meshi.util.mathTools
Class Spline2D

java.lang.Object
  meshi.util.mathTools.Spline2D

public class Spline2D
extends java.lang.Object

The class creates a 2D cubic spline object from given parameters, and allows for the calculation of the spline value and derivative at any given point inside the spline intervals. After the method calc(x,y) is run, the public fields s s_tag_x and s_tag_y are updated: s - the spline value at x,y. s_tag_x - the spline first derivative at x,y with respect to x. s_tag_y - the spline first derivative at x,y with respect to y. Note: 1) calc will not work for values outside the range [break 1 , break n]. 2) The class operates on any set of break points. However, if the break points are evenly spaced (in both axes) then the calculation of calc(x,y) will be faster. 3) See the constructor documention for more details on how to set up the class properly.

Field Summary

private double	breakIntervalX
private double	breakIntervalY
private double[]	breaksX
private double[]	breaksY
private double[][][]	coefs
private boolean	evenBreaks
double	s
double	s_tag_x
double	s_tag_y

Constructor Summary

Spline2D(java.lang.String dataLine)
The constructor can create a specific spline object from a string with the format (Note that following 6 lines should appear in the SAME line, but I broke it for clarity).

Spline2D(java.util.StringTokenizer st)

Method Summary

void	calc(double x, double y)
private void	calcEvenBreaks(double x, double y)
private boolean	testForEvenBreaks(double[] vec)

Methods inherited from class java.lang.Object

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

Field Detail

breaksX

private double[] breaksX

breaksY

private double[] breaksY

coefs

private double[][][] coefs

evenBreaks

private boolean evenBreaks

breakIntervalX

private double breakIntervalX

breakIntervalY

private double breakIntervalY

s

public double s

s_tag_x

public double s_tag_x

s_tag_y

public double s_tag_y

Constructor Detail

Spline2D

public Spline2D(java.lang.String dataLine)

The constructor can create a specific spline object from a string with the format (Note that following 6 lines should appear in the SAME line, but I broke it for clarity). Just to make it perfectly clear, this object is created from ONE very long test-line: {Number of breaks in X axis} {Number of breaks in Y axis} {break 1X} ... {break nX} {break 1Y} ... {break nY} {square(1,1) constant coef} {square(1,1) X coef} {square(1,1) X^2 coef} {square(1,1) X^3 coefficient} {square(1,1) Y coef} {square(1,1) Y*X coef} {square(1,1) Y*X^2 coef} {square(1,1) Y*X^3 coefficient} {square(1,1) Y^2 coef} {square(1,1) Y^2*X coef} {square(1,1) Y^2*X^2 coef} {square(1,1) Y^2*X^3 coefficient} {square(1,1) Y^3 coef} {square(1,1) Y^3*X coef} {square(1,1) Y^3*X^2 coef} {square(1,1) Y^3*X^3 coefficient} {square(1,2) constant coef} {square(1,2) X coef} ... Note: 1) There is an alternative constructor that requires a tokenizer of a string with the above format. 2) The breaks must increase monotonicly. 3) The spline coefficients are not verified. Therefore, derivability is obtained only if the coefficients are of a derivable spline. 4) In order to have numerical stability, the relative precision of the values in the dataLine must be at least 1e-10.

Spline2D

public Spline2D(java.util.StringTokenizer st)

Method Detail

calc

public final void calc(double x,
                       double y)

calcEvenBreaks

private final void calcEvenBreaks(double x,
                                  double y)

testForEvenBreaks

private boolean testForEvenBreaks(double[] vec)