Torus Class Reference

A simple torus. More...

#include <torus.h>

Inheritance diagram for Torus:

Public Member Functions
	Torus (const Vector &, const Vector &, const double &=1.0, const double &=1.0)
	Creates a torus.
	Torus (const Circle &, const double &=1.0)
	Create a torus.
	Torus (const double &, const double &=1.0)
	Create a horizontal torus centered at origin.
	~Torus ()
	Empty.
int	Intersect (const Ray &, double *, Vector *) const
	Computes the intersection depths and the normals between a ray and a torus.
bool	Inside (const Vector &) const
	Check if a point is inside or outside the torus.
Box	GetBox () const
	Computes the bounding box of a torus.
double	R (const Vector &) const
	Compute the squared Euclidean distance between a point and the torus.
double	Signed (const Vector &) const
	Compute the signed Euclidean distance between a point and the torus.
Vector	Normal (const Vector &) const
	Computes the distance vector between a torus and a given point.
double	Area () const
	Compute the surface area of a torus.
double	Volume () const
	Compute the volume of a torus.
double	Small () const
	Return the small radius of the torus.
void	Scale (const double &)
	Uniformly scales a torus.
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the dodecahedron.
Public Member Functions inherited from Circle
	Circle ()
	Empty.
	Circle (const double &)
	Creates a circle.
	Circle (const Vector &, const Vector &, const double &)
	Creates a circle.
	Circle (const Vector &, const Vector &, const Vector &)
	Creates a circle given three points.
	~Circle ()
	Empty.
bool	Intersect (const Ray &, double &) const
	Compute the ray-disc intersection.
Vector	Center () const
	Gets the center of a circle.
Vector	Axis () const
	Axis of the circle.
double	Radius () const
	Radius of the circle.
double	R (const Vector &) const
	Compute the distance between a point and a circle.
Vector	Normal (const Vector &) const
	Computes the distance vector between a circle and a point.
void	Rotate (const Matrix &)
	Rotates a circle.
void	Translate (const Vector &)
	Translates a circle.
void	Scale (const double &)
	Uniformly scales a circle.
Box	GetBox () const
	Compute the axis aligned bounding box of a circle.
double	Area () const
	Area of a circle.
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the circle.
Vector	RandomOn (Random &=Random::R239) const
	Generate a random vector on the circle.
Vector	Vogel (int, int) const
	Generate a spiraling vector in the disc.

Static Public Attributes
static constexpr const double	epsilon = 1e-06
	Epsilon constant for some inside-outside functions.
static const Torus	Unit
	Unit vertical torus, major and minor radii equal to 1.

Protected Attributes
double	s = 1.0
	Small radius of the torus.
Protected Attributes inherited from Circle
Vector	c = Vector::Null
	Center of the circle.
Vector	axis = Vector::Z
	Axis.
double	r = 1.0
	Radius.

Friends
std::ostream &	operator<< (std::ostream &s, const Torus &torus)
	Overloaded.

Additional Inherited Members
Static Public Member Functions inherited from Circle
static double	Area (const double &)
	Area of a circle given its radius.
Static Protected Attributes inherited from Circle
static constexpr const double	epsilon = 1.0e-10
	Internal epsilon constant.

Detailed Description

A simple torus.

The structure does not store the squared radius of the torus so as to save memory.

Rotation and translation are inherited from Circle.

Constructor & Destructor Documentation

Torus() [1/3]

Torus::Torus ( const Vector & c, const Vector & axis, const double & r = 1.0, const double & s = 1.0 )

explicit

Creates a torus.

Parameters

c	Center.
axis	Axis, which should be normalized.
r,s	Major and minor (small) radii.

Torus() [2/3]

Torus::Torus ( const Circle & c, const double & s = 1.0 )

explicit

Create a torus.

Parameters

c	Circle.
s	Minor (small) radius.

Torus() [3/3]

Torus::Torus ( const double & r, const double & s = 1.0 )

explicit

Create a horizontal torus centered at origin.

Parameters

r,s	Major and minor radii.

Member Function Documentation

Inside()

bool Torus::Inside

(

const Vector &

p

)

const

Check if a point is inside or outside the torus.

Parameters

p

Point.

Intersect()

int Torus::Intersect	(	const Ray &	ray,
		double *	depth,
		Vector *	normal ) const

Computes the intersection depths and the normals between a ray and a torus.

The quartic polynomial in t is derived from the canonical algebraic expression. Roots are found using the fast analytical Quartic::Solve() function of the Quartic class. This function returns an integer which is the number of intersections found. Note that intersections are sorted.

Parameters

ray	The ray.
depth	Array of intersection depths.
normal	Array of surface normals at intersection points.

Normal()

Vector Torus::Normal

(

const Vector &

p

)

const

Computes the distance vector between a torus and a given point.

This function projects the point in the plane of the circle and computes the distance to the circle in its plane, before adding the extra term along the normal.

Parameters

p

Point.

R()

double Torus::R

(

const Vector &

p

)

const

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

Parameters

p

Point.

RandomInside()

Vector Torus::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the dodecahedron.

Uses a simple rejection method.

Parameters

random

Random number generator.

Scale()

void Torus::Scale

(

const double &

s

)

Uniformly scales a torus.

Parameters

s	Scaling factor.

Signed()

double Torus::Signed

(

const Vector &

p

)

const

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

Parameters

p

Point.

Small()

double Torus::Small ( ) const

inline

Return the small radius of the torus.

Use Torus::Radius() to get the major radius.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Torus & torus )

friend

Overloaded.

Parameters

s	Stream.
torus	The torus.