Ellipsoid Class Reference

Symmetric ellipsoids, i.e., ellipsoids with the same radial coefficients. More...

#include <ellipse.h>

Public Member Functions
	Ellipsoid ()
	Empty.
	Ellipsoid (const Vector &, const Vector &, const double &, const double &)
	Create an ellipsoid. More...
	Ellipsoid (const Vector &, const Vector &, const double &)
	Create an ellipsoid. More...
	~Ellipsoid ()
	Empty.
Vector	Center () const
	Gets the center.
Vector	GetAxis () const
	Gets the center.
double	A () const
	Major radius of the ellipse.
double	B () const
	Minor radius of the ellipse.
Box	GetBox () const
	Compute the bouding box.
Ellipsoid	Rotated (const Matrix &) const
	Rotates an ellipsoid. More...
Ellipsoid	Translated (const Vector &) const
	Translates an ellipsoid. More...
double	R (const Vector &) const
	Compute the squared distance between a point and the ellipse. More...
double	Volume () const
	Compute the volume of an ellipsoid.

Protected Member Functions
double	Value (const Vector &) const
	Compute the field function value of an ellipsoid. More...

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).

Detailed Description

Symmetric ellipsoids, i.e., ellipsoids with the same radial coefficients.

Symmetric ellipsoids 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

Ellipsoid() [1/2]

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

explicit

Create an ellipsoid.

Parameters

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

Ellipsoid() [2/2]

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

explicit

Create an ellipsoid.

Parameters

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

Member Function Documentation

R()

double Ellipsoid::R

(

const Vector &

p

)

const

Compute the squared distance between a point and the ellipse.

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

Parameters

p

Point.

See also

Ellipse2::R(const Vector2&)

Rotated()

Ellipsoid Ellipsoid::Rotated

(

const Matrix &

r

)

const

Rotates an ellipsoid.

Parameters

r	Rotation matrix.

Translated()

Ellipsoid Ellipsoid::Translated

(

const Vector &

t

)

const

Translates an ellipsoid.

Parameters

t	Translation vector.

Value()

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

protected

Compute the field function value of an ellipsoid.

Parameters

p

Point.