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Mathematical Problems in Engineering
Volume 2017, Article ID 5897892, 13 pages
https://doi.org/10.1155/2017/5897892
Research Article

Stretching of Dynamic Mathematical Symbols Taking Care of Similarity and Geometric Characterization

1LAPSSII (LAboratoire des Process, Signaux, Systemes Industriels et Informatique), Ecole Supérieure de Technologie, Cadi Ayyad University, Dar Si Aïssa Road, B.P. 89, 46000 Safi, Morocco
2Faculty of Sciences Semlalia, Cadi Ayyad University, 12 Bd. Prince My Abdellah, B.P. 2390, 40000 Marrakesh, Morocco

Correspondence should be addressed to Abdelouahad Bayar; am.acu@rayab.a

Received 3 February 2017; Accepted 11 April 2017; Published 1 August 2017

Academic Editor: Stefan Balint

Copyright © 2017 Abdelouahad Bayar and Khalid Sami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.