Modeling 3D geometry in the Clifford algebra \(\mathbb R(4,4)\)

DOI10.1007/s00006-017-0798-7zbMath1386.15045OpenAlexW2739229856MaRDI QIDQ1686875

Stephen Mann, Juan Du, Ronald N. Goldman

Publication date: 18 December 2017

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-017-0798-7

zbMATH Keywords

affine geometrycomputer graphicsmother algebra

Mathematics Subject Classification ID

Clifford algebras, spinors (15A66)

Related Items (8)

Paravectors and the geometry of 3D Euclidean space ⋮ Quadric conformal geometric algebra of \({\mathbb {R}}^{9,6}\) ⋮ Projective geometric algebra as a subalgebra of conformal geometric algebra ⋮ Self-reverse elements and lines in an algebra for 3D space ⋮ On the Clifford algebraic description of transformations in a 3D Euclidean space ⋮ Three-dimensional quadrics in extended conformal geometric algebras of higher dimensions from control points, implicit equations and axis alignment ⋮ Garamon: a geometric algebra library generator ⋮ New applications of Clifford's geometric algebra

Uses Software

• Gaigen

Cites Work

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• Geometric algebra with applications in engineering
• \(R(4, 4)\) as a computational framework for 3-dimensional computer graphics
• 3D oriented projective geometry through versors of \(\mathbb R^{3,3}\)
• Geometric algebras for Euclidean geometry
• Lie groups as spin groups
• Conic and cyclidic sections in double conformal geometric algebra G8,2 with computing and visualization using Gaalop
• Line Geometry in Terms of the Null Geometric Algebra over ℝ3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms
• On the Homogeneous Model of Euclidean Geometry
• Computational line geometry

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