Stretching of dynamic mathematical symbols taking care of similarity and geometric characterization

Abstract

The scientific document industry has undergone an important progress in all steps especially in processing and presentation. However, it is still confronted with major obstacles when it has to manipulate documents containing mathematical formulas which are based on dynamic or variable-sized mathematical symbols and taking care of optical scaling. Normally, in processing documents, the composition of mathematical formulas is based on static fonts. The support of dynamic mathematical symbols requires, in addition to the choice of adequate type of fonts and text formatting tools, the development of a mathematical model allowing parametrizing the symbols to support optical scaling. In this paper, we present a method to supply stretching of Bézier curves representing symbols without losing the aspect of similarity and the geometric characteristics of the concerned symbols. The curves of dynamic symbols to be parametrized are designed on the basis of a new method that allows measuring similarity. The model can be extended later for the development of dynamic fonts respecting the rules of Arabic calligraphy. The method to evaluate the similarity can also be easily adapted in other fields such as image processing.