raycasting: how to properly apply a projection matrix?

Question

Hi,

I am currently working on some raycasting in GLSL which works fine. Anyways I want to go from orthogonal projection to perspective projection now but I am not sure how to properly do so. Are there any good links on how to use a projection Matrix with raycasting? I am not even sure what I have to apply the matrix to (propably to the ray direction somehow?). Right now I do it like this (pseudocode):

vec3 rayDir = (0.0, 0.0, -1.0); //down the negative -z axis in parallel;

but now I would like to use a projMatrix which works similar to gluPerspective function so that I can simply define an aspect ratio, fov and near and far plane. So basically, can anybody provide me a chunk of code to set up a proj matrix similar to gluProjection does? And secondly tell me if it is correct to multiply it with the rayDirection?

Thanks!

Answer 1

don't try to modify your rays. Instead do this:

a) create matrix using the location/rotation of your camera. b) invert the matrix c) apply it to all the models in the scene d) render it using your normal methods.

This is actually the way OpenGL does it as well. Rotating the camera to the right is the same as rotating the world to the left.

Answer 2

To shoot rays out into the scene, you want to start by putting yourself (mentally) into the world after the projection matrix has been applied. This means that the view frustrum is now a 2x2x1 box - this is known as the canonical view volume. (The opposing corners of the box are (-1, -1, 0) and (1, 1, -1).) The rays you generate will (in the post-projection transformed world) start at the origin and hit the rear clipping plane (located at z=-1). The "destination" of your first ray should be (-1, 1, -1) - the upper-left-hand corner of the far clipping plane. (Subsequent rays "destinations" are calculated based on the resolution of your viewport.)

Now that you have this ray in the canonical view volume, you need to get it into standard world coordinates. How do you do this? Simple - just multiply by the inverse of the projection matrix, often called the viewing transformation. This will put your rays into the same coordinate system as the objects in your scene, making ray collision testing nice and easy.