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

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 = Vector::Null
	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).