Fast and Accurate Smoothing Method Using A Modified Allen–Cahn Equation

This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2D shapes and volume smoothing of 3D shapes. The modified AC equation has a good smoothing dynamics and it is coupled with a fidelity term. The fidelity term forces the solution of the equation to be a close approximation to the original data. We use a hybrid explicit finite difference method to solve the equation. Therefore, we do not have any restriction on the shape of the computational domains. Several numerical tests for both the curve and surface smoothing problems are performed to demonstrate the robustness and efficiency of the proposed method. In particular, the proposed algorithm is useful for the 3D printing applications.