Rotation Matrices and Formulas

See the rotations in action at

This may be of interest to those looking for some concrete formulas for matrix rotations.  Some time ago (September 7, 2005) I posted a page about Rotation About an Arbitrary Axis in 3 Dimensions (PDF version below); I updated this paper in July 2011 when someone at the example site kindly pointed out a typo in the paper (not in the Java code; the error was that (bu - av) should have been (av - bu) in the 3,4 entries in the last 4x4 matrices).

This has been a popular reference for people seeking complete formulas for rotations about a line not through the origin.  Similar expositions for the simpler problem of rotations about an arbitrary axis through the origin are found here in Section 2.3.1 and in The Nested dimensions section of the Rotation matrix article on Wikipedia (the matrix Q_u(theta) in the Wikipedia article is the matrix for rotation about the origin I give in Rotation About an Arbitrary Axis in 3 Dimensions).  The last time I checked these articles lacked formulas for the rotations as functions.

Below I've attached Java code for the rotations described in the paper.  This uses the same notations as in the paper.  As a programming exercise I've written a web application that gives a visualization of rotations at
Glenn Murray,
Aug 28, 2013, 8:37 AM
Glenn Murray,
Jun 6, 2013, 9:48 PM