Iterative Method for Edge Length Equalization

Abstract This paper presents a method for triangular surface remeshing to obtain new faces whose edge lengths are as close as possible to a target value m. The process uses as input a 2-manifold mesh with arbitrary geometry and topology. The proposed algorithm runs iteratively, automatically adjusting the necessary amount of vertices, and applies a global relaxation process using a variation of Laplace-Beltrami discrete operator. We introduce geometry constraints in order to preserve salient features of the original model. The method results on a grid with edge lengths near to m with low standard deviation, i.e. the vertices are uniformly distributed over the original surface. The dual space of the final triangular surface results in a trivalent, mostly hexagonal mesh, suitable for several applications.

[1]  Mark Meyer,et al.  Interactive geometry remeshing , 2002, SIGGRAPH.

[2]  Eugene Zhang,et al.  Editing operations for irregular vertices in triangle meshes , 2010, ACM Trans. Graph..

[3]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[4]  Martin Isenburg,et al.  Isotropic surface remeshing , 2003, 2003 Shape Modeling International..

[5]  Eugene Zhang,et al.  Hexagonal Global Parameterization of Arbitrary Surfaces , 2010, IEEE Transactions on Visualization and Computer Graphics.

[6]  Craig Gotsman,et al.  Explicit Surface Remeshing , 2003, Symposium on Geometry Processing.

[7]  Dong-Ming Yan,et al.  Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram , 2009, Comput. Graph. Forum.

[8]  Pierre Alliez,et al.  Periodic global parameterization , 2006, TOGS.

[9]  Pierre Alliez,et al.  Polygon Mesh Processing , 2010 .

[10]  Donald W. Brenner,et al.  A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons , 2002 .

[11]  Paolo Cignoni,et al.  Almost Isometric Mesh Parameterization through Abstract Domains , 2010, IEEE Transactions on Visualization and Computer Graphics.

[12]  H. Chatley.  Cohesion , 1921, Nature.

[13]  Bruno Levy.  Constrained Texture Mapping , 2000, SIGGRAPH 2000.

[14]  D. Bommes,et al.  Mixed-integer quadrangulation , 2009, SIGGRAPH 2009.

[15]  Leif Kobbelt,et al.  A remeshing approach to multiresolution modeling , 2004, SGP '04.