25: Using Tensor Diagrams to Represent and Solve Geometric Problems



Monday, Half Day
1:30 – 5:15 pm
River Room 001

Introduction to tensor diagrams, a really cool algebraic manipulation tool that can help solve many problems in analytic geometry.

Prerequisites
Familiarity with homogeneous coordinate geometry and basic matrix operations. Distaste for page-long algebraic expressions.

Topics
Review of homogeneous coordinate math. Notational problems with matrices. Einstein Index notation. How tensor diagrams represent basic operations. Application of tensor diagrams to 1D homogeneous equations (polynomials), 2D homogeneous equations (curves), 3D homogeneous equations (surfaces). Unsolved (at least to the knowledge of the speaker) problems.

Organizer/Lecturer
James F. Blinn
Microsoft Corporation


Schedule


Module 1 – Basic Tools
1:30 Problems With Conventional Notation
Blinn
1:45 Overview of Tensor Diagrams
Blinn
2:30 Substitution and Unknown Roots
Blinn
2:50 The Epsilon-Delta Identity
Blinn
3:15 Break
Module 2 - Applications
3:30 1D Homogeneous Problems (Polynomials)
Blinn
4:00 2D Homogeneous Problems (Curves)
Blinn
4:45 3D Homogeneous Problems (Surfaces)
Blinn
5:00 Review of Main Points and Unsolved Problems
Blinn




Additional information from SIGGRAPH 2002 Courses is available in the Course Notes
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