Consistently Oriented Dart-based 3D Modelling by Means of Geometric Algebra and Combinatorial Maps

• Published in: Advances in applied Clifford algebras Vol. 29; no. 1; pp. 1 - 53
• Main Authors: Soto-Francés, Víctor-Manuel, Sarabia-Escrivá, Emilio-José, Pinazo-Ojer, José-Manuel
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2019; Springer Nature B.V
• Subjects: Algebra; Applications of Mathematics; Boundary representation; Combinatorial analysis; Computation; Constructive solid geometry; Embedding; Mathematical and Computational Physics; Mathematical Methods in Physics; Orbits; Physics; Physics and Astronomy; Properties (attributes); Robustness (mathematics); Source code; Theoretical; Three dimensional models; Topology; gmaps; Combinatorial maps; Solid modelling; Building energy simulation; Geometric algebra; Multi-vectors; Darts; Clifford algebra; Flags

The modelling of real world objects is not a straightforward subject. There are many different schemes; constructive solid geometry (CSG), cell decomposition, boundary representation, etcetera. Obviously, somehow, any scheme will be related to any other since they have a common goal. The paper shows...