less than 4

Parameters

points

List of points defining the prism. The last point denotes the apex of the pyramid, the rest denote the points of the base of the pyramid in CCW order (viewed from the top)

<3>

CreatePolygonalPyramid() [2/2]

template<typename... T>

Polytope< 3 > CreatePolygonalPyramid ( std::size_t  p1, T...  pN  )

related

Creates a polytope for a pyramid by extending polygon to a point.

Template Parameters

T	Should be convertible to std::size_t

Parameters

p1,pN

List of points defining the prism. The last point denotes the apex of the pyramid, the rest denote the points of the base of the pyramid in CCW order (viewed from the top)

<3>

CreatePrism()

template<std::size_t DIM>

Polytope< 3 > CreatePrism ( std::size_t  p1, std::size_t  p2, std::size_t  p3, std::size_t  p4, std::size_t  p5, std::size_t  p6  )

related

Creates a polytope for a triangular prism element.

Parameters

p1,p2,p3	The points of base triangle of the prism in CCW order (viewed from the top)
p4,p5,p6	The points of top triangle of the prism in CCW order (viewed from the top)

<3>

CreatePyramid()

template<std::size_t DIM>

Polytope< 3 > CreatePyramid ( std::size_t  p1, std::size_t  p2, std::size_t  p3, std::size_t  p4, std::size_t  apex  )

related

Creates a polytope for a pyramid element.

Parameters

p1,p2,p3,p4	The base points of the pyramid in CCW order (viewed from the top)
apex	The apex point

<3>

CreateTetrahedron()

template<std::size_t DIM>

Polytope< 3 > CreateTetrahedron ( std::size_t  p1, std::size_t  p2, std::size_t  p3, std::size_t  apex  )

related

Creates a polytope for a tetrahedron element.

Parameters

p1,p2,p3	The base points of the tetrahedon in CCW order (viewed from the top)
apex	The apex point

<3>

operator!=()

template<std::size_t DIM>

bool operator!= ( const Polytope< DIM > &  lhs, const Polytope< DIM > &  rhs  )

related

Checks if the specified polytopes are not equivalent (different faces)

Returns

true if not equivalent; false otherwise

operator<()

template<std::size_t DIM>

bool operator< ( const Polytope< DIM > &  lhs, const Polytope< DIM > &  rhs  )

related

Less than operator for strict ordering of polytopes.

Returns

lhs.Compare(rhs) < 0

operator<=()

template<std::size_t DIM>

bool operator<= ( const Polytope< DIM > &  lhs, const Polytope< DIM > &  rhs  )

related

Less than or equal operator for strict ordering of polytopes.

Returns

lhs.Compare(rhs) <= 0

operator==()

template<std::size_t DIM>

bool operator== ( const Polytope< DIM > &  lhs, const Polytope< DIM > &  rhs  )

related

Checks if the specified polytopes are equivalent (same faces)

Returns

true if equivalent; false otherwise

operator>()

template<std::size_t DIM>

bool operator> ( const Polytope< DIM > &  lhs, const Polytope< DIM > &  rhs  )

related

Greater than operator for strict ordering of polytopes.

Returns

lhs.Compare(rhs) > 0

operator>=()

template<std::size_t DIM>

bool operator>= ( const Polytope< DIM > &  lhs, const Polytope< DIM > &  rhs  )

related

Greater than or equal operator for strict ordering of polytopes.

Returns

lhs.Compare(rhs) >= 0

---

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

• ptems/polytope.hpp