Arc-length preserving curve deformation based on subdivision

Abstract

An arc-length preserving deformation for curves is presented by combining subdivision and inverse kinematic. A curve is discreted into polyline first, then the polyline is deformed with its arc-length preserved in the sense of minimizing energy. Subdivision method is applied to obtain a smooth curve (at least C 1 continuity) with proper weights selected to keep the length of the resulting curve equal to the original curve. This technique also provides interactive response by progressively refining the solution of the optimization problem.