Core Concepts
Efficiently process and analyze geometric algebra computations using SUGAR in Matlab.
Abstract
The content introduces Symbolic and User-friendly Geometric Algebra Routines (SUGAR) for computations in Matlab. It discusses the significance of geometric algebra, its applications in robotics, and the challenges faced due to complexity. SUGAR aims to simplify geometric algebra operations by providing user-friendly functions tailored for high-dimensional GAs, supporting both numeric and symbolic computations. The toolbox efficiently handles functions of multivectors, enhancing its applicability across various engineering domains.
Introduction to Geometric Algebra
GA as a mathematical tool for geometric computing.
Applications in robotics and simplification of complex equations.
State of the Art
Overview of computational libraries like CLICAL, Versor, Ganja.js.
Implementations in programming languages and specialized packages.
Overview of SUGAR Toolbox
Features include GA creation, multivector definition, symbolic coefficients handling.
Basic operations like addition and subtraction of multivectors.
Stats
For instance, within the GA G3,0,0, a multivector ๐ดcan be defined as: A=e1+5e2+4e12-7*e123
Quotes
"GA simplifies the process to the multiplication of special elements called rotors."
"SUGAR facilitates translation of GA concepts into Matlab with user-friendly functions."