B spline basis function seems to produce incorrect values

Question

i wanted to implement B-splines in an Java Swing application. And since 4. May i tried nearly everything and spend every minute of my free time, but i don't get them right - i have headach since yesterday :/

To implement the B spline i used the specification from wikipedia

And i made (relating to MCVE) an demo version which can be found here: gist.github.com/soraphis/b-spline

the code shows the problem, its made to be called in an swing JPanel drawcomponent method. But you can comment this line and uncomment 71.

Some additional informations:

• a and b in my basis function returns values < 0 or >1 which should not be (see wikipedia)
• i want to implement the b splines myself - i dont want to use a library
• referencinc to the wikipedia artikel:
  • basisFunc is B(x)
  • DeBoor is S(x)

i rly need help with the basis function, and i would like to know how to build up the knot vector "correctly"

Im thankful for every kind of reply
and thx for reading this

Answer 1

I can't imagine an appropriate answer that does not consist of a piece of code that you just can compile and run (without having to insert a main method and the surrounding GUI ... * wink *), regardless of how different it is from your code.

However, the weights that you have assigned to your T-array seemed odd, and the indices of the basis function seemed to be off +/-1. I tried to fix this, but it's still not entirely correct, maybe you or someone else likes to continue debugging this.

import java.awt.Color;
import java.awt.Graphics;
import java.awt.GridLayout;
import java.util.Arrays;

import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.SwingUtilities;

public class BSplineTest
{
    public static void main(String[] args)
    {
        SwingUtilities.invokeLater(new Runnable()
        {
            @Override
            public void run()
            {
                createAndShowGUI();
            }
        });
    }

    private static void createAndShowGUI()
    {
        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.getContentPane().setLayout(new GridLayout(1, 1));

        BSplineTestPanel bSplineTestPanel = new BSplineTestPanel();
        frame.getContentPane().add(bSplineTestPanel);
        frame.setSize(500,500);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
    }
}

class BSplineTestPanel extends JPanel
{
    @Override
    protected void paintComponent(Graphics g)
    {
        super.paintComponent(g);
        Bspline bspline = new Bspline();
        bspline.calculatePath(g);
    }
}

class Bspline
{
    double[][] P;
    double[] T;
    int _k = 3;

    public Bspline()
    {
        P = new double[4][2];
        P[0][0] = 100;
        P[0][1] = 100;
        P[1][0] = 50;
        P[1][1] = 50;
        P[2][0] = 100;
        P[2][1] = 200;
        P[3][0] = 50;
        P[3][1] = 200;
        update();
    }

    private void update()
    {
        if (P.length < 2)
            return;
        T = new double[_k + P.length + 1];
        double d = 1.0 / (T.length-1);
        for (int i = 0; i<T.length; i++)
        {
            T[i] = i * d;
        }
        System.out.println(Arrays.toString(T));

    }

    private double basisFunc(int i, int k, double t)
    {
        if (k == 0)
        {
            if (T[i] <= t && t < T[i + 1])
                return 1;
            return 0;
        }
        double a = (t - T[i]) / (T[i + k] - T[i]);
        double b = (T[i + k + 1] - t) / (T[i + k + 1] - T[i + 1]);
        return a * basisFunc(i, k - 1, t) + b * basisFunc(i + 1, k - 1, t);
    }

    private double[] DeBoor(double t)
    {
        double[] V = new double[2];
        for (int i = 0; i < P.length; i++)
        {
            double scale = basisFunc(i, _k, t);
            V[0] += P[i][0] * scale;
            V[1] += P[i][1] * scale;
        }
        return V;
    }

    public void calculatePath(Graphics g)
    {
        if (P.length < 2)
        {
            return; // zu wenige punkte um ein pfad zu zeichnen
        }
        double[] v = null;
        double delta = 1 / 32.0;
        for (double t = T[2]; t < T[5]; t += delta)
        {
            double[] p = DeBoor(t);
            if (v != null)
            {
                g.setColor(new Color((int)(t*255), 0, 0));
                g.drawLine((int) v[0], (int) v[1], (int) p[0], (int) p[1]);
            }
            v = p;
        }

        for (int i = 0; i < P.length; i++)
        {
            int x = (int)P[i][0];
            int y = (int)P[i][1];
            g.setColor(Color.RED);
            g.fillOval(x-2, y-2,  4,  4);
            g.drawString(String.valueOf(i), x, y+15);
        }
    }
}

(Compare to http://www.ibiblio.org/e-notes/Splines/basis.html, "Quadratic B-spline (n = 3, k = 3)")

Apart from that I wonder how such an overly complicated **** like deBoors algorithm could become so "famous". Use De-Casteljau and you'll be done in a few minutes, without a single debugging run.

---

EDIT A port of the code from http://chi3x10.wordpress.com/2009/10/18/de-boor-algorithm-in-c/

// From http://chi3x10.wordpress.com/2009/10/18/de-boor-algorithm-in-c/
double[] deBoor(int k,int degree, int i, double x, double knots[], double ctrlPoints[][])
{
    if( k == 0)
    {
        i = Math.max(0, Math.min(ctrlPoints.length-1, i));
        return ctrlPoints[i];
    }
    else
    {  
        double alpha = (x-knots[i])/(knots[i+degree+1-k]-knots[i]);
        double p0[] = deBoor(k-1,degree, i-1, x, knots, ctrlPoints);
        double p1[] = deBoor(k-1,degree, i, x, knots, ctrlPoints);
        double p[] = new double[2];
        p[0] = p0[0] *(1-alpha ) + p1[0]*alpha;
        p[1] = p0[1] *(1-alpha ) + p1[1]*alpha;
        return p;
    }
}    
int WhichInterval(double x, double knot[], int ti)
{
    int index = -1;

    for(int i = 1; i <= ti - 1; i++)
    {
        if(x < knot[i]) {
            index = i - 1;
            break;
        }
    }
    if(x == knot[ti - 1]) {
        index = ti - 1;
    }
    return index;
}

private double[] DeBoor(double t)
{
    int i = WhichInterval(t, T, T.length);
    return deBoor(_k, 3, i, t, T, P);
}