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Discrete Calabi Flow: A Unified Conformal Parameterization Method
Author(s) -
Su KH,
Li CC,
Zhou YM,
Xu X,
Gu XF
Publication year - 2019
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13873
Subject(s) - conformal map , robustness (evolution) , computer science , polygon mesh , embedding , ricci flow , computer graphics , geometry processing , conformal geometry , yamabe flow , flow (mathematics) , boundary (topology) , algorithm , mathematics , mathematical optimization , geometry , computer graphics (images) , mathematical analysis , artificial intelligence , ricci curvature , curvature , conformal field theory , biochemistry , chemistry , scalar curvature , sectional curvature , gene
Abstract Conformal parameterization for surfaces into various parameter domains is a fundamental task in computer graphics. Prior research on discrete Ricci flow provided us with promising inspirations from methods derived via Riemannian geometry, which is rigorous in theory and effective inpractice. In this paper, we propose a unified conformal parameterization approachfor turning triangle meshes into planar and spherical domains using discrete Calabi flow onpiecewise linear metric. We incorporate edge‐flipping surgery to guarantee convergence as well as other significant improvements including approximate Newton's method, optimal step‐lengths, priority embedding and boundary customizing, which achieve better performance and functionality with robustness and accuracy.