3D oriented projective geometry through versors of \(\mathbb R^{3,3}\)

DOI10.1007/s00006-015-0625-yzbMath1379.51001OpenAlexW2301269329WikidataQ59461408 ScholiaQ59461408MaRDI QIDQ2360817

Leo Dorst

Publication date: 29 June 2017

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

Full work available at URL: https://doi.org/10.1007/s00006-015-0625-y

zbMATH Keywords

rotorcomputer graphicsClifford algebraprojective geometrygeometric algebrahomogeneous coordinatesPlücker coordinatesprojective collineationversororiented projective geometryoriented linesbivector generatororiented reflection

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Clifford algebras, spinors (15A66) Quadratic and bilinear forms, inner products (15A63) General theory of linear incidence geometry and projective geometries (51A05) Exterior algebra, Grassmann algebras (15A75) Quadratic spaces; Clifford algebras (11E88)

Related Items (9)

Matrices of \(\mathrm{SL}(4,\mathbb R)\) that are the product of two skew-symmetric matrices ⋮ Paravectors and the geometry of 3D Euclidean space ⋮ Quadric conformal geometric algebra of \({\mathbb {R}}^{9,6}\) ⋮ Modeling 3D geometry in the Clifford algebra \(\mathbb R(4,4)\) ⋮ Complementary orientations in geometric algebras ⋮ Connections between matrix products for 3-vectors and geometric algebra ⋮ On the Clifford algebraic description of transformations in a 3D Euclidean space ⋮ Consistently oriented dart-based 3D modelling by means of geometric algebra and combinatorial maps ⋮ Basis-free formulas for characteristic polynomial coefficients in geometric algebras

Cites Work

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• A Clifford algebraic approach to line geometry
• \(R(4, 4)\) as a computational framework for 3-dimensional computer graphics
• Lie groups as spin groups
• Line Geometry in Terms of the Null Geometric Algebra over ℝ3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms
• Computational line geometry

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