How to create your own surface class

This is an example to show how to create a new surface class with the surfaceLib in processing. For this example I take the Handkerchief surface as described here. Paul Bourke's side is an great source for different surface formulas. Also the german side 3d-meier has an enormous range of surface for you.

Let's take a look at the formula:

x = u
y = v
z = u3 / 3 + u v2 + a (u2 - v2)
-1 <= u <= 1, -1 <= v <= 1, a = 1

Ok, this formula is quite simple cause only the z value have some calculations. So what does u and v means. This are degrees between a given range, in this case both between -1 and 1. When you initialize your surface like new someSurface(g, 10,10) this creates two arrays of 10 values between the given range of the surface formula.

Now lets start. Open a new tab and call it Handkerchief. Then we create a new class, called Handkerchief which extends the Surface class.

class Handkerchief extends Surface{ }

Then we add the constructor, which calls the constructor of the main Surface class. Here we add the range parameters for u and v.

Handkerchief( final PGraphics i_g,
     final int i_phiSteps,
     final int i_thetaSteps) { 
    super(i_g, i_phiSteps, i_thetaSteps, -1, 1, -1, 1, null);
 }

To increase the speed of the initialization there are some LookupTable? classes. Lookup Table? Look, a surface consist of phiSteps x thetaSteps points. A new someSurface(g, 10,10) gives us 100 points and all have to be calculated at the above formula. So we calculate 100 times u3 although there are only 10 u values. Therefore we create a lookup table at the beginning, who's pre-compute and save the 10 values for u3. Ok now add the lookupTable. There are a bunch of tables classes for sin, cos, tan and pow and you can create other by your needs. We only need the PowerTable for u2, u3 and v2. The parameters phi/thetaSteps, minPhi/Theta and maxPhi/Theta are private variables of the main Surface class. 2 and 3 you guess, are the exponents for the pow() method.

class Handkerchief extends Surface{
  LookUpTable thetaPow2Table;
  LookUpTable phiPow3Table;
  LookUpTable phiPow2Table;

  Handkerchief( final PGraphics i_g, 
                final int i_phiSteps, 
                final int i_thetaSteps) {
    super(i_g, i_phiSteps, i_thetaSteps, -1, 1, -1, 1, null);
  }

  void initValues() {
    phiPow2Table = new PowerTable(phiSteps, minPhi, maxPhi, 2);
    phiPow3Table = new PowerTable(phiSteps, minPhi, maxPhi, 3);
    thetaPow2Table = new PowerTable(thetaSteps, minTheta, maxTheta, 2);
  }
}

At last we need to calculated the x, y and z values. It's quite easy for x and y. At the z value exchange u2 in the formula above with phiPow2Table and so on. So at the end the class looks like this:

class Handkerchief extends Surface{
  LookUpTable thetaPow2Table;
  LookUpTable phiPow3Table;
  LookUpTable phiPow2Table;

  Handkerchief( final PGraphics i_g, 
                final int i_phiSteps, 
                final int i_thetaSteps) {
    super(i_g, i_phiSteps, i_thetaSteps, -1, 1, -1, 1, null);
  }

  void initValues() {
    phiPow2Table = new PowerTable(phiSteps, minPhi, maxPhi, 2);
    phiPow3Table = new PowerTable(phiSteps, minPhi, maxPhi, 3);
    thetaPow2Table = new PowerTable(thetaSteps, minTheta, maxTheta, 2);
  }
  float calculateX(final int i_phiStep, final int i_thetaStep) {
    return i_thetaStep;
  }

  float calculateY(final int i_phiStep, final int i_thetaStep) {
    return i_phiStep;
  }

  float calculateZ(final int i_phiStep, final int i_thetaStep) {
    return phiPow3Table.getValue(i_phiStep)/3+i_phiStep*thetaPow2Table.getValue(i_thetaStep)+2*(phiPow2Table.getValue(i_phiStep)-thetaPow2Table.getValue(i_thetaStep));
  }
}