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タイトル: Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface
著者: Hayashi, Kazuki  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0002-4026-8234 (unconfirmed)
Jikumaru, Yoshiki
Ohsaki, Makoto  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0003-4935-8874 (unconfirmed)
Kagaya, Takashi
Yokosuka, Yohei
著者名の別形: 林, 和希
大﨑, 純
キーワード: Form-finding
Discrete differential geometry
Linear Weingarten surface
Gaussian curvature flow
Energy minimization
発行日: May-2021
出版者: Elsevier BV
誌名: Computer-Aided Design
巻: 134
論文番号: 102992
抄録: A method is presented for generating a discrete piecewise constant Gaussian curvature (CGC) surface. An energy functional is first formulated so that its stationary point is the linear Weingarten (LW) surface, which has a property such that the weighted sum of mean and Gaussian curvatures is constant. The CGC surface is obtained using the gradient derived from the first variation of a special type of the energy functional of the LW surface and updating the surface shape based on the Gaussian curvature flow. A filtering method is incorporated to prevent oscillation and divergence due to unstable property of the discretized Gaussian curvature flow. Two techniques are proposed to generate a discrete piecewise CGC surface with preassigned internal boundaries. The step length of Gaussian curvature flow is adjusted by introducing a line search algorithm to minimize the energy functional. The effectiveness of the proposed method is demonstrated through numerical examples of generating various shapes of CGC surfaces.
著作権等: © 2021 The Author(s). Published by Elsevier Ltd.
This is an open access article under the CC BY license.
URI: http://hdl.handle.net/2433/276535
DOI(出版社版): 10.1016/j.cad.2021.102992
出現コレクション:学術雑誌掲載論文等

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