This content explores the application of Geometric Algebra, specifically Projective Geometric Algebra ($mathbb R_{3,0,1}$), in computer graphics and machine learning. Despite its wide range of uses, PGA’s adoption in traditional 3D graphics has been limited. The ‘Look, Ma, No Matrices!’ project introduces a modern 3D engine that integrates PGA algebra to broaden its applicability. The project aims to explore solutions and techniques necessary for a successful transition to PGA implementation. It challenges the common belief that matrices are the fastest choice and provides efficient implementations for geometric products, composition of transformations, transformation of points and directions, normalization, square roots, and the exponential map.
https://enkimute.github.io/LookMaNoMatrices/