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We provide a new term for evolution of the tangential component
that depends only on single parameter , instead of two
completely unknown parameters and in (4), but still gives
an even redistribution of points. Further, assuming the natural
periodic boundary conditions for closed contours, one can have
an exact expression for . This assumption is, however, not
valid for evolution of an open curve where the boundary conditions
are already given. In this case, we use a simple numerical
discretization scheme for calculation of . This avoids any
heuristic selection of the control parameter . Further, we provide
the necessary proof of boundedness of the curve evolution.

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