QuadCover – surface parameterization using branched coverings. We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2-manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2-manifold and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes.

References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Novello, Tiago; Paixão, João; Tomei, Carlos; Lewiner, Thomas: Discrete line fields on surfaces (2021)
  2. Zheng, Xiaopeng; Zhu, Yiming; Chen, Wei; Lei, Na; Luo, Zhongxuan; Gu, Xianfeng: Quadrilateral mesh generation. III: Optimizing singularity configuration based on Abel-Jacobi theory (2021)
  3. Groen, Jeroen P.; Stutz, Florian C.; Aage, Niels; Bærentzen, Jakob A.; Sigmund, Ole: De-homogenization of optimal multi-scale 3D topologies (2020)
  4. Karčiauskas, Kȩstutis; Peters, Jörg: Low degree splines for locally quad-dominant meshes (2020)
  5. Lei, Na; Zheng, Xiaopeng; Luo, Zhongxuan; Luo, Feng; Gu, Xianfeng: Quadrilateral mesh generation. II: Meromorphic quartic differentials and Abel-Jacobi condition (2020)
  6. Maquart, Tristan; Wenfeng, Ye; Elguedj, Thomas; Gravouil, Anthony; Rochette, Michel: 3D volumetric isotopological meshing for finite element and isogeometric based reduced order modeling (2020)
  7. Poelke, Konstantin; Polthier, Konrad: Discrete Poincaré duality angles as shape signatures on simplicial surfaces with boundary (2020)
  8. Xiao, Zhoufang; He, Shouping; Xu, Gang; Chen, Jianjun; Wu, Qing: A boundary element-based automatic domain partitioning approach for semi-structured quad mesh generation (2020)
  9. Chen, Wei; Zheng, Xiaopeng; Ke, Jingyao; Lei, Na; Luo, Zhongxuan; Gu, Xianfeng: Quadrilateral mesh generation. I: Metric based method (2019)
  10. Karčiauskas, Kȩstutis; Peters, Jörg: Localized G-splines for quad & T-gon meshes (2019)
  11. Viertel, Ryan; Osting, Braxton: An approach to quad meshing based on harmonic cross-valued maps and the Ginzburg--Landau theory (2019)
  12. Bobenko, Alexander I.; Tsarev, Sergey: The curvature line parametrization from circular nets on a surface (2018)
  13. Xiao, Shiwei; Kang, Hongmei; Fu, Xiao-Ming; Chen, Falai: Computing IGA-suitable planar parameterizations by polysquare-enhanced domain partition (2018)
  14. Zhou, Jiaran; Campen, Marcel; Zorin, Denis; Tu, Changhe; Silva, Claudio T.: Quadrangulation of non-rigid objects using deformation metrics (2018)
  15. Al Akhras, H.; Elguedj, T.; Gravouil, A.; Rochette, M.: Towards an automatic isogeometric analysis suitable trivariate models generation -- application to geometric parametric analysis (2017)
  16. Ali, Zaib; Tucker, Paul G.; Shahpar, Shahrokh: Optimal mesh topology generation for CFD (2017)
  17. Fogg, Harold J.; Armstrong, Cecil G.; Robinson, Trevor T.: Automatic generation of multiblock decompositions of surfaces (2015)
  18. Shi, Ling; Wang, Jun; Pottmann, Helmut: Smooth surfaces from rational bilinear patches (2014)
  19. Hildebrandt, Klaus; Polthier, Konrad: Generalized shape operators on polyhedral surfaces (2011)
  20. Kovacs, Denis; Myles, Ashish; Zorin, Denis: Anisotropic quadrangulation (2011)

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