Dynamic Arabic Mathematical Fonts Mostafa Banouni [email protected] Mohamed Elyaakoubi [email protected] Azzeddine Lazrek [email protected] Department of Computer Sciences Faculty of Sciences University Cadi Ayyad P.O. Box 2390 Marrakech, Morocco http://www.ucam.ac.ma/fssm/rydarab Abstract This contribution describes a font family designed to meet the requirements of typesetting mathematical documents in an Arabic presentation. Thus, not only is the text written in an Arabic alphabet-based script, but specific symbols are used and mathematical expressions also spread out from right to left. Actually, this font family consists of two components: an Arabic mathematical font and a dy- namic font. The construction of this font family is a first step of a project aiming at providing a complete and homogeneous Arabic font family, in the OpenType format, respecting Arabic calligraphy rules. Keywords: Mathematical font, Dynamic font, Variable-sized symbols, Ara- bic mathematical writing, Multilingual documents, Unicode, PostScript, Open- Type. 1 Overview ics take their place over or under the characters, The Arabic language is native for roughly three hun- and that is also context dependent. Moreover, the dred million people living in the Middle East and kashida, a small flowing curve placed between Ara- North Africa. Moreover, the Arabic script is used, bic characters, is to be produced and combined with in various slightly extended versions, to write many characters and symbols. The kashida is also used major languages such as Urdu (Pakistan), Persian for the text justification. The techniques for man- and Farsi (Iran, India), or other languages such as aging the kashida are similar to those that can be Berber (North Africa), Sindhi (India), Uyghur, Kir- used for drawing curvilinear extensible mathemati- giz (Central Asia), Pashtun (Afghanistan), Kurdish, cal symbols, such as sum, product or limit. Jawi, Baluchi, and several African languages. A There are several Arabic font styles. Of course, great many Arabic mathematical documents are still it is not easy to make available all existing styles. written by hand. Millions of learners are concerned The font style Naskh was the first font style adopted in their daily learning by the availability of systems for computerization and standardization of Arabic for typesetting and structuring mathematics. typography. So far, only Naskh, Koufi, Ruqaa, and Creating an Arabic font that follows calligra- to a limited extent Farsi have really been adapted phic rules is a complex artistic and technical task, to the computer environment. Styles like Diwani due in no small part to the necessity of complex or Thuluth, for example, don’t allow enough sim- contextual analysis. Arabic letters vary their form plification, they have a great variation in characters according to their position in the word and accord- shapes, the characters don’t share the same baseline, ing to the neighboring letters. Vowels and diacrit- and so on. Considering all that, we have decided to use the Naskh style for our mathematical font. 48 Preprints for the 2004 Annual Meeting Dynamic Arabic Mathematical Fonts The RyDArab [10] system was developed for the Now we will describe the way we constructed purpose of typesetting Arabic mathematical expres- the OpenType Arabic mathematical font RamzArab. sions, written from right to left, using specific sym- The construction of the font started by drawing the bols. RyDArab is an extension of the TEX system. It whole family of characters by hand. This task was runs with K. Lagally’s Arabic system ArabTEX [8] performed by a calligrapher. Then the proofs were or with Y. Haralambous and J. Plaice’s multilingual scanned to transform them into vectors. The scan- Ω [6] system. The RyDArab system uses characters ning tools alone don’t produce a satisfying result, so belonging to the ArabTEX font xnsh or to the omsea once the design is finalized, the characters are pro- font of Ω, respectively. Further Arabic alphabetic cessed and analyzed using special software to gener- symbols in different shapes can be brought from the ate the file defining the font. font NasX that has been developed, for this special In Arabic calligraphy, the feather’s head (ka- purpose, using METAFONT. The RyDArab system lam) is a flat rectangle. The writer holds it so that also uses symbols from Knuth’s Computer Modern the largest side makes an angle of approximately 70◦ family, obtained through adaptation to the right-to- with the baseline. Except for some variations, this left direction of Arabic. orientation is kept all along the process of drawing Since different fonts are in use, it is natural that the character. Furthermore, as Arabic writing goes some heterogeneity will appear in mathematical ex- from right to left, some boldness is produced around pressions typeset with RyDArab [9]. Symbol sizes, segments from