Icosidodecahedron Class Reference

An icosidodecahedron. More...

#include <dodecahedron.h>

Public Member Functions
	Icosidodecahedron (const Vector &, const double &)
	Create an icosidodecahedron given its center and radius.
	Icosidodecahedron (const double &)
	Create an icosidodecahedron given its radius.
double	Volume () const
	Compute the volume.
double	Area () const
	Compute the area.
double	Radius () const
	Return the radius of the circmscribed sphere of the icosi-dodecahedron.
Vector	Vertex (int) const
	Return the i-th vertex.
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.
QVector< Vector >	Vertexes () const
	Get all vertexes.
Box	GetBox () const
	Return the bounding box of the shape.
Plane	GetPlane (int) const
	Return the plane of the k-th face.
bool	Intersect (const Ray &, double &, double &, int &, int &) const
	Compute the intersection with a ray.
bool	Inside (const Vector &) const
	Check if a point is inside.
double	Signed (const Vector &) const
	Compute the approximate signed distance to the icosahedron.

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

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

Static Protected Attributes
static const double	R2 = sqrt(3.0)
	Radius of the circumscribed sphere of an icosidodecahedron with edge length 2.0/Phi.
static const double	Phi = (1 + sqrt(5.0)) / 2.0
	Golden ratio.
static const Vector	vertex [30]
	Array of vertices.
static const Vector	normal [32]
	Array of normals.
static const int	pentagon [12][5]
	Array of pentagons.
static const int	triangle [20][3]
	Array of triangles.

Friends
std::ostream &	operator<< (std::ostream &s, const Icosidodecahedron &icosi)
	Overloaded.

Detailed Description

An icosidodecahedron.

See also

Dodecahedron, Icosahedron

Constructor & Destructor Documentation

Icosidodecahedron() [1/2]

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

explicit

Create an icosidodecahedron given its center and radius.

Parameters

c	Center.
r	Radius.

Icosidodecahedron() [2/2]

Icosidodecahedron::Icosidodecahedron ( const double & r )

explicit

Create an icosidodecahedron given its radius.

Parameters

r

Radius.

Member Function Documentation

GetPlane()

Plane Icosidodecahedron::GetPlane

(

int

k

)

const

Return the plane of the k-th face.

Parameters

k	Face, pentagon if k in [0,11], and triangle if k in [12,31]

Inside()

bool Icosidodecahedron::Inside

(

const Vector &

p

)

const

Check if a point is inside.

Parameters

p	The point.

Intersect()

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

Compute the intersection with a ray.

Parameters

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

Normal()

Vector Icosidodecahedron::Normal ( int i ) const

inline

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

Parameters

i

Index.

Signed()

double Icosidodecahedron::Signed

(

const Vector &

p

)

const

Compute the approximate signed distance to the icosahedron.

Parameters

p

Point.

Vertex() [1/2]

Vector Icosidodecahedron::Vertex ( int i ) const

inline

Return the i-th vertex.

Parameters

i

Index.

Vertex() [2/2]

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

inline

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

Parameters

i	Face number, starting with the 12 pentagons, and following with the 20 triangles.
j	Index representing the j-th vertex of the face.

VertexPentagonIndex()

int Icosidodecahedron::VertexPentagonIndex ( int i, int j )

inlinestatic

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

Parameters

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

VertexTriangleIndex()

int Icosidodecahedron::VertexTriangleIndex ( int i, int j )

inlinestatic

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

Parameters

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

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Icosidodecahedron & icosi )

friend

Overloaded.

Parameters

s	Stream.
icosi	The icosidodecahedron.