Class Circle

java.lang.Object

org.episteme.core.mathematics.geometry.curves.Circle

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 Circle
extends Object
implements ParametricCurve

Represents a circle as a parametric curve.

2D circle: C(t) = center + (r*cos(t), r*sin(t)) 3D circle: C(t) = center + r*(cos(t)*u + sin(t)*v) where u and v are orthonormal vectors in the plane of the circle.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Circle(PointND center, Real radius)	Creates a 2D circle in the XY plane.
Circle(PointND center, Real radius, Vector<Real> normal)	Creates a circle in 3D space with specified plane orientation.

Method Summary

Modifier and Type	Method	Description
PointND	at(Real t)	Evaluates the curve at parameter t.
Real	circumference()	Returns the circumference of the circle.
Real	curvature(Real t, Real h)	Returns the curvature at parameter t.
int	dimension()	Returns the dimension of the ambient space.
PointND	getCenter()	Returns the center of the circle.
Real	getRadius()	Returns the radius of the circle.
VectorND	tangent(Real t, Real h)	Returns the tangent vector at parameter t.
String	toString()

Methods inherited from class Object

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

Circle

public Circle(PointND center,
 Real radius)

Creates a 2D circle in the XY plane.

Parameters:

center - the center point

radius - the radius

Circle

public Circle(PointND center,
 Real radius,
 Vector<Real> normal)

Creates a circle in 3D space with specified plane orientation.

Parameters:

center - the center point

radius - the radius

normal - the normal vector to the plane (will be normalized)

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 VectorND 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

getCenter

public PointND getCenter()

Returns the center of the circle.

Returns:

the center point

getRadius

public Real getRadius()

Returns the radius of the circle.

Returns:

the radius

circumference

public Real circumference()

Returns the circumference of the circle.

Returns:

2Ï€r

toString

public String toString()

Overrides:

toString in class Object