edu.mines.jtk.interp

Class RadialInterpolator2.WesselBercovici

java.lang.Object

edu.mines.jtk.interp.RadialInterpolator2.WesselBercovici

Enclosing class:

RadialInterpolator2

public static class RadialInterpolator2.WesselBercovici
extends java.lang.Object

The Wessel-Bercovici basis function g(r) for splines with tension. This function is K0(p*r)+log(p*r)+c, where p = sqrt(t/(1-t)), t is a tension parameter in the range [0,1), and c is a constant such that g(r) = 0. K0 denotes the modified Bessel function of the second kind and order zero. For the special case where tension t = p = 0, the biharmonic basis function g(r) = r*r*(log(r)-1) is used instead.

For consistency when using the same tension parameter t for different sets of data, distances r should be normalized to be dimensionless. A scale factor s may be specified that divides all distances r, so that the basis function becomes g(r/s). The scale factor suggested by Wessel and Bercovici is s = rmax/50, where rmax is the maximum seperation between points to be interpolated.

See Wessel and Bercovici, 1998, Interpolation with splines in tension: a Green's function approach: Mathematical Geology 30, 77-93.

Constructor Summary

Constructors

Constructor and Description
RadialInterpolator2.WesselBercovici(double tension) Constructs a basis for the specified tension.
RadialInterpolator2.WesselBercovici(double tension, double scale) Constructs a basis for the specified tension and scale factor.

Method Summary

Methods

Modifier and Type	Method and Description
double	evaluate(double r) Evaluates this basis function for the specified distance.

Methods inherited from class java.lang.Object

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

Constructor Detail

RadialInterpolator2.WesselBercovici

public RadialInterpolator2.WesselBercovici(double tension)

Constructs a basis for the specified tension. This basis does not normalize distances r.

Parameters:

tension - the tension; must be in the range [0,1).

RadialInterpolator2.WesselBercovici

public RadialInterpolator2.WesselBercovici(double tension,
                                   double scale)

Constructs a basis for the specified tension and scale factor.

Parameters:

tension - the tension; must be in the range [0,1).

scale - the factor by which to divide distances r.

Method Detail

evaluate

public double evaluate(double r)

Evaluates this basis function for the specified distance.

Parameters:

r - the radial distance.

Returns:

the value of this basis function.