Projection Matrix Tricks

Speakers: Eric Lengyel

Track: Programming

Format: Lecture

Experience Level: Intermediate

Description: There are several mathematical tricks that can be applied to the ordinary perspective projection matrix to achieve various effects. While some of these effects can be implemented using special hardware capabilities, doing so can incur a performance penalty in addition to extra shader management headaches. In this session, the inner workings of the perspective projection matrix are examined, and several techniques for modifying the properties of the projection matrix to solve specific rendering problems are discussed. In particular, techniques are presented for modifying the projected depth of polygons and for moving the near clipping plane to an arbitrary oblique position.

Idea Takeaway: The attendee will learn several mathematical techniques for modifying the projection matrix to achieve particular effects at no performance cost in cases where using special rendering hardware to achieve the same effect would incur a performance penalty. Each technique has previously been published by the speaker, peer reviewed, and battle tested in real-world projects.

Intended Audience: This session is intended for intermediate graphics engine programmers who have a good grasp of the standard vertex transformation pipeline.