Spheroid Class Reference

Spheroids are symmetric ellipsoids, i.e., with the same radial coefficients a = b ≠ c. More...

#include <ellipse.h>

Public Member Functions
	Spheroid ()
	Empty.
	Spheroid (const Vector &, const Vector &, const double &, const double &)
	Create a spheroid.
	Spheroid (const Vector &, const Vector &, const double &)
	Create a spheroid.
	~Spheroid ()
	Empty.
Vector	Center () const
	Gets the center.
Vector	GetAxis () const
	Gets the axis.
double	A () const
	Major radius of the ellipsoid.
double	B () const
	Minor radius of the ellipsoid.
Box	GetBox () const
	Compute the bouding box.
Sphere	GetSphere () const
	Compute the bouding sphere.
Spheroid	Rotated (const Matrix &) const
	Rotates a spheroid.
Spheroid	Translated (const Vector &) const
	Translates a spheroid.
double	R (const Vector &) const
	Compute the squared distance between a point and the spheroid.
int	Intersect (const Ray &, double &, double &) const
	Computes the intersection between a ray and the spheroid.
double	Volume () const
	Compute the volume of an ellipsoid.

Protected Member Functions
double	Value (const Vector &) const
	Compute the field function value of a spheroid.

Protected Attributes
Vector	c = Vector::Null
	Center of the ellipsoid.
Vector	axis = Vector::Z
	Axis.
double	b = 1.0
	Axis length, and radial length (revolution).

Friends
std::ostream &	operator<< (std::ostream &s, const Spheroid &spheroid)
	Overloaded stream operator.

Detailed Description

Spheroids are symmetric ellipsoids, i.e., with the same radial coefficients a = b ≠ c.

Symmetric spheroids are surfaces of revolution, thus the Euclidean distance of a point or the signed distance can be computed analytically.

See also

Ellipse2

Constructor & Destructor Documentation

Spheroid() [1/2]

Spheroid::Spheroid ( const Vector & c, const Vector & axis, const double & a, const double & b )

explicit

Create a spheroid.

Parameters

c	Center.
axis	Axis (should be normalized).
a,b	Axis length and radial length.

Spheroid() [2/2]

Spheroid::Spheroid ( const Vector & c, const Vector & axis, const double & r )

explicit

Create a spheroid.

Parameters

c	Center.
axis	Axis of revolution, whose norm will define the first radius.
r	Radial length.

Member Function Documentation

Intersect()

int Spheroid::Intersect	(	const Ray &	ray,
		double &	tmin,
		double &	tmax ) const

Computes the intersection between a ray and the spheroid.

Underlying equation is : \(x^2 / b^2 + y^2 / b^2 + z^2 / a^2 - 1 = 0 \equiv a^2 (x^2 + y^2) + b^2 z^2 - a^2 b^2 = 0\)

Parameters

ray	The ray.
tmin,tmax	Intersection depths.

R()

double Spheroid::R

(

const Vector &

p

)

const

Compute the squared distance between a point and the spheroid.

It is possible to compute the closed form expression of the distance to a spheroid if the spheroid is symmetrical in one axis, in which case the spheroid is a surface of revolution, and the computation boils down to evaluating the distance between a point and an ellipse.

Parameters

p

Point.

See also

Ellipse2::R(const Vector2&)

Rotated()

Spheroid Spheroid::Rotated

(

const Matrix &

r

)

const

Rotates a spheroid.

Parameters

r	Rotation matrix.

Translated()

Spheroid Spheroid::Translated

(

const Vector &

t

)

const

Translates a spheroid.

Parameters

t	Translation vector.

Value()

double Spheroid::Value ( const Vector & p ) const

protected

Compute the field function value of a spheroid.

Parameters

p

Point.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Spheroid & spheroid )

friend

Overloaded stream operator.

Parameters

s	Stream.
spheroid	Spheroid.