Essential Math Weblog Thoughts on math for games

So GDC 2013 has come and gone, and with it another tutorial session. This year I did not run the Physics Tutorial, passing that on to Erin Catto’s more than capable hands. Instead, I organized the Math Tutorial for the first day, with the following lineup:

• Interpolation and Splines – Squirrel Eiserloh (The Guildhall at SMU)
• Matrix Transformations – Squirrel Eiserloh (The Guildhall at SMU)
• Understanding Quaternions – Jim Van Verth (Google)
• Dual Numbers – Gino van den Bergen (Dtecta)
• Orthogonal Matching Pursuit and K-SVD for Sparse Encoding – Robin Green (Microsoft) and Manny Ko (Imaginations Technologies)
• Computational Geometry – Graham Rhodes (Applied Research Associates Inc.)
• Interaction with 3D Geometry – Stan Melax (Intel)

Overall, I thought it was a good mix of beginning and advanced topics. So a big thank you to all the speakers — I learn something from them every year, and without them it wouldn’t be possible. And as time goes on, I’ll add links to the slides as they come in.

Before I close, I have one comment on my talk. As I was discussing the matrix form of the quaternion, I mentioned that multiplying by a rotation on the left is the same as multiplying by the inverse of the rotation on the right. As I think I made clear later, this is not true. I was trying to convey how I originally — and incorrectly — thought about it but I fear I may have misled some in the audience. What was thinking was that if you multiply a column vector on the right by a rotation matrix, i.e. Rv, this is the same as multiplying a row vector on the left by the inverse, i.e. v^TR^-1. But of course, we’re not multiplying vectors, we’re multiplying a matrix Q which represents a quaternion, which in turn represents a vector. So, not quite the same thing, and the end the result is not the same. I’ve modified the notes in the slides to make this clearer.