Class Curl

java.lang.Object

org.episteme.core.mathematics.analysis.vectorcalculus.Curl

public class Curl
extends Object

Computes the curl of a 3D vector field.

The curl measures the rotation or circulation of a vector field.

Definition (3D only): ∇×F = (∂F₃/∂y - ∂F₂/∂z, ∂F₁/∂z - ∂F₃/∂x, ∂F₂/∂x - ∂F₁/∂y)

Physical interpretation: - Measures local rotation/vorticity - Fluid dynamics: vorticity ω = ∇×v - Electromagnetism: Faraday's law ∇×E = -∂B/∂t - Ampère's law: ∇×B = μ₀J + μ₀ε₀∂E/∂t - Conservative fields have zero curl: ∇×(∇φ) = 0

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Curl()

Method Summary

Modifier and Type	Method	Description
static VectorField<PointND>	asField(VectorField<PointND> field, Real h)	Returns a vector field representing the curl of the input field.
static Vector<Real>	compute(VectorField<PointND> field, PointND point, Real h)	Computes the curl of a 3D vector field at a point.

Methods inherited from class Object

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

Constructor Details

Curl

public Curl()

Method Details

compute

public static Vector<Real> compute(VectorField<PointND> field,
 PointND point,
 Real h)

Computes the curl of a 3D vector field at a point.

The curl is only defined for 3D vector fields.

Parameters:

field - the vector field (must be 3D)

point - the point at which to compute curl

h - the step size for numerical differentiation

Returns:

the curl vector

Throws:

IllegalArgumentException - if field is not 3D

asField

public static VectorField<PointND> asField(VectorField<PointND> field,
 Real h)

Returns a vector field representing the curl of the input field.

Parameters:

field - the vector field (must be 3D)

h - the step size for numerical differentiation

Returns:

the curl as a vector field