New development of discrete differential geometry by discrete integrable systems

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Discrete differential geometry has been considered, which is a mathematical framework describing the dynamics of geometric objects on computers. Theory of discrete integrable systems has been developed, which was successfully applied to discretize the planar curve dynamics on Eucledian plane and to construct explicit formulas in terms of the z functions. As by-products, highaccuracy stable numerical schemes for curve dynamics with adaptive step size control, and seeds of new development to the theory of discrete conformal mappings have been obtained.