# Science at the triple point between mathematics, mechanics and materials science

## Publication 44

### Fast and Accurate Redistancing via Directional Optimization

##### Authors:

Matt Elsey
Courant Institute of Mathematical Sciences
New York University

Selim Esedoglu
Department of Mathematics
University of Michigan

##### Abstract:
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 $O(N log N)$ 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.
##### Get the paper in its entirety
FastandAccurateElsey.pdf

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