Class Helix

java.lang.Object

org.episteme.core.mathematics.geometry.curves.Helix

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 Helix
extends Object
implements ParametricCurve

Represents a 3D helix (spiral) curve.

A helix is a curve that winds around a cylinder at a constant angle. Parametric form: C(t) = (r·cos(t), r·sin(t), h·t) where r is the radius and h is the pitch (height per radian).

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Helix(Point3D center, Real radius, Real pitch)	Creates a helix with the given 3D center, radius, and pitch.
Helix(PointND center, Real radius, Real pitch)	Creates a helix with the given center, radius, and pitch.
Helix(Real radius, Real pitch)	Creates a helix with the given radius and pitch.

Method Summary

Modifier and Type	Method	Description
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.
PointND	getCenter()	Returns the center point.
Real	getPitch()	Returns the pitch of the helix.
Real	getRadius()	Returns the radius of the helix.
Real	heightPerTurn()	Returns the total height for one complete turn (2Ï€ radians).
Vector3D	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

Helix

public Helix(Real radius,
 Real pitch)

Creates a helix with the given radius and pitch.

Parameters:

radius - the radius of the helix

pitch - the pitch (height per radian)

Helix

public Helix(PointND center,
 Real radius,
 Real pitch)

Creates a helix with the given center, radius, and pitch.

Parameters:

center - the center point (axis passes through this)

radius - the radius of the helix

pitch - the pitch (height per radian)

Helix

public Helix(Point3D center,
 Real radius,
 Real pitch)

Creates a helix with the given 3D center, radius, and pitch.

Parameters:

center - the center point

radius - the radius of the helix

pitch - the pitch (height per radian)

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 Vector3D 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

getRadius

public Real getRadius()

Returns the radius of the helix.

Returns:

the radius

getPitch

public Real getPitch()

Returns the pitch of the helix.

Returns:

the pitch

getCenter

public PointND getCenter()

Returns the center point.

Returns:

the center

heightPerTurn

public Real heightPerTurn()

Returns the total height for one complete turn (2Ï€ radians).

Returns:

the height per turn