ADAPTIVE REMESHING FOR EDGE LENGTH INTERVAL CONSTRAINING

Authors

  • JO~AO VITOR DE SA HAUCK Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil
  • RAMON NOGUEIRA DA SILVA Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil
  • MARCELO BERNARDES VIEIRA Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil
  • RODRIGO LUIS DE SOUZA DA SILVA Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil

Keywords:

iterative remeshing, edge length equalization, interval constraining

Abstract

This paper presents a method for explicitly remesh an arbitrary input surface into a mesh with all edge lengths within a xed interval. The process starts with an arbitrary triangular 2-manifold mesh. The proposed method is iterative and uses stellar operations to achieve the necessary amount of vertices and triangles. It also applies a technique to uniformly distribute the vertices of the model over the surface. At earlier stages of the algorithm, this technique is an approximation of the Laplacian lter. In order to preserve the geometry of the model, some constraints are added to the lter. At later stages, we replace the global uniformization strategy with a nonlinear optimizer, that performs only locally. A projection step is also applied at each iteration, to prevent the geometric distortions caused by the method. We also apply a post processing step to correct the nal edges, if the standard iterations do not converge. Our method results in a very regular mesh, with uniform distribution of vertices. The dual trivalent mesh obtained by this mesh can be useful for several applications. The main contribution of this work is a new approach for edge length equalization, with explicit constraints denition, higher computational performance and lower global geometry losses if compared to previous works.

 

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2015-07-26

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