Equivolumetric Evolution of Planar Curves

Figure 2

The velocity fields of two types of normal evolution for the elliptical initial front are shown. (a) The velocity field of a constant speed normal evolution is plotted. Two segments corresponding to the shaded regions have the same arc-length. Due to the curvature effect, their areas are different. (b) The velocity field of an equivolumetric evolution is plotted. Two regions occupied by the velocity field corresponding to the segments of the same arc-length are the same.

(a)

(b)