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• W3119754065 abstract "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." @default.
• W3119754065 created "2021-01-18" @default.
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• W3119754065 date "2021-05-01" @default.
• W3119754065 modified "2023-09-27" @default.
• W3119754065 title "Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface" @default.
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• W3119754065 doi "https://doi.org/10.1016/j.cad.2021.102992" @default.
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