Ellipsoid Class Reference

Ellipsoids. More...

#include <ellipse.h>

Public Member Functions
	Ellipsoid ()
	Empty.
	Ellipsoid (const double &, const double &, const double &)
	Create an ellipsoid.
	Ellipsoid (const Vector &, const Vector &, const Vector &, const double &, const double &, const double &)
	Create an ellipsoid.
	Ellipsoid (const Frame &, const double &, const double &, const double &)
	Create an ellipsoid.
	Ellipsoid (const Spheroid &)
	Create an ellipsoid.
	Ellipsoid (const Matrix &, const Vector &)
	Create an ellipsoid.
	~Ellipsoid ()
	Empty.
Vector	Center () const
	Return the center.
Frame	GetFrame () const
	Return the frame.
FrameScaled	GetFrameScaled () const
	Return the scaled frame.
double	A () const
	X radius of the ellipsoid.
double	B () const
	Y radius of the ellipsoid.
double	C () const
	Z radius of the ellipsoid.
Box	GetBox () const
	Compute the bouding box.
Sphere	GetSphere () const
	Compute the bouding sphere.
double	Signed (const Vector &) const
	Compute the (conserevative, not Euclidean) signed distance bound to the ellipsoid.
Ellipsoid	Rotated (const Matrix &) const
	Rotates an ellipsoid.
Ellipsoid	Translated (const Vector &) const
	Translates an ellipsoid.
double	Volume () const
	Compute the volume of an ellipsoid.

Static Public Member Functions
static Ellipsoid	FromPoints (const std::vector< Vector > &, const double &=0.05)
	Builds an ellipsoid enveloping a point cloud, using a Minium Volume Ellipsoid algorithm.

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

Protected Attributes
Frame	frame
	Frame.
double	c = 1.0
	% Radii.

Friends
std::ostream &	operator<< (std::ostream &s, const Ellipsoid &ellipsoid)
	Overloaded stream operator.

Detailed Description

Ellipsoids.

See also

Spheroid

Constructor & Destructor Documentation

Ellipsoid() [1/5]

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

explicit

Create an ellipsoid.

Parameters

a,b,c

Axis lengths.

Ellipsoid() [2/5]

Ellipsoid::Ellipsoid ( const Vector & e, const Vector & x, const Vector & y, const double & a, const double & b, const double & c )

explicit

Create an ellipsoid.

Parameters

e	Center.
x,y	Axes, should be normalized.
a,b,c	Axis lengths.

Ellipsoid() [3/5]

Ellipsoid::Ellipsoid ( const Frame & frame, const double & a, const double & b, const double & c )

explicit

Create an ellipsoid.

Parameters

frame	The frame.
a,b,c	Axis lengths.

Ellipsoid() [4/5]

Ellipsoid::Ellipsoid ( const Spheroid & e )

explicit

Create an ellipsoid.

Parameters

e

Spheroid.

Ellipsoid() [5/5]

Ellipsoid::Ellipsoid ( const Matrix & A, const Vector & center )

explicit

Create an ellipsoid.

(p - c)^t . A . (p - c)

Parameters

A	Ellipsoid matrix (symmetric positive-definite).
center	Ellipsoid center.

Member Function Documentation

FromPoints()

Ellipsoid Ellipsoid::FromPoints ( const std::vector< Vector > & p, const double & t = 0.05 )

static

Builds an ellipsoid enveloping a point cloud, using a Minium Volume Ellipsoid algorithm.

Parameters

p	Points.
t	Tolerance

Rotated()

Ellipsoid Ellipsoid::Rotated

(

const Matrix &

r

)

const

Rotates an ellipsoid.

Parameters

r	Rotation matrix.

Signed()

double Ellipsoid::Signed

(

const Vector &

p

)

const

Compute the (conserevative, not Euclidean) signed distance bound to the ellipsoid.

Parameters

p

Point.

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.

Volume()

double Ellipsoid::Volume ( ) const

inline

Compute the volume of an ellipsoid.

Note that the surface area of a general (triaxial) ellipsoid involves incomplete elliptic integrals of the first and second kind respectively.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Ellipsoid & ellipsoid )

friend

Overloaded stream operator.

Parameters

s	Stream.
ellipsoid	Ellipsoid.