I'm going thru sethian's book on level sets.i dont understand how the level set function that is initialized as a signed distance function loses the property.and why does the speed function have to be defined again and again, as in the extension velocity method? it can just be computed directly from the values of the level set function phi itself, for example, in the case of curvature dependent flows. any answers? LS rookie

You can calculate the distance function loses the property under simple shear flow, say a droplet.

Check it out, because there is exact solution.