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We present a numerical method for computing the signed distance to a piecewise-smooth surface dened as the zero set of a function. It is based on a marching method by Kim (Kim01) and a hybrid discretization of rst- 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 rst-order accurate, and computes the correct entropy solution in the presence of kinks in the initial surface.

A second-order accurate method for solving the signed distance function equation