Consistently oriented dart-based 3D modelling by means of geometric algebra and combinatorial maps

DOI10.1007/s00006-018-0927-yzbMath1452.68248OpenAlexW2910788985WikidataQ128625133 ScholiaQ128625133MaRDI QIDQ1728285

Emilio-José Sarabia-Escrivá, José-Manuel Pinazo-Ojer, Víctor-Manuel Soto-Francés

Publication date: 22 February 2019

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

Full work available at URL: https://doi.org/10.1007/s00006-018-0927-y

zbMATH Keywords

Clifford algebrageometric algebraflagscombinatorial mapssolid modellingdarts\(n\)-gmapsbuilding energy simulationmulti-vectors

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Polyhedra and polytopes; regular figures, division of spaces (51M20) Clifford algebras, spinors (15A66)

Uses Software

• CGAL
• CLIFFORD
• CGoGN
• EnergyPlus
• GitHub
• CGAP
• MOKA
• geoma

Cites Work

• Unnamed Item
• Why starting from differential equations for computational physics?
• Clifford algebra to geometric calculus. A unified language for mathematics and physics
• Topological models for boundary representation: A comparison with \(n\)- dimensional generalized maps
• Projective geometry with Clifford algebra
• Representing geometric structures in \(d\) dimensions: Topology and order
• Homology of cellular structures allowing multi-incidence
• 3D oriented projective geometry through versors of \(\mathbb R^{3,3}\)
• Mechanics in space and counterspace
• N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS
• On the Homogeneous Model of Euclidean Geometry
• Combinatorial Maps
• Combinatorial Image Analysis

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