On the optimality of splines for expressing the hand-writing process

For the model of writing letters with a pen steered by hand so as to minimize the mean-square jerk under the constraints of passing through several via points and pausing at some of them, the optimal function is proven to be quintic B-splines with the knots placed at the via points and especially double knots at the pause points. A steeple like the left bottom of ‘h’ is a pause point where the pen must pause at a moment to alter its direction. Application to automatic generation of words in script style from individual letters and feature extraction of hand-written letters are presented.