Find the line corresponding to a single projected point in Processing (P3D assumed)

gistfile1.java

/*
  Find the 3D coordinates at depth z that project onto planar coordinates (x,y). 
  Screen position is at z-1 in the screen coordinate system, so z should be less than -1
  (basically inverse for screenX/screenY)
 */
PVector screenToDepth(float x, float y, float z) {
  // first get the transforms in place
  PMatrix3D M = (PMatrix3D) g.getMatrix();
  PMatrix3D P = (PMatrix3D) ((PGraphics3D) g).getProjection();
  P.apply(M);
  // compute scaling variables for this z-depth
  // not sure how general this is for arbitrary M and P - but works for default camera setup
  float[] in = new float[4];
  in[0] = 0;
  in[1] = 0;
  in[2] = z;
  in[3] = 1;
  float[] out = new float[4];
  P.mult(in,out);
  // setup input for projection inverse
  x = x*2/width-1;
  y = y*2/height-1;
  float fw = out[3];
  float fz = out[2];
  in[0] = x*fw;
  in[1] = y*fw;
  in[2] = fz;
  in[3] = fw;
  // and the actual computation
  P.invert();
  P.mult(in, out);
  return new PVector(out[0], out[1], out[2]);
}