Rotation About an Arbitrary Axis Authors: John McDonald DePaul University Rotation matrices are one of the first topics covered in introductory graphics courses, and yet the details of arbitrary rotation matrices often get swept under the rug due to their complexity. This CGEM presents a direct, constructive derivation of the matrix for a rotation about an arbitrary axis, enhanced with animations that help build intuition for the calculation. The details of this derivation can be described in an intuitive manner that builds on the procedure for calculating the matrices for rotations about the coordinate axes. This treatment is suitable for use as a handout for students to use as a supplement to the usual course text. Submission type: Lessons / Teaching GEMS Published at: 18/7/2006 License: This work is granted for Academic Fair Use Download (3,8 MB) Categories: 3D animation, Fundamentals: Mathematics Keywords: Animation 3D, Linear algebra Other Keywords: Fundamental Algorithms, Graphics Foundations Requirements: The animations are encoded with the "Cinepak" codec which is distributed with nearly all versions of Microsoft Windows, and with the Macs operating system as well. The animations will also be made available in two different MPEG4 formats at the following two addresses: http://mcdonald.cs.depaul.edu/ArbitraryRotation/MicrosoftMPEG4.zip http://mcdonald.cs.depaul.edu/ArbitraryRotation/DivxMPEG4.zip Intended Audience: University courses in the Foundations of Computer Graphics Prerequisites: This module assumes that students in the course have covered the following material, either in a previous course or earlier in the same course: * Basic vector operations * Linear transformations and their representations as matrics A more detailed list of prerequisite topics is supplied in the course module.