Strings in Script Style Based on Minimum Principle

A method for synthesizing a string of letters in script style is developed based on the minimum principle for handwriting, whereby the pen motion is organized so as to minimize the integral of squared jerk subject to visiting a series of spatial points. Let the series of spatial points characterizing a string be a concatenation of those taken from individual letters. The pen motion is best expressed in the form of a linear combination of quintic B-splines. Then, synthesis of the pen motion to write the string is reduced to optimization of the times at which the pen visits the characteristic points. The main contribution of this paper is a number of recurrence formulae that make it possible to evaluate arithmetically the gradients of the integral of squared jerk with respect to visiting times. An optimization algorithm is compiled incorporating the recurrence formulae in a gradient method. Several examples of synthesized letter strings are presented.