This Numberphile video is well worth your time. Wouldn’t Tony DeRose make a great guest speaker in a math class?
How do 3D animated characters look so smooth? Pixar researcher Tony DeRose explains – with mathematics.
http://graphics.pixar.com/research/
Tony DeRose papers: http://bit.ly/DeRosePapers
Ed Catmull’s paper: http://bit.ly/1stJNht
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