TY - JOUR
T1 - Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface
AU - Hayashi, Kazuki
AU - Jikumaru, Yoshiki
AU - Ohsaki, Makoto
AU - Kagaya, Takashi
AU - Yokosuka, Yohei
N1 - Funding Information:
This study is partially supported by JST CREST Grant No. JPMJCR1911 , Japan. Valuable comments from Profs. Miyuki Koiso and Shizuo Kaji at Institute of Mathematics for Industry, Kyushu University are appreciated.
Publisher Copyright:
© 2021 The Author(s)
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.cad.2021.102992
DO - 10.1016/j.cad.2021.102992
M3 - Article
AN - SCOPUS:85100045781
VL - 134
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
SN - 0010-4485
M1 - 102992
ER -