Quasi-Isometric Mesh Parameterization Using Heat-Based Geodesics and Poisson Surface Fills

• Published in: Mathematics (Basel) Vol. 7; no. 8; p. 753
• Main Authors: Mejia-Parra, Daniel, Sánchez, Jairo R., Posada, Jorge, Ruiz-Salguero, Oscar, Cadavid, Carlos
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2019
• Subjects: Algorithms; Approximation; CAD; Computer aided design; Food science; geodesic maps; Geodesy; Heat; heat transfer analysis; Mapping; mesh parameterization; Optimization; Parameterization; Partial differential equations; Poisson fills; Reverse engineering; Thermodynamics

In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ϕ from the original mesh M ∈ R 3 to the planar domain ϕ ( M ) ∈ R 2 . The mapping may preserve angles, areas, or dista...