Eric Lengyel, Terathon Software LLC, USA
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.