How to find a normal vector pointing directly from virtual world to screen in Java3D?

Question

I think it can be done by applying the transformation matrix of the scenegraph to z-normal (0, 0, 1), but it doesn't work. My code goes like this:

Vector3f toScreenVector = new Vector3f(0, 0, 1);
Transform3D t3d = new Transform3D();
tg.getTransform(t3d); //tg is Transform Group of all objects in a scene
t3d.transform(toScreenVector);

Then I tried something like this too:

Point3d eyePos = new Point3d();
Point3d mousePos = new Point3d();
canvas.getCenterEyeInImagePlate(eyePos);
canvas.getPixelLocationInImagePlate(new Point2d(Main.WIDTH/2, Main.HEIGHT/2), mousePos); //Main is the class for main window.

Transform3D motion = new Transform3D();
canvas.getImagePlateToVworld(motion);
motion.transform(eyePos);
motion.transform(mousePos);

Vector3d toScreenVector = new Vector3f(eyePos);
toScreenVector.sub(mousePos);
toScreenVector.normalize();

But still this doesn't work correctly. I think there must be an easy way to create such vector. Do you know what's wrong with my code or better way to do so?

Answer 1

If I get this right, you want a vector that is normal to the screen plane, but in world coordinates?

In that case you want to INVERT the transformation from World -> Screen and do Screen -> World of (0,0,-1) or (0,0,1) depending on which axis the screen points down.

Since the ModelView matrix is just a rotation matrix (ignoring the homogenous transformation part), you can simply pull this out by taking the transpose of the rotational part, or simple reading in the bottom row - as this transposes onto the Z coordinate column under transposition.

Answer 2

Yes, you got my question right. Sorry that I was a little bit confused yesterday. Now I have corrected the code by following your suggestion and mixing two pieces of code in the question together:

Vector3f toScreenVector = new Vector3f(0, 0, 1);

Transform3D t3d = new Transform3D();
canvas.getImagePlateToVworld(t3d);
t3d.transform(toScreenVector);

tg.getTransform(t3d); //tg is Transform Group of all objects in a scene
t3d.transform(toScreenVector);

Thank you.