  We study evolution of a closed embedded plane curve with the normal velocity
depending on the curvature, the orientation and the position of the curve. We
propose a new method of tangential redistribution of points by curvature
adjusted control in the tangential motion of evolving curves. The tangential
velocity distributes grid points along the curve not only uniform but also lead
to a suitable concentration and/or dispersion depending on the curvature. Our
study is based on solutions to the governing system of nonlinear parabolic
equations for the position vector, tangent angle and curvature of a curve. We
furthermore present a semi-implicit numerical discretization scheme based on
the flowing finite volume method. Several numerical examples illustrating
capability of the new tangential redistribution method are also presented in
this paper.
