ABF++: Fast and robust angle based flattening. Conformal parameterization of mesh models has numerous applications in geometry processing. Conformality is desirable for remeshing, surface reconstruction, and many other mesh processing applications. Subject to the conformality requirement, these applications typically benefit from parameterizations with smaller stretch. The Angle Based Flattening (ABF) method, presented a few years ago, generates provably valid conformal parameterizations with low stretch. However, it is quite time-consuming and becomes error prone for large meshes due to numerical error accumulation. This work presents ABF++, a highly efficient extension of the ABF method, that overcomes these drawbacks while maintaining all the advantages of ABF. ABF++ robustly parameterizes meshes of hundreds of thousands and millions of triangles within minutes. It is based on three main components: (1) a new numerical solution technique that dramatically reduces the dimension of the linear systems solved at each iteration, speeding up the solution; (2) a new robust scheme for reconstructing the 2D coordinates from the angle space solution that avoids the numerical instabilities which hindered the ABF reconstruction scheme; and (3) an efficient hierarchical solution technique. The speedup with (1) does not come at the expense of greater distortion. The hierarchical technique (3) enables parameterization of models with millions of faces in seconds at the expense of a minor increase in parametric distortion. The parameterization computed by ABF++ are provably valid, that is they contain no flipped triangles. As a result of these extensions, the ABF++ method is extremely suitable for robustly and efficiently parameterizing models for geometry-processing applications.

References in zbMATH (referenced in 27 articles )

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  1. Choi, Gary P. T.; Liu, Yechen; Lui, Lok Ming: Free-boundary conformal parameterization of point clouds (2022)
  2. Choi, Gary P. T.: Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory (2021)
  3. Kuo, Yueh-Cheng; Lin, Wen-Wei; Yueh, Mei-Heng; Yau, Shing-Tung: Convergent conformal energy minimization for the computation of disk parameterizations (2021)
  4. Naitsat, Alexander; Naitzat, Gregory; Zeevi, Yehoshua Y.: On inversion-free mapping and distortion minimization (2021)
  5. Choi, Gary P. T.; Leung-Liu, Yusan; Gu, Xianfeng; Lui, Lok Ming: Parallelizable global conformal parameterization of simply-connected surfaces via partial welding (2020)
  6. Yueh, Mei-Heng; Huang, Hsiao-Han; Li, Tiexiang; Lin, Wen-Wei; Yau, Shing-Tung: Optimized surface parameterizations with applications to Chinese virtual broadcasting (2020)
  7. Choi, Gary P. T.; Rycroft, Chris H.: Density-equalizing maps for simply connected open surfaces (2018)
  8. Choi, Gary Pui-Tung; Lui, Lok Ming: A linear formulation for disk conformal parameterization of simply-connected open surfaces (2018)
  9. Zhao, Hui; Li, Xuan; Ge, Huabin; Lei, Na; Zhang, Min; Wang, Xiaoling; Gu, Xianfeng: Conformal mesh parameterization using discrete Calabi flow (2018)
  10. Yueh, Mei-Heng; Lin, Wen-Wei; Wu, Chin-Tien; Yau, Shing-Tung: An efficient energy minimization for conformal parameterizations (2017)
  11. Meng, Ting Wei; Choi, Gary Pui-Tung; Lui, Lok Ming: TEMPO: feature-endowed Teichmüller extremal mappings of point clouds (2016)
  12. Su, Kehua; Cui, Li; Qian, Kun; Lei, Na; Zhang, Junwei; Zhang, Min; Gu, Xianfeng David: Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation (2016)
  13. Choi, Pui Tung; Lui, Lok Ming: Fast disk conformal parameterization of simply-connected open surfaces (2015)
  14. Huang, Wei-Qiang; Gu, Xianfeng David; Lin, Wen-Wei; Yau, Shing-Tung: A novel symmetric skew-Hamiltonian isotropic Lanczos algorithm for spectral conformal parameterizations (2014)
  15. Song, Peng; Fu, Chi-Wing; Goswami, Prashant; Zheng, Jianmin; Mitra, Niloy J.; Cohen-Or, Daniel: An interactive computational design tool for large reciprocal frame structures (2014) ioport
  16. Zhang, Kang; Li, Xin: Searching geometry-aware pants decomposition in different isotopy classes (2014)
  17. Zeng, Wei; Lui, Lok Ming; Luo, Feng; Chan, Tony Fan-Cheong; Yau, Shing-Tung; Gu, David Xianfeng: Computing quasiconformal maps using an auxiliary metric and discrete curvature flow (2012)
  18. Ben Chen, Mirela; Gortler, Steven J.; Gotsman, Craig; Wormser, Camille: Distributed computation of virtual coordinates for greedy routing in sensor networks (2011)
  19. Cartade, Colin; Malgouyres, Rémy; Mercat, Christian; Samir, Chafik: A simple and flexible mesh parameterization method (2011)
  20. Li, Wen-Long; Yin, Zhou-Ping; Huang, Yong-An; Xiong, You-Lun: Automatic registration for 3D shapes using hybrid dimensionality-reduction shape descriptions (2011) ioport

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