High-quality surface remeshing using harmonic maps-Part II: Surfaces with high genus and of large aspect ratio

E. Marchandise, C. Carton de Wiart, W. G. Vos, C. Geuzaine, J.-F. Remacle
2011 International Journal for Numerical Methods in Engineering  
This paper follows a previous one that was dealing with high quality surface remeshing using harmonic maps [1]. In [1] , it has been demonstrated that harmonic parametrizations can be used as input for surface meshers to produce high quality triangulations. However, two important limitations were pointed out, namely surfaces with high genus and/or of large aspect ratio. This papers addresses those two issues. We first develop a multiscale version of the harmonic parametrization of [1] and then
more » ... ombine it with a multilevel partitioning algorithm to come up with an automatic remeshing algorithm that overcomes the above mentioned limitations of harmonic maps. The overall procedure is implemented in the open-source mesh generator Gmsh [2]. Prepared using nmeauth.cls † For example, a sphere has a genus G = 0 and N B = 0, a disk has G = 0 but N B = 1 and a torus has G = 1 and N B = 0 Prepared using nmeauth.cls § Note that the pathological sets of triangles which contain only very few triangles are not taken into account. The triangles belonging to those sets are then tagged as T * 0,good .
doi:10.1002/nme.3099 fatcat:rvrtuzo63ncvxddq6ouhwy6owq