Fast and Accurate Redistancing by Directional Optimization

A fast and accurate algorithm for the reinitialization of the signed distance function in two and three spatial dimensions is presented. The algorithm has computational complexity O(N logN) for the reinitialization of N grid points. The order of accuracy of the reinitialization is demonstrated to depend primarily on the interpolation algorithm used. Bicubic interpolation is demonstrated to result in fourth-order accuracy for smooth interfaces. Simple numerical examples demonstrating the convergence and computational complexity of the reinitialization algorithm in two and three dimensions are presented as verification of the algorithm.