A novel local/global approach to spherical parameterization

作者：Wang, Zhao; Luo, Zhongxuan^*; Zhang, Jielin; Saucan, Emil

来源：Journal of Computational and Applied Mathematics, 2018, 329: 294-306.

DOI：10.1016/j.cam.2017.05.011

• Geometric modeling
• Spherical parameterization
• Stretch operator

This paper proposes a novel local global spherical parameterization for the genus-zero triangular mesh, which naturally extends the planar approach to the spherical case. In our method, we derive two fitting matrices (conformal and isometric) in 3D space. By optimizing the so-called spring energy, the spherical results are achieved by solving a nonlinear system with spherical constraints. Intuitively, it represents the stitching together of the 1-ring patches to form a unit sphere. Moreover, the derivation of the 3D fitting matrices can also be applied to planar triangles directly, so that we can obtain a class of novel planar approaches (conformal, isometric, authalic) to the problem of flattening triangular meshes. In order to enhance robustness of the proposed spherical method, a stretch operator is introduced for dealing with high-curvature models. Numerical results demonstrate that our method is simple, efficient and convergent, and it outperforms several state-of-the-art methods in terms of trading-off the distortions of angle, area and stretch. Furthermore, it achieves better visualization in texture mapping.

• 出版日期2018-2
• 单位中国科学技术大学; 大连理工大学; 吉林大学