## FAll 2020 - EN.500.111.05 HEART: Geometric Algebra Computing and Its Applications

Geometric Algebra (GA) is an extension of Linear Algebra, popularized by the physicist David Hestenes. Linear Algebra manipulates one-dimensional objects, the vectors, using only algebraic expressions and without referencing a coordinate system; Geometric Algebra generalizes this concept to manipulate higher dimensional objects algebraically and without defining the objects in coordinate systems. As a result, GA provides a unified mathematical language to model various kinds of problems across different areas, including physics (special and general relativity), computer sciences (computer graphics), engineering (robotics), etc.

This course is for freshmen who have no background in Linear and Geometric Algebra. We will begin with tutorial and hands-on in-class exercises to explore Compass Ruler Algebra. Then, we will learn the mathematical foundations of GA, starting with 2D Euclidean geometry that students should have learned in high school, and extend the concept to Compass Ruler Algebra. At last, we will study its applications in robot kinematics, computer vision, and computer graphics.

### Logistic

• Period: 09/08/2020 - 11/20/2020
• Times: Monday, 17:00-18:15

### References

• [IGAC] “Introduction to Geometric Algebra Computing”, Dietmar Hildenbrand, CRC Press (2019).
• [FGAC] “Foundations of Geometric Algebra Computing”, Dietmar Hildenbrand, Springer (2013). Online access
• [UGA] “Understanding Geometric Algebra”, Kenichi Kanatani, CRC Press (2015). Online access
• [GACS] “Geometric Algebra for Computer Science”, Leo Dorst, Daniel Fontijne, Stephen Mann, Morgan Kaufmann (2010). Online access
• [GACG] “Geometric Algebra for Computer Graphics”, John Vince, Springer (2008). Online access

### Schedule

#

Days

Topics & keynotes

Files

Videos

References

01

09/14

IGAC Ch1, FGAC Ch1

02

09/21

IGAC Ch2 & Ch3, FGAC Ch10, GAALOP, Maxima - Win64, Linux64

03

09/28

IGAC Ch2 & Ch3, FGAC Ch10

04

10/05

IGAC Ch4, FGAC Ch2, GACG Ch2 & Ch3

05

10/12

IGAC Ch2 & Ch5, GACG Ch7

06

10/19

IGAC Ch6, FGAC Ch3, GACG Ch8

07

10/26

IGAC Ch7, FGAC Ch3, GACG Ch7 & Ch8

08

11/02

IGAC Ch8, FGAC Ch3

09

11/09

IGAC Ch10 & Ch13, CGVAS, FGAC Ch5

10

11/16

IGAC Ch9 & Ch14, FGAC Ch7 & Ch8