Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface

Kazuki Hayashi, Yoshiki Jikumaru, Makoto Ohsaki, Takashi Kagaya, Yohei Yokosuka

研究成果: Contribution to journalArticle査読


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.

ジャーナルCAD Computer Aided Design
出版ステータス出版済み - 5 2021

All Science Journal Classification (ASJC) codes

  • コンピュータ サイエンスの応用
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 産業および生産工学