Global Conformal Parameterization via an Implementation of Holomorphic Quadratic Differentials

Zhao, Hui; Wang, Shaodong; Wang, Wencheng

doi:10.1109/tvcg.2020.3016574

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Holomorphic Quadratic Differential Algorithm1

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2022

2023

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Cited by 3 publications

(1 citation statement)

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“…Zhao et al [13] proposed a new three-step diffusion ergodic method, which successfully solved the vertex problem and generated a harmonic leaf structure without vertexes. In the first step, the paper uses Whitehead to move and traverse the vertices, and a leaf-like structure diagram is obtained from the traversal result.…”

Section: Holomorphic Quadratic Differential Algorithmmentioning

confidence: 99%

A survey of global conformal parameterization

Shen¹

2023

International Conference on Pure, Applied, and Computational Mathematics (PACM 2023)

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This paper mainly introduces several kinds of global conformal parameterization theories and algorithms, which can deal with complex surfaces under different genus. Pure first-order differential algorithm and pure second-order differential algorithm are based on the contents of global differential geometry, whose core ideas come from Riemann's single-valued theorem and Teichmuller theory. Ricci flow algorithm and quasi-conformal mapping algorithm are based on the contents of the field of geometric partial differential equations, which can be optimized by minimizing energy to get results. The optimal transport algorithm is based on convex differential geometry and geometric variational principle, which can be transformed into computational geometry algorithm to find the solution.

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Section: Holomorphic Quadratic Differential Algorithmmentioning

confidence: 99%