Dodecahedron Class Reference

A dodecahedron. More...

#include <dodecahedron.h>

Public Member Functions
	Dodecahedron (const double &=1.0)
	Create a dodecahedron. More...
	Dodecahedron (const Vector &, const double &)
	Create a dodecahedron. More...
double	Volume () const
	Compute the volume of the dodecahedron.
double	Area () const
	Compute the area of the dodecahedron.
double	Radius () const
	Compute the radius of the circmscribed sphere of the dodecahedron.
Vector	Vertex (int) const
	Return the i-th vertex. More...
Vector	Vertex (int, int) const
	Return the j-th vertex of the i-th face. More...
Vector	Normal (int) const
	Return the normal to the i-th face as a normalized vector. More...
Box	GetBox () const
	Return the bounding box of the shape.
Plane	GetPlane (int) const
	Return the plane of the k-th face. More...
bool	Inside (const Vector &) const
	Check if a point is inside. More...
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the dodecahedron. More...
double	Signed (const Vector &) const
	Compute the approximate signed distance to the dodecahedron. More...
bool	Intersect (const Ray &, double &, double &, int &, int &) const
	Compute the intersection between a dodecahedron 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. More...

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

Static Protected Attributes
static const double	R2 = sqrt(3.0)
	Radius of the circumscribed sphere of an dodecahedron with edge length 2.0/Phi.
static const double	Phi = (1 + sqrt(5.0)) / 2.0
	Golden ratio.
static const Vector	vertex [20]
	Array of vertices.
static const Vector	normal [12]
	Array of normals.
static const int	face [12][5]
	Array of pentagons.

Detailed Description

A dodecahedron.

The following Cartesian coordinates define the vertices of a dodecahedron with edge-length 2/ φ, centered at the origin.

( ± 1, ± 1, ± 1)

(0, ± 1/ φ, ± φ)

( ± 1/ φ, ± φ, 0)

( ± φ, 0, ± 1/ φ)

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

Constructor & Destructor Documentation

Dodecahedron() [1/2]

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

explicit

Create a dodecahedron.

Parameters

r

Radius.

Dodecahedron() [2/2]

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

explicit

Create a dodecahedron.

Parameters

c	Center.
r	Radius.

Member Function Documentation

GetPlane()

Plane Dodecahedron::GetPlane

(

int

k

)

const

Return the plane of the k-th face.

Parameters

k

Index.

Inside()

bool Dodecahedron::Inside

(

const Vector &

p

)

const

Check if a point is inside.

Parameters

p	The point.

Intersect()

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

Compute the intersection between a dodecahedron and a ray.

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

Parameters

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

Normal()

Vector Dodecahedron::Normal ( int  i ) const

inline

Return the normal to the i-th face as a normalized vector.

Parameters

i

Index.

RandomInside()

Vector Dodecahedron::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the dodecahedron.

Uses a simple rejection method.

Parameters

random

Random number generator.

Signed()

double Dodecahedron::Signed

(

const Vector &

p

)

const

Compute the approximate signed distance to the dodecahedron.

Parameters

p

Point.

Vertex() [1/2]

Vector Dodecahedron::Vertex ( int  i ) const

inline

Return the i-th vertex.

Parameters

i

Index.

Vertex() [2/2]

Vector Dodecahedron::Vertex ( int  i, int  j  ) const

inline

Return the j-th vertex of the i-th face.

Parameters

i	Face (pentagon).
j	Index representing the j-th vertex of the face.

VertexIndex()

constexpr int Dodecahedron::VertexIndex ( int  i, int  j  )

inlinestaticconstexpr

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

Parameters

i	Face (pentagon).
j	Index representing the j-th vertex of the face.