Parametric Curves Variations with Respect to a Given Direction

Abstract

Modeling dynamic characters, in observance of calligraphic rules can be done with the help of parametric curves. The class of Bézier curves is a powerful tool for modeling the outlines of the surface razed by a nib's calligrapher. Unfortunately, after capturing the character's hand-drawn outlines, the surface delimited by the outlines doesn't correspond to the space to shade when writing the character. Some of the curves pieces of the outlines are to be subdivided at some appropriate points. In order to identify these points, decompositions of the Bézier curves involved, with respect to particular directions, are necessary. This paper presents a simple and e ective mathematical method for doing such decompositions.The proposed method helps to determine the points as extrema of certain functions. Then, the method is implemented and used to design some Arabic dynamical characters. This will help in building dynamic fonts respecting calligraphic strong rules.