top left toward the bottom right and shapes, levels of boldness, positions on the base- conversely, segments from top right to the bottom line will not quite be in harmony. So, we undertook left will rather be slim as in Figure 1. building a new font in OpenType format with two The RamzArab font in Figure 4 contains only main design goals: on the one hand, all the symbols symbols specific to Arabic mathematics presentation will be drawn with harmonious dimensions, propor- plus some usual symbols found even in text mode. tions, boldness, etc., and on the other hand, the font It is mainly composed of the following symbols: should contain the majority of the symbols in use in • alphabetic symbols: Arabic letters in various the scientific and technical writing based on an Ara- forms, such as characters in isolated standard bic script. form, isolated double-struck, initial standard, Both Arabic texts and mathematical expres- initial with tail, initial stretched and with loop sions need some additional variable-sized symbols. (e.g., v ¥ ¹ ¶ respectively); We used the CurExt [11] system to generate such • punctuation marks (e.g., ; : 9 ! > ); symbols. This application was designed to gener- • digits as used in the Maghreb Arab (North Afri- ate automatically curvilinear extensible symbols for ca), and as they are in the Machreq Arab (Mid- T X with the font generator METAFONT. The new E dle East); extension of CurExt does the same with the font gen- • accents to be combined with alphabetic symbols erator PostScript. XTsTtT While METAFONT generates bitmap fonts and (e.g., ); thus remains inside the TEX environment, Open- • ordinary mathematical symbols such as delim- Type [14] gives outline and multi-platform fonts. iters, arithmetic operators, etc. Moreover, since Adobe and Microsoft have devel- • mirror image of some symbols such as sum, in- oped it jointly, OpenType has become a standard tegral, etc. combining the two technologies TrueType and Post- In Arabic mathematics, the order of the alpha- Script. In addition, it offers some additional typo- betic symbols differs from the Arabic alphabetic or- graphic layout possibilities thanks to its multi-table der. Some problems can appear with the alphabetic feature. symbols in their multi-form. Generally, in Arabic mathematical expressions, 2 A Mathematical Font alphabetic@ A B symbols are written without dots (e.g., The design and the implementation of a mathemat- T T T ) or diacritics. This helps to avoid confu- ical font are not easy [5]. It becomes harder when sions with accents. The dots can be added when- it is oriented to Arabic presentation. Nevertheless, ever they are needed, however. Thus, few symbols independent attempts to build an Arabic mathemat- are left. ical font have been undertaken. In fact, F. Alhar- Moreover, some deviation from the general rules gan [1] has sent us proofs of some Arabic mathemat- will be necessary: in a mathematical expression, the ical symbols in TrueType format. isolated form of the letter ALEF can be confused with the Machreq Arab digit ONE. The isolated Preprints for the 2004 Annual Meeting 49 1 1 1 1 Mostafa Banouni, Mohamed Elyaakoubi and Azzeddine Lazrek form of the letter HEH can also present confusion with the Machreq Arab digit FIVE. The choice of the glyphs Z and ¸y to denote respectively these two characters will help to avoid such confusions. −→ −→ Even though these glyphs are not in conformity with the homogeneity of the font style and calligraphic Figure 1: Sum symbol with vertical then rules, they are widely used in mathematics. In the horizontal mirror image same way, the isolated form of the letter KAF c , resulting from the combination of two other basic el- ements, will be replaced by the KAF glyph in Ruqaa style, ^. Other symbols with mirror image forms already 1 For the four letters ALEF, DAL, REH and WAW, in use are not added to this font. Of course, Latin the initial and the isolated forms are the same, and and Greek alphabetic symbols can be used in Arabic these letters will be withdrawn from the list of letters mathematical expressions. In this first phase of the in initial form. On the other hand, instead of a project, we aren’t integrating these symbols into the unique cursive element, the stretched form of each of font. They can be brought in from other existing the previous letters will result from the combination fonts. of two elements. It follows that these letters will not 3 A Dynamic Font be present in the list of the letters in the stretched form. The composition of variable-sized letters and curvi- The stretched form of a letter is obtained by the linear symbols is one of the hardest problems in addition of a MADDA-FATHA or ALEF in its final digital typography. In high-quality printed Arabic form ¶ to the initial form of the letter to be stretched works, justification of the line is performed through (e.g., + ¶ −→ ¶).