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The signed distance function between an arbitrary point in 3D space and a given closed surface returns the minimum distance from that point to the collection of triangles representing the surface. By convention, the sign is positive if the point is outside and negative if the point is inside the region determined by the surface.
In the context of Computational Fluid Dynamics, not only the signed distance function is useful to locate the separation interface between two different fluids with constant (but possibly different) material properties as its zero level-set surface but also it determines for each Eulerian grid point its instantaneous mass density and viscosity (one fluid is represented by the positive values and the other one by the negative ones).
Although there are other ways to compute the signed distance function, when the number of Lagrangian points (vertices of the triangles) is less than N*log(N), where N is the number of points in the Eulerian grid, a
