How do I create a bounding frustum from a view & projection matrix?

Question

Given a left-handed Projection matrix, a left-handed View matrix, a ViewProj matrix of View * Projection - How do I create a bounding Frustum comprised of near, far, left, right and top, bottom planes?

The only example I could find on Google (Tutorial 16: Frustum Culling) seems to not work; for example, if the math is used as given, the near-plane's distance is a negative. This places the near-plane behind the camera...

Answer 1

The easiest way I know of is to construct the view frustum in post-projective space (so-called NDC space), where the frustum is a cube, then transform it through the inverse view-projection matrix and construct the planes in world space.

The frustum in NDC space runs from -1 to +1 along the x and y axes, and from -1 to +1 on z if you're in OpenGL, or 0 to 1 on z if you're in D3D. Build the eight corners of this cube (setting w = 1), then multiply them by the inverse view-projection matrix, and divide by w to convert back to regular 3D points.

The result should be the frustum corners in world space, and you can then build the planes by using groups of 3 points and the usual formula for calculating a plane equation from 3 points.

This general technique should work with any kind of view-projection matrix - perspective or orthographic, oblique or straight, any FoV or aspect ratio, etc. There are ways to simplify it by making some assumptions about the form of the matrix, but those tend to break if any of the assumptions are changed.