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PPGA Racing

A racing game using Plane-Based Projective Geometric Algebra instead of matrices

Project Overview

This innovative racing game uses Plane-Based Projective Geometric Algebra (PPGA) instead of traditional matrix transformations. It demonstrates how sandwich products can replace matrix operations for transformations in game development.

PPGA Mathematics

Uses geometric algebra instead of matrices for all transformations

Sandwich Product

Employs the sandwich product for rotations and translations

3-Car Racing

Features player-controlled car and two AI opponents

Game Showcase

Plane-Based Projective Geometric Algebra

PPGA is a cutting-edge mathematical framework that uses geometric algebra instead of traditional matrix transformations. Instead of using transformation matrices for rotations, translations, and scaling, PPGA uses multivectors and sandwich products.

Traditional Approach

  • Uses 4x4 transformation matrices
  • Matrix multiplication for transformations
  • Separate matrices for each transformation type
  • Requires matrix inversion for certain operations

PPGA Approach

  • Uses multivectors to represent objects and transformations
  • Sandwich product (versor) for all transformations
  • Unified representation for rotations, translations, etc.
  • More intuitive geometric operations

Technical Implementation

  • All car movements controlled through PPGA operations
  • Camera transformations implemented with sandwich products
  • Physics calculations using geometric algebra
  • No matrix libraries used in the entire project

Game Features

Player Controls

Mouse-based steering - click where you want the car to rotate toward

Speed Control

Dynamic acceleration and braking mechanics

AI Opponents

Two AI-controlled cars with pathfinding logic

PPGA Camera

Camera movement implemented with geometric algebra

Project Documentation

PPGA Implementation Details

Download PDF

Technical Highlights

PPGA Concepts

Game Implementation

Designed and built by Ivans Minajevs.