OpenGL Programming Guide: The Official Guide to Learning OpenGL, Version 4.3, Eighth Edition

Rotation

Let v = (x, y, z)^T, and u = v/||v|| = (x′, y′, z′)^T. Also let

and,

M = uu^T + cos θ(I – uu^T) + sin θ S

where

Then

where m represents the elements from M, which is the 3×3 matrix defined on the preceding page. The R matrix is always defined. If x = y = z = 0, then R is the identity matrix. You can obtain the inverse of R, R^–1, by substituting –θ for θ, or by transposition.

Often, you’re rotating about one of the coordinate axes; the corresponding ...