Cuboctahedron Class Reference

A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. More...

#include <cuboctahedron.h>

Public Member Functions
	Cuboctahedron (const Vector &, const double &)
	Creates a cuboctahedron.
	Cuboctahedron (const double &)
	Creates a cuboctahedron.
double	Volume () const
	Compute the volume of the cuboctahedron.
double	Area () const
	Compute the area of the cuboctahedron.
Vector	Vertex (int) const
	Return the i-th vertex as a vector.
Vector	Vertex (int, int) const
	Return the j-th vertex of the i-th face.
Vector	Normal (int) const
	Return the normal of the i-th face.
bool	Inside (const Vector &) const
	Check if a point is inside a cuboctahedron.
double	Signed (const Vector &) const
	Compute the signed distance approximation.
double	R (const Vector &) const
	Compute the squared distance approximation.
Box	GetBox () const
	Return the bounding box of the cuboctahedron.

Static Public Member Functions
static constexpr int	VertexIndex (int, int)
	Return the index of the j-th vertex of the i-th face.

Protected Member Functions
double	EdgeLength () const
	Compute the length of an edge.

Protected Attributes
Vector	c = Vector::Null
	Center.
double	r = 1.0
	Radius.

Static Protected Attributes
static const Vector	vertex [12]
	Array of vertices.
static const Vector	normal [14]
	Array of normals.

Detailed Description

A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square.

Constructor & Destructor Documentation

Cuboctahedron() [1/2]

Cuboctahedron::Cuboctahedron ( const Vector & c, const double & r )

explicit

Creates a cuboctahedron.

Parameters

c	Center.
r	Radius.

Cuboctahedron() [2/2]

Cuboctahedron::Cuboctahedron ( const double & r )

explicit

Creates a cuboctahedron.

Parameters

r

Radius.

Member Function Documentation

Inside()

bool Cuboctahedron::Inside

(

const Vector &

p

)

const

Check if a point is inside a cuboctahedron.

Parameters

p

Point.

Normal()

Vector Cuboctahedron::Normal ( int i ) const

inline

Return the normal of the i-th face.

Note that the first 8 faces are triangles, and the 6 last are squares.

Parameters

i	Index, should be 0 ≤ i ≤ 14.

R()

double Cuboctahedron::R

(

const Vector &

p

)

const

Compute the squared distance approximation.

Parameters

p

Point.

Signed()

double Cuboctahedron::Signed

(

const Vector &

p

)

const

Compute the signed distance approximation.

Parameters

p

Point.