Package org.opentrafficsim.core.geometry

Class Fresnel

java.lang.Object

org.opentrafficsim.core.geometry.Fresnel

public class Fresnel
extends Object

Utility class to create clothoid lines, in particular the Fresnel integral based on:

• W.J. Cody (1968) Chebyshev approximations for the Fresnel integrals. Mathematics of Computation, Vol. 22, Issue 102, pp. 450–453.

Copyright (c) 2023-2024 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
BSD-style license. See OpenTrafficSim License.

Author:

Alexander Verbraeck, Peter Knoppers, Wouter Schakel

See Also:

• Cody (1968)

Method Summary

Modifier and Type	Method	Description
static double[]	fresnel(double x)	Approximate the Fresnel integral.

Methods inherited from class java.lang.Object

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

Method Details

fresnel

public static double[] fresnel(double x)

Approximate the Fresnel integral. The method used is based on Cody (1968). This method applies rational approximation to approximate the clothoid. For clothoid rotation beyond 1.6 rad, this occurs in polar form. The polar form is robust for arbitrary large numbers, unlike polynomial expansion, and will at a large threshold converge to (0.5, 0.5). There are 5 regions with different fitted values for the rational approximations, in Cartesian or polar form.

W.J. Cody (1968) Chebyshev approximations for the Fresnel integrals. Mathematics of Computation, Vol. 22, Issue 102, pp. 450–453.

Parameters:

x - double; length along the standard Fresnel integral (no scaling).

Returns:

double[]; array with two double values c and s

See Also:

• Cody (1968)