High-quality surface remeshing using harmonic maps

• Published in: International journal for numerical methods in engineering Vol. 83; no. 4; pp. 403 - 425
• Main Authors: Remacle, J.-F., Geuzaine, C., Compère, G., Marchandise, E.
• Format: Journal Article Web Resource
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 23.07.2010; Wiley; John Wiley & Sons
• Subjects: Applied sciences; Computer aided design; Computer science; Computer science; control theory; systems; Copyrights; Curved; Engineering, computing & technology; Exact sciences and technology; Freeware; harmonic map; Harmonics; Ingénierie, informatique & technologie; Mechanical engineering. Machine design; Representations; Sciences informatiques; Software; STL file format; surface mapping; surface parametrization; surface remeshing; surface smoothing; Triangles; Harmonic; Triangulation; harmonic map; STL format; Stereolithography; Topology; surface remeshing; Parameterization; Automatic mesh generation; Open source software; surface parametrization; Computational geometry; Smoothing; surface mapping; Rapid prototyping; STL file format; Cubics; Curvature; surface smoothing; Computer aided design; Surface conditions; Mesh generation; File format
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.2824

In this paper, we present an efficient and robust technique for surface remeshing based on harmonic maps. We show how to ensure a one‐to‐one mapping for the discrete harmonic map and introduce a cubic representation of the geometry based on curved PN triangles. Topological and geometrical limitations of harmonic maps are also put to the fore and discussed. We show that, with the proposed approach, we are able to recover high quality meshes from both low input STL triangulations and complex surfaces defined by many CAD patches. The overall procedure is implemented in the open‐source mesh generator Gmsh. Copyright © 2010 John Wiley & Sons, Ltd.