OpenGL Frustum Pedagogy

3
votes

i've been drawing directly into homogenous clip space (the 2x2x2 cube centered around 0,0,0) in opengl and i've realized that the perspective transformation matrix transforms all geometry from one right-parallelipid (view-space) to another right-parallelipid (homogenous clip-space).

so, why the heck does every opengl article use a non-right-parallelipid frustum to illustrate how projection works? i understand that the perspective transformation matrix will cause everything to get scaled by a term containing its distance from the camera and the camera's distance from the plane... is the traditional frustum illustration trying to explain that? or are we truly entered some warped space at some point in the perspective transformation? if so, how are we ending up back at a right-parallelipid (homogenous clip-space) at the end of it all?

1
openglgeometryglsllinear-algebraperspectivecamera
What makes you think we end at clip-space? The next step is NDC (at this point perspective is applied because of the division by w), and then window-space after the viewport transformation is applied. NDC and window-space are also 4D, if you divide them by w you actually go back to the cube you had in clip-space because NDC_w and window_w are 1/clip_w. – Andon M. Coleman

1 Answers

6
votes

You are right in the sense that there is just some affine, linear transformation and no real perspective distortion - when you just interpret the clip space as a 4-dimensional vector space.

But the clip space is not the "end of it all". The perspective effect is a nonlinear transformation which is finally achieved by the perspective division which will be done after the transformation to clip space. The projection matrix determines the w value that will be the divisor for this, and which is typically just -z_eye.