Icosahedron Class Reference

An icosahedron. More...

#include <icosahedron.h>

Public Member Functions
	Icosahedron (const Vector &, const double &)
	Creates an icosahedron given its center and radius. More...
	Icosahedron (const double &=1.0)
	Creates an icosahedron. More...
double	Volume () const
	Compute the volume of the icosahedron.
double	Area () const
	Compute the area of the icosahedron.
double	Radius () const
	Compute the radius of the circmscribed sphere of the icosahedron.
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 to the i-th face as a normalized vector.
Box	GetBox () const
	Return the bounding box.
Plane	GetPlane (int) const
	Return the plane of the k-th face.
bool	Inside (const Vector &) const
	Check if a point is inside. More...
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the icosahedron. More...
double	Signed (const Vector &) const
	Compute the approximate signed distance to the icosahedron. More...
bool	Intersect (const Ray &, double &, double &, int &, int &) const
	Compute the intersection between an icosahedron and a ray. More...

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

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

Static Protected Attributes
static const double	R2 = (1.0 / 4.0) * sqrt(10 + 2.0 * sqrt(5.0)) * 2.0
	Radius of the circumscribed sphere of an icosahedron with edge length 2.
static const double	Phi = (1 + sqrt(5.0)) / 2.0
	Phi.
static const Vector	vertex [12]
	Array of vertices.
static const Vector	normal [20]
	Array of normals.
static const int	edge [30][2]
	Array of edges.
static const int	face [20][3]
	Array of pentagons.

Detailed Description

An icosahedron.

The following Cartesian coordinates define the vertices of an icosahedron with edge-length 2, centered at the origin.

(0, ± 1, ± φ)

( ± 1, ± φ,0)

( ± φ,0, ± 1)

where φ=(1+sqrt(5))/2 is the golden ratio.

Constructor & Destructor Documentation

Icosahedron() [1/2]

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

explicit

Creates an icosahedron given its center and radius.

Parameters

c	Center.
r	Radius.

Icosahedron() [2/2]

Icosahedron::Icosahedron ( const double &  r = 1.0 )

explicit

Creates an icosahedron.

Parameters

r

Radius.

Member Function Documentation

Inside()

bool Icosahedron::Inside

(

const Vector &

p

)

const

Check if a point is inside.

Parameters

p	The point.

Intersect()

bool Icosahedron::Intersect	(	const Ray &	ray,
		double &	ta,
		double &	tb,
		int &	fa,
		int &	fb
	)		const

Compute the intersection between an icosahedron and a ray.

Intersect the ray with the planes corresponding to the faces of the convex icosahedron.

Parameters

ray	The ray.
ta,tb	Intersection depths.
fa,fb	Index of the intersected faces.

RandomInside()

Vector Icosahedron::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the icosahedron.

Uses a simple rejection method.

Parameters

random

Random number generator.

Signed()

double Icosahedron::Signed

(

const Vector &

p

)

const

Compute the approximate signed distance to the icosahedron.

Parameters

p

Point.

VertexEdgeIndex()

constexpr int Icosahedron::VertexEdgeIndex ( int  i, int  j  )

inlinestaticconstexpr

Return the index of the j-th vertex of the i-th edge.

Parameters

i	Edge.
j	Vertex (should be O or 1).