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2010 A second-order accurate method for solving the signed distance function equation
Peter Schwartz, Phillip Colella
Commun. Appl. Math. Comput. Sci. 5(1): 81-97 (2010). DOI: 10.2140/camcos.2010.5.81


We present a numerical method for computing the signed distance to a piecewise-smooth surface defined as the zero set of a function. It is based on a marching method by Kim (2001) and a hybrid discretization of first- and second-order discretizations of the signed distance function equation. If the solution is smooth at a point and at all of the points in the domain of dependence of that point, the solution is second-order accurate; otherwise, the method is first-order accurate, and computes the correct entropy solution in the presence of kinks in the initial surface.


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Peter Schwartz. Phillip Colella. "A second-order accurate method for solving the signed distance function equation." Commun. Appl. Math. Comput. Sci. 5 (1) 81 - 97, 2010.


Received: 5 February 2008; Revised: 9 July 2009; Accepted: 27 December 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1190.65162
MathSciNet: MR2600823
Digital Object Identifier: 10.2140/camcos.2010.5.81

Primary: 65-02
Secondary: 76-02

Keywords: eikonal , Hamilton–Jacobi , narrow band , signed distance function

Rights: Copyright © 2010 Mathematical Sciences Publishers

Vol.5 • No. 1 • 2010
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