Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface

A method is presented for generating a discrete piecewise constant Gaussian curvature (CGC) surface. An energy functional first formulated so that its stationary point the linear Weingarten (LW) surface, which has property such weighted sum of mean and curvatures constant. The CGC surface obtained using gradient derived from variation special type LW updating shape based on flow. filtering incorporated to prevent oscillation divergence due unstable discretized Two techniques are proposed generate with preassigned internal boundaries. step length flow adjusted by introducing line search algorithm minimize functional. effectiveness demonstrated through numerical examples various shapes surfaces.