Introducing Geometric Algebra to Geometric Computing Software Developers: A Computational Thinking Approach

TL;DR

This paper advocates for using Geometric Algebra as a unifying mathematical language in Geometric Computing software development, emphasizing computational thinking for effective integration and addressing current design challenges.

Contribution

It introduces Geometric Algebra to software engineers through a high-level, conceptual approach and promotes computational thinking methods for developing geometric computing systems.

Findings

GA provides a unifying algebraic framework for geometric models

Applying computational thinking facilitates GA integration in software engineering

Enhances software design and maintenance in geometric computing

Abstract

Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying algebraic system to describe geometric models, the use of software abstractions alone can result in many design and maintenance problems. Geometric Algebra (GA) can be a universal abstract algebraic language for software engineering geometric computing applications. Few sources, however, provide enough information about GA-based software implementations targeting the software engineering community. In particular, successfully introducing GA to software engineers requires quite different approaches from introducing GA to mathematicians or physicists. This article provides a high-level introduction to the abstract concepts and algebraic representations behind the elegant GA mathematical structure. The article focuses on the conceptual and representational abstraction levels behind GA mathematics with sufficient references for more details. In addition, the article strongly recommends applying the methods of Computational Thinking in both introducing GA to software engineers, and in using GA as a mathematical language for developing Geometric Computing software systems.