This paper presents an efficient method to smoothly transform one polyline into another. The method makes use of a moving adapted frame associated to each curve. % Several choices are presented and discussed for the moving frame. We introduce a simple propagation equation involving the moving frame which accounts for the transition between two consecutive points of a polyline. The curve transformation is performed using the interpolation of the quantities involved in this propagation equation. Depending on the type of interpolation, we propose two algorithms to compute the intermediary shape of the curve. Moreover, we define a measure of the transformation and minimize this measure to distinguish a «minimal transformation» which the user can modify through the addition of simple parameters.