Global Anisotropic Quad-Dominant Remeshing

This paper proposes an anisotropic quad-dominant remeshing algorithm suitable for meshes of arbitrary topology.It takes an approach to the challenging problem of obtaining an anisotropic quad-dominant mesh.The method consists of operations that sample surface geometry by dense principle curvature lines and sort curvature-lines by variations of surface normal and volume related to them.The anisotropic sampling of curvature lines is then obtained by implementing a prioritization scheme of curvature lines elimination.The strategy is simple and straightforward to implement.It is flexible to produce anisotropic quad-dominant meshes ranging from dense to coarse too.The resulting meshes exhibit better anisotropic distribution than comparable methods while maintaining high geometric fidelity.

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

[2]  Konrad Polthier,et al.  QuadCover ‐ Surface Parameterization using Branched Coverings , 2007, Comput. Graph. Forum.

[3]  Bruno Lévy,et al.  Mesh parameterization: theory and practice , 2007, SIGGRAPH Courses.

[4]  E. Zhang,et al.  Rotational symmetry field design on surfaces , 2007, SIGGRAPH 2007.

[5]  Steven J. Gortler,et al.  Geometry images , 2002, SIGGRAPH.

[6]  R. B. Simpson.  Anisotropic mesh transformations and optimal error control , 1994 .

[7]  Leif Kobbelt,et al.  Resampling Feature and Blend Regions in Polygonal Meshes for Surface Anti‐Aliasing , 2001, Comput. Graph. Forum.

[8]  Leif Kobbelt,et al.  A Robust Two‐Step Procedure for Quad‐Dominant Remeshing , 2006, Comput. Graph. Forum.

[9]  S. Rusinkiewicz.  Estimating curvatures and their derivatives on triangle meshes , 2004 .

[10]  Shi-Min Hu,et al.  An incremental approach to feature aligned quad dominant remeshing , 2008, SPM '08.

[11]  Valerio Pascucci,et al.  Spectral surface quadrangulation , 2006, SIGGRAPH 2006.

[12]  Pierre Alliez,et al.  Anisotropic polygonal remeshing , 2003, ACM Trans. Graph..

[13]  L. Kobbelt,et al.  Spectral quadrangulation with orientation and alignment control , 2008, SIGGRAPH 2008.

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

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

[16]  Marco Attene,et al.  Recent Advances in Remeshing of Surfaces , 2008, Shape Analysis and Structuring.

[17]  Pierre Alliez,et al.  Designing quadrangulations with discrete harmonic forms , 2006, SGP '06.

[18]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

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

[20]  Eduardo F. D'Azevedo,et al.  Are Bilinear Quadrilaterals Better Than Linear Triangles? , 2000, SIAM J. Sci. Comput..

[21]  Konstantin Mischaikow,et al.  Vector field design on surfaces , 2006, TOGS.

[22]  Bruno Lévy,et al.  N-symmetry direction field design , 2008, TOGS.

[23]  Pedro V. Sander,et al.  Multi-Chart Geometry Images , 2003, Symposium on Geometry Processing.

[24]  David Bommes,et al.  Quadrangular Parameterization for Reverse Engineering , 2008, MMCS.

[25]  Mathieu Desbrun,et al.  Variational shape approximation , 2004, SIGGRAPH 2004.

[26]  Leif Kobbelt,et al.  Direct anisotropic quad-dominant remeshing , 2004, 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings..