Work

Geometric algebra for quadrics—transformations and their efficient implementation

Year: 2026

Type: article

Abstract: This paper describes the geometric algebra for quadrics (GAQ) with a focus on elements representing Euclidean transformations, particularly translations and rotations. We provide general methods of deriving the generators of such transformations and verify their correctness on examples. We also show how to compute the versors numerically, yet their exact form is rather technical and extensive because of the high dimension of GAQ. Thus, we introduce a convenient C++ implementation. This article is part of the theme issue 'Modern applications of geometric algebra'.

Source: Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

DOI: 10.1098/rsta.2025.0098

Authors: Aleš Návrat, Ludvík Procházka, Petr Vašík

Institution: Brno University of Technology

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W7202385935

FWCI: 2.198

Cites: 12

Cited by: 1

Related to: 10