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Review October 2021

Figure 5, page 9

  • Update the notation of the bottom right graph. Instead of a 'R', use a 'r' to represent radius.
  • Use the real value of the radius, i.e., without rescaling by the grid resolution. In this figure, that means that we are going to use '5' instead of '0.625' and '16' instead of '2'.

Section 3, page 2

  • In paragraph 2: We could be clearer about what we mean by exact sampling. For example, if P and Q are in our finite exact sampling set, then P and Q belong to C.
    Maybe something like: "...but instead, we have a finite set of points that is an exact sampling of C, that is, if P and Q belong to our exact sampling, than P and Q belong to C."

  • At the end paragraph 2: "as long as the sampling points are sufficiently numerous"

  • Page 3, just after multigrid convergence definition: "...is no longer necessary". I guess I can add a reference to one of Jaco paper about multigrid convergence estimators.

  • Page 4, second paragraph: "... as a scaling factor of the difference between the intersection area of the estimation disk of radius r centered..."

  • Page 5, second paragraph: "... to evolve the shape towards the zero-level set of the balance coefficient function (see figure 2). This evolution process is closely related with the curve-shortening flow (CSF is the one dimensional version of the mean curvature flow).