A Bigger Mathematical Picture for Computer Graphics
Slideshow & audio of Eric Lengyel’s keynote in the 2012 WSCG conference in Plzeň, Czechia, on geometric algebra for computer graphics.
Timestamps:
0:00 Introduction
2:07 History
3:41 Outline of the talk
4:48 Grassmann algebra in 3-4 dimensions: wedge product, bivectors, trivectors, transformations
37:04 Homogeneous model
47:26 Practical applications: Geometric computation
56:27 Programming considerations
1:01:41 Summary
Short abstract: "This talk introduces the basic concepts of the exterior algebra (aka geometric algebra or Clifford algebra) and presents a bigger mathematical picture that enables a deeper understanding of computer graphics concepts such as homogeneous coordinates for representing points, lines, and planes, the operations that can be performed among them using the progressive and regressive products, and incomplete pieces of the bigger picture, such as Plücker coordinates."
● Full abstract: http://wscg.zcu.cz/wscg2012/tutorial/...
● Slides (pdf): http://www.terathon.com/wscg12_lengye...
● About the author: http://www.terathon.com/lengyel/
● About geometric algebra: https://en.wikipedia.org/wiki/Geometr...
● Some photos of the keynote: http://imgur.com/a/JrPRX
Note: most of this information (including the video, available for both streaming and download as mp4) is available at the website of the Centre of Computer Graphics and Visualization of the University of West Bohemia: http://graphics.zcu.cz/seminars/?grap...