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org.apache.jmeter.visualizers
Class Spline3

java.lang.Object
  extended by org.apache.jmeter.visualizers.Spline3

public class Spline3
extends Object

This class implements the representation of an interpolated Spline curve.

The curve described by such an object interpolates an arbitrary number of fixed points called nodes. The distance between two nodes should currently be constant. This is about to change in a later version but it can last a while as it's not really needed. Nevertheless, if you need the feature, just write me a note and I'll write it asap.

The interpolated Spline curve can't be described by an polynomial analytic equation, the degree of which would be as high as the number of nodes, which would cause extreme oscillations of the curve on the edges.

The solution is to split the curve accross a lot of little intervals : an interval starts at one node and ends at the next one. Then, the interpolation is done on each interval, according to the following conditions :

  1. the interpolated curve is degree 3 : it's a cubic curve ;
  2. the interpolated curve contains the two points delimiting the interval. This condition obviously implies the curve is continuous ;
  3. the interpolated curve has a smooth slope : the curvature has to be the same on the left and the right sides of each node ;
  4. the curvature of the global curve is 0 at both edges.
Every part of the global curve is represented by a cubic (degree-3) polynomial, the coefficients of which have to be computed in order to meet the above conditions.

This leads to a n-unknow n-equation system to resolve. One can resolve an equation system by several manners ; this class uses the Jacobi iterative method, particularly well adapted to this situation, as the diagonal of the system matrix is strong compared to the other elements. This implies the algorithm always converges ! This is not the case of the Gauss-Seidel algorithm, which is quite faster (it uses intermediate results of each iteration to speed up the convergence) but it doesn't converge in all the cases or it converges to a wrong value. This is not acceptable and that's why the Jacobi method is safer. Anyway, the gain of speed is about a factor of 3 but, for a 100x100 system, it means 10 ms instead of 30 ms, which is a pretty good reason not to explore the question any further :)

Here is a little piece of code showing how to use this class :

 // ... float[] nodes = {3F, 2F, 4F, 1F, 2.5F, 5F, 3F}; Spline3 curve =
 new Spline3(nodes); // ... public void paint(Graphics g) { int[] plot =
 curve.getPlots(); for (int i = 1; i < n; i++) { g.drawLine(i - 1, plot[i -
 1], i, plot[i]); } } // ...

 


Field Summary
protected  float[][] _A
           
protected  float[] _B
           
protected  float[][] _coefficients
           
protected  int _m
           
protected  int _maxIterations
           
protected  float _minPrecision
           
protected  int _n
           
protected  float[] _r
           
protected  float[] _rS
           
protected static int DEFAULT_MAX_ITERATIONS
           
protected static float DEFAULT_PRECISION
           
 
Constructor Summary
Spline3(float[] r)
          Creates a new Spline curve by calculating the coefficients of each part of the curve, i.e. by resolving the equation system implied by the interpolation condition on every interval.
 
Method Summary
protected  boolean converge()
          Test if the Jacobi resolution of the equation system converges.
 void debugCheck()
          Manual check of the curve at the interpolated points.
 int getDefaultMaxIterations()
           
 float getDefaultPrecision()
           
 int getMaxIterations()
           
 int[] getPlots(int width, int height)
          Computes drawable plots from the curve for a given draw space.
 float getPrecision()
           
protected  void interpolation()
          Computes the coefficients of the Spline interpolated curve, on each interval.
protected  void jacobi()
          Resolves the equation system by a Jacobi algorithm.
protected  float precision(float[] oldX, float[] newX)
          Computes the current precision reached.
 void setMaxIterations(int iterations)
           
 void setPrecision(float precision)
           
 void setToDefaultMaxIterations()
           
 void setToDefaultPrecision()
           
 float value(float t)
          Computes a (vertical) Y-axis value of the global curve.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

_coefficients

protected float[][] _coefficients

_A

protected float[][] _A

_B

protected float[] _B

_r

protected float[] _r

_rS

protected float[] _rS

_m

protected int _m

_n

protected int _n

DEFAULT_PRECISION

protected static final float DEFAULT_PRECISION
See Also:
Constant Field Values

DEFAULT_MAX_ITERATIONS

protected static final int DEFAULT_MAX_ITERATIONS
See Also:
Constant Field Values

_minPrecision

protected float _minPrecision

_maxIterations

protected int _maxIterations
Constructor Detail

Spline3

public Spline3(float[] r)
Creates a new Spline curve by calculating the coefficients of each part of the curve, i.e. by resolving the equation system implied by the interpolation condition on every interval.

Parameters:
r - an array of float containing the vertical coordinates of the nodes to interpolate ; the vertical coordinates start at 0 and are equidistant with a step of 1.
Method Detail

interpolation

protected void interpolation()
Computes the coefficients of the Spline interpolated curve, on each interval. The matrix system to resolve is AX=B


jacobi

protected void jacobi()
Resolves the equation system by a Jacobi algorithm. The use of the slower Jacobi algorithm instead of Gauss-Seidel is choosen here because Jacobi is assured of to be convergent for this particular equation system, as the system matrix has a strong diagonal.


converge

protected boolean converge()
Test if the Jacobi resolution of the equation system converges. It's OK if A has a strong diagonal.


precision

protected float precision(float[] oldX,
                          float[] newX)
Computes the current precision reached.


value

public float value(float t)
Computes a (vertical) Y-axis value of the global curve.

Parameters:
t - abscissa
Returns:
computed ordinate

debugCheck

public void debugCheck()
Manual check of the curve at the interpolated points.


getPlots

public int[] getPlots(int width,
                      int height)
Computes drawable plots from the curve for a given draw space. The values returned are drawable vertically and from the bottom of a Panel.

Parameters:
width - width within the plots have to be computed
height - height within the plots are expected to be drawed
Returns:
drawable plots within the limits defined, in an array of int (as many int as the value of the width parameter)

setPrecision

public void setPrecision(float precision)

getPrecision

public float getPrecision()

setToDefaultPrecision

public void setToDefaultPrecision()

getDefaultPrecision

public float getDefaultPrecision()

setMaxIterations

public void setMaxIterations(int iterations)

getMaxIterations

public int getMaxIterations()

setToDefaultMaxIterations

public void setToDefaultMaxIterations()

getDefaultMaxIterations

public int getDefaultMaxIterations()

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