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.
Vector	GetPrincipalAxis () const
	Get the principal axis of the 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.

GetPrincipalAxis()

Vector Ellipsoid::GetPrincipalAxis

(

)

const

Get the principal axis of the ellipsoid.

Returns

The principal axis.

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.