3D Parallel projection algorithm

Question

Hi all,
I'm not sure if directing this question here is appropriate but you guys seem to know pretty much everything Java-oriented.
Basically I'm trying to do some parallel projection without using Java native classes. I am using "Introduction to Computer Graphics" by Foley et al as a guide. I follow the steps outlined in order to perform the parallel projection namely:-
1. Translate VRP to the origin;
2. Rotate VRC such that the n axis (VPN) becomes the z-axis, the u axis becomes the x axis, and the v axis becomes the y axis.
3. Shear such that the direction of projection becomes parallel to the z axis.
4. Translate and scale into the parallel-projection canonical view volume.
Each point has its own matrix which are multiplied together in order to create one big matrix. I think that I then need to take my original points and transform them by that matrix. The problem I keep getting is that when I try to transform the Point3D's x, y, z values are either NaN or Infinity. I've tried all different values but cannot seem to get it to work. My code is below.
If anyone could make head-or-tail just where the problem could lie I will be extremely grateful.
//no matter these three values are the damn thing doesn't work
Point3D vrp = new Point3D(0, 0, 0);
Vector3D vpn = new Vector3D(0, 0, 1);
Vector3D vup = new Vector3D(0, 1, 0);
public void orthogonalProjection(Point3D vrp, Vector3D dop, Vector3D vup){
         setPoints(); //sets points of house and stores them in an array
         Point3D p;
         int F = 1;
         int B = 0;
         int umin = -1;
         int umax = 17;
         int vmin = -1;
         int vmax = 17;
         //Translate VRP to the origin
         Matrix T = new Matrix();
         T.setTranslationMatrix(-vrp.x, -vrp.y, -vrp.z);
         //Rotate VRC such that the n-axis (VPN) becomes the z-axis, the u axis
         //becomes the x axis, and the v axis becomes the y axis.
         //vpn = dop in parallel projection
         Vector3D rz = dop.copy();
         rz.normalise();
         Vector3D rx = vup.crossProduct(rz);
            rx.normalise();
            Vector3D ry = rz.crossProduct(rx);
            Matrix R = new Matrix();
            R.m[0][0]=rx.x; R.m[0][1]=rx.y; R.m[0][2]=rx.z;
            R.m[1][0]=ry.x; R.m[1][1]=ry.y; R.m[1][2]=ry.z;
            R.m[2][0]=rz.x; R.m[2][1]=rz.y; R.m[2][2]=rz.z;
            //here we would shear but as orthographic it results in an identity matrix
            Matrix SHpar = new Matrix();
            SHpar.setIdentityMatrix();
            //translate centre of front clipping plane to origin
            Matrix Tpar = new Matrix();
            Tpar.setTranslationMatrix(-(umax + umin) / 2, -(vmax + vmin) / 2, -F);
            //scale into canonical view volume
            Matrix Spar = new Matrix();
            Spar.m[0][0] = 2 / (umax + umin);
            Spar.m[1][1] = 2 / (vmax + vmin);
            Spar.m[2][2] = 1 / (F - B);
            Spar.m[3][3] = 1;
            //multiply all matrices Npar = Spar.Tpar.SHpar.R.T(-VRP)
            //remembering that SHpar is only an identity
            //matrix.
            Matrix Npar = new Matrix();
            //multiply the matrices
            Npar = ((((Spar.multiplyMatrix(Tpar)).multiplyMatrix(SHpar)).multiplyMatrix(R)).multiplyMatrix(T));
            Npar.outputMatrix();
         //transform each point using the matrix
         for(int i = 0; i < pointArr3D.length;i++){
              p = pointArr3D;
          System.out.println("p.x before is " + p.x);
          System.out.println("p.y before is " + p.y);
          System.out.println("p.y before is " + p.z);
          //p.normalise();
          p.transform(Npar);
          System.out.println("p.x after is " + p.x);
          System.out.println("p.y after is " + p.y);
          System.out.println("p.y after is " + p.z);     
Thanks,
Chris

Answer 1

I ripped the following example from some old code of mine, so, for
the sake of the example lets call the axes r, g and b,where r sticks out
of your screen towards you, g goes from left to right and b points upwards.
Suppose you're looking at an object in a cube. The cube has size MAX
in all three dimensions and is located at the origin with one of its
cornerpoints, neatly alligned with the r, g, b axes.
Suppose your eyepoint is 'dist' away from the origin, delta rotated around
the b axis and phi rotated around the g axis. Let cf, sf, cd, sd be
cos(phi), sin(phi), cos(delta), sin(delta) respectively.
Also suppose that the focuspoint (the point the eye is staring at is) is
fr, fg, fb.
Finally, the picture should be SCALE pixels in both directions, translated
XOFS, YOFS from the origin.
Here are the little methods that finds the x and y coordinates for you:     private double rr, gg, bb;
     int xT(int r, int g, int b) {
          // scale and centre around the origin
          rr= ((double)r)/MAX-fr/MAX;
          gg= ((double)g)/MAX-fg/MAX;
          bb= ((double)b)/MAX-fb/MAX;
          // rotate around green axis
          double rrr= cf*rr-sf*gg;
          double ggg= sf*rr+cf*gg;
          double bbb= bb;
          // rotate around blue axis
          rr= cd*rrr-sd*bbb;
          bb= sd*rrr+cd*bbb;
          gg= ggg;
          double x= (dist*gg/(dist-rr)*SCALE+XOFS);
          // do the X projection
          return (int)x;
     int yT() {
          // do the Y projection
          return (int)(-dist*bb/(dist-rr)*SCALE+YOFS);
     }I hope this helps you out a bit.
kind regards,
Jos