Class Ellipse

java.lang.Object

org.episteme.core.mathematics.geometry.curves.Ellipse

All Implemented Interfaces:

Function<Real, Vector<Real>>, ContinuousFunction<Real, Vector<Real>>, DifferentiableFunction<Real, Vector<Real>>, Function<Real, Vector<Real>>, Relation<Real, Vector<Real>>, ParametricCurve

public class Ellipse
extends Object
implements ParametricCurve

Represents an ellipse curve.

An ellipse is a conic section with two focal points. Parametric form: C(t) = (a·cos(t), b·sin(t)) where a is the semi-major axis and b is the semi-minor axis.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Ellipse(PointND center, Real semiMajorAxis, Real semiMinorAxis)	Creates a 2D ellipse with the given center and semi-axes.
Ellipse(Real semiMajorAxis, Real semiMinorAxis)	Creates a 2D ellipse with the given semi-axes.

Method Summary

Modifier and Type	Method	Description
Real	area()	Returns the area of the ellipse.
PointND	at(Real t)	Evaluates the curve at parameter t.
Real	curvature(Real t, Real h)	Returns the curvature at parameter t.
int	dimension()	Returns the dimension of the ambient space.
Real	eccentricity()	Returns the eccentricity of the ellipse. e = √(1 - (b/a)²)
PointND	getCenter()	Returns the center point.
Real	getSemiMajorAxis()	Returns the semi-major axis.
Real	getSemiMinorAxis()	Returns the semi-minor axis.
Real	perimeter()	Returns the approximate perimeter using Ramanujan's approximation.
Vector<Real>	tangent(Real t, Real h)	Returns the tangent vector at parameter t.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface ContinuousFunction

isContinuous

Methods inherited from interface DifferentiableFunction

isDifferentiable

Methods inherited from interface Function

compose

Methods inherited from interface Function

andThen, apply, compose, contains, evaluate, getBackend, setBackend

Methods inherited from interface ParametricCurve

arcLength, differentiate, evaluate, getOutputDimension, normal, unitTangent

Methods inherited from interface Relation

getCodomain, getDomain

Constructor Details

Ellipse

public Ellipse(Real semiMajorAxis,
 Real semiMinorAxis)

Creates a 2D ellipse with the given semi-axes.

Parameters:

semiMajorAxis - the semi-major axis (a)

semiMinorAxis - the semi-minor axis (b)

Ellipse

public Ellipse(PointND center,
 Real semiMajorAxis,
 Real semiMinorAxis)

Creates a 2D ellipse with the given center and semi-axes.

Parameters:

center - the center point

semiMajorAxis - the semi-major axis (a)

semiMinorAxis - the semi-minor axis (b)

Method Details

at

public PointND at(Real t)

Description copied from interface: ParametricCurve

Evaluates the curve at parameter t.

Specified by:

at in interface ParametricCurve

Parameters:

t - the parameter value

Returns:

the point on the curve

dimension

public int dimension()

Description copied from interface: ParametricCurve

Returns the dimension of the ambient space.

Specified by:

dimension in interface ParametricCurve

Returns:

the dimension

tangent

public Vector<Real> tangent(Real t,
 Real h)

Description copied from interface: ParametricCurve

Returns the tangent vector at parameter t.

The tangent vector is the derivative: C'(t) = dC/dt

Specified by:

tangent in interface ParametricCurve

Parameters:

t - the parameter value

h - the step size for numerical differentiation

Returns:

the tangent vector

curvature

public Real curvature(Real t,
 Real h)

Description copied from interface: ParametricCurve

Returns the curvature at parameter t.

Curvature: κ = ||C'(t) × C''(t)|| / ||C'(t)||³

For 2D curves: κ = |x'y'' - y'x''| / (x'² + y'²)^(3/2)

Specified by:

curvature in interface ParametricCurve

Parameters:

t - the parameter value

h - the step size for numerical differentiation

Returns:

the curvature

getSemiMajorAxis

public Real getSemiMajorAxis()

Returns the semi-major axis.

Returns:

the semi-major axis

getSemiMinorAxis

public Real getSemiMinorAxis()

Returns the semi-minor axis.

Returns:

the semi-minor axis

getCenter

public PointND getCenter()

Returns the center point.

Returns:

the center

eccentricity

public Real eccentricity()

Returns the eccentricity of the ellipse. e = √(1 - (b/a)²)

Returns:

the eccentricity

area

public Real area()

Returns the area of the ellipse. A = πab

Returns:

the area

perimeter

public Real perimeter()

Returns the approximate perimeter using Ramanujan's approximation. P ≈ π(3(a+b) - √((3a+b)(a+3b)))

Returns:

the approximate perimeter