Octahedron Class Reference

An axis aligned octahedron. More...

#include <octahedron.h>

Public Member Functions
	Octahedron (const Vector &, const Vector &)
	Creates an octahedron given the vertices of its bounding box. More...
	Octahedron (const Vector &, const double &)
	Creates an octahedron given its center and radius. More...
	Octahedron (const double &)
	Creates an octahedron. More...
double	Volume () const
	Compute the volume of the octahedron. More...
double	Area () const
	Compute the area of the octahedron. More...
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
	Compute the normal to the i-th face as a normalized vector.
Vector	Normal (const Vector &) const
	Compute the normal vector between a point and the octahedron. More...
double	R (const Vector &) const
	Compute the squared Euclidean distance between a point and the octahedron. More...
double	Signed (const Vector &) const
	Compute the signed Euclidean distance between a point and the octahedron. More...
Plane	GetPlane (int) const
	Return the plane of the k-th face. More...
Box	GetBox () const
	Return the bounding box of the octahedron.
bool	Inside (const Vector &) const
	Check if a point is inside the octahedron. More...

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

Protected Attributes
Vector	center
	Center.
Vector	half
	Half diagonal of the box.
Vector	planenormal
	Normal to the plane in the first octant.
Vector	ezxn
	Edge normals.

Static Protected Attributes
static const int	face [8][3]
	Array of triangles.
static const Vector	vertex [6]
	Array of internal vertexes for computing vertices.

Detailed Description

An axis aligned octahedron.

Constructor & Destructor Documentation

Octahedron() [1/3]

Octahedron::Octahedron ( const Vector &  a, const Vector &  b  )

explicit

Creates an octahedron given the vertices of its bounding box.

Parameters

a,b

Vectors.

Octahedron() [2/3]

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

explicit

Creates an octahedron given its center and radius.

Parameters

c	Center.
r	Radius.

Octahedron() [3/3]

Octahedron::Octahedron ( const double &  r )

explicit

Creates an octahedron.

Parameters

r

Radius.

Member Function Documentation

Area()

double Octahedron::Area ( ) const

inline

Compute the area of the octahedron.

It is 8 times the area of one of its triangular faces.

The code has been optimized, instead of computing the normal of the triangle using Triangle::Normal(), the cross product has been inlined.

GetPlane()

Plane Octahedron::GetPlane

(

int

k

)

const

Return the plane of the k-th face.

Parameters

k

Index.

Inside()

bool Octahedron::Inside

(

const Vector &

p

)

const

Check if a point is inside the octahedron.

Parameters

p

Point.

Normal()

Vector Octahedron::Normal

(

const Vector &

p

)

const

Compute the normal vector between a point and the octahedron.

Parameters

p

Point.

R()

double Octahedron::R

(

const Vector &

p

)

const

Compute the squared Euclidean distance between a point and the octahedron.

Parameters

p	The point.

Signed()

double Octahedron::Signed

(

const Vector &

p

)

const

Compute the signed Euclidean distance between a point and the octahedron.

Parameters

p

Point.

Volume()

double Octahedron::Volume ( ) const

inline

Compute the volume of the octahedron.

It is 8 times the volume of a tetrahedron. Since three vectors are orthogonal, the volume is 1/6 the volume of a half box (thus 1/48 the volume of the box).