A Bigger Mathematical Picture for Computer Graphics

Written by Eric Lengyel (external)

Eric Lengyel

Terathon Software LLC, USA

Invited talk in English
WSCG 2012
June 25, 2012
University of West Bohemia

Media

Presentation video (56 MB) watch online or download.

Abstract

Some of the most brilliant mathematical discoveries of the 1800s were pushed aside for over a century in favor of the vector analysis and linear algebra that we are all familiar with. However, these old ideas have recently been rediscovered in the field of computer graphics by researchers who understand how they can unify many of the geometric operations that are used every day.

This talk introduces the basic concepts of the exterior algebra and presents a bigger mathematical picture that enables a deeper understanding of the homogeneous representation of points, lines, and planes, as well as the operations that can be performed among them using the progressive and regressive products. Some emphasis is placed on the history of related mathematics and the past development of incomplete pieces of the bigger picture, such as Plucker coordinates. The goal is to help the audience unlearn some longstanding misnomers in 3D geometry and to provide the knowledge of a larger, unified world into which many familiar mathematical concepts fit together.