## Contextual typesetting of mathematical symbols taking care of optical scaling (1993)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Andre93contextualtypesetting,

author = {Jacques Andre and Irine Vatton},

title = {Contextual typesetting of mathematical symbols taking care of optical scaling },

year = {1993}

}

### OpenURL

### Abstract

Typesetting of mathematical formulae has conflicting requirements: on the one hand, optical scaling is a need for large symbols; in the other hand, large symbols are made of composite items that are neither easily nor nicely put together.

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Citation Context ...re documents are represented by their logical structure rather than by their graphical aspect. In this respect it is comparable to syntax-driven editors used for editing programs. It is based on SGML =-=[29]-=- Document Type Definitions (DTD), which sepcify the logical organization of the document to be processed. More precisely, a DTD specifies the types of the elements constituting a document and of the r... |

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Citation Context ... is described. 1 Fonts for mathematical formulae 1.1 The needs Mathematical formulae are made of letters from different families ("a", "a", "ff", "A", "@&q=-=uot;, etc.) and of a "menagerie" (as Lamport says [5]) of mathematical symbol ("\Theta", "u",-=- "\Omega ", "1", "!", ",", etc.) at different point sizes (if, in a i , a is at 12 point size then i is at 10 point size). Furthermore, miscellaneous rules (e.g... |

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Citation Context ...nts available on laser printers or phototypesetters, only few of them are concerned with mathematics. Today, the main ones are: ffl cmexnn (math extension) fonts created by M E T A F O N T for T E X (=-=[4]-=-, appendix F); ffl Symbol font , one of the four fonts that have always been installated on any PostScript system (the three other ones are Times, Courier and Helvetica); refer to [6], appendix E.11; ... |

74 |
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Citation Context ...ae symbols. Due to our involvement into the Grif project, this editor was a good place to check this font. 3.1 Grif overview Grif is an interactive system for editing and formatting complex documents =-=[26]-=- [27] where documents are represented by their logical structure rather than by their graphical aspect. In this respect it is comparable to syntax-driven editors used for editing programs. It is based... |

52 | Interactively editing structured documents
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Citation Context ...mbols. Due to our involvement into the Grif project, this editor was a good place to check this font. 3.1 Grif overview Grif is an interactive system for editing and formatting complex documents [26] =-=[27]-=- where documents are represented by their logical structure rather than by their graphical aspect. In this respect it is comparable to syntax-driven editors used for editing programs. It is based on S... |

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Citation Context ... Optical Scaling Formatting of mathematical formulae is a hard task. Significant progress had been made by the end of the 70s when the tree structure of formulae was used in batch systems such as EQN =-=[1]-=- and T E X [2]. At the beginning of the 80s, systems like Titus [3] allowed interactive formatting of formulae. Today, almost all of the commercial products offer facilities to handle high quality mat... |

14 | Arabic Formatting with ditroff/ffortid
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Citation Context ... examples 2 to 4, this could be decided by an intelligent editor and by using large sets of characters, more interesting are the fonts where you need continuous variations, like for arabic characters =-=[23]-=- and for : : : mathematics. Math-Fly is a font we are designing to handle dynamic mathematical symbols. It uses movetox, movetoy, linetox, : : : operators as described in section 2.1. Various classes ... |

9 |
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Citation Context ...ng Formatting of mathematical formulae is a hard task. Significant progress had been made by the end of the 70s when the tree structure of formulae was used in batch systems such as EQN [1] and T E X =-=[2]-=-. At the beginning of the 80s, systems like Titus [3] allowed interactive formatting of formulae. Today, almost all of the commercial products offer facilities to handle high quality mathematical form... |

7 |
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Citation Context ...Lucida familly that offers both a LucidaMath-Symbol almost equivalent to Adobe's Symbol and a LucidaMath-Extension where one can find symbols that belong to T E X's cmex and some other ones; refer to =-=[7]. ffl Two new versions of Times (by Spivak and by Jungers) that offers T E X-=-'s math extension as Lucida does. 4 Jacques Andre & Irene Vatton �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� - �� �� ... |

7 |
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Citation Context ...0x1.5-200 /dy 90 def % 270x1.3-270 (L) show % figure e Such analytical computing of characters outline is possible with M E T A F O N T . It is used, for example, to compute arabic or khmer ligatures =-=[10]-=- [11] or even random fonts [12]. However, M E T A F O N T computes the shapes before bitmaps are loaded: analytical variables are not re-evaluated every time a character is used. Even here, if the fol... |

7 |
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Citation Context ...s are special cases of neighbouring: a contextual font may decide to change the shape of a, say, "s" at the end of a word; or to modify the bearing of a character at the (right or left) end =-=of a line [20]-=-. 6 Because setcharwidth does not ask for any caching mechanisme, the bounding box coordinates have not to be passed to. 10 Jacques Andre & Irene Vatton Figure 8: Pochoir simulates inkspreading caused... |

5 |
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Citation Context ...re 2). 3. More generally, any typographical requirement such as kerning on the fly, optical scaling, etc. may be considered as a contextual problem. Even, researches are done to get automatic kerning =-=[25]-=-. 4. Other contexts may be used, such as phonetic [21] or even stack-mechanims [22]. 5. While in the examples 2 to 4, this could be decided by an intelligent editor and by using large sets of characte... |

5 |
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Citation Context ...s Andre & Irene Vatton 4 Comparaison with other mechanisms Let us compare four ways of font generation, namely PostScript (with and without cache mechanism), M E T A F O N T and Adobe Master fonts[32]=-=[33]-=-. Other ones exist, like MultiType by URW [20], however they resemble one of these. 1. PostScript, with cache mechanism, works at print time. It receives outline descriptions. At the first instantiati... |

4 |
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Citation Context ...igure 2) and optical scaling has to be used instead. However, nonlinear scaling methods (and even principles) have remained largely unexplored. We may only quote recent theses by Bridget Lynn Johnson =-=[24]-=- and by Claude Betrisey [25]. Johnson proposed a nonlinear scaling model, used it to generate letters and compared them with handcut fonts. Betrisey, in the other hand is, Contextual Typesetting of Ma... |

4 |
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Citation Context ...anguage, called P language, is used to describe presentation rules for each type of element defined in the DTD. Interpretation of these presentation rules is based on the concept of abstract pictures =-=[31]-=-. When Grif has a document to print or to display in a window, it first builds an abstract picture which is a high-level description of that document image. This description is device-independent and ... |

3 |
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Citation Context ... optical scaling, etc. may be considered as a contextual problem. Even, researches are done to get automatic kerning [25]. 4. Other contexts may be used, such as phonetic [21] or even stack-mechanims =-=[22]-=-. 5. While in the examples 2 to 4, this could be decided by an intelligent editor and by using large sets of characters, more interesting are the fonts where you need continuous variations, like for a... |

2 |
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Citation Context .... Significant progress had been made by the end of the 70s when the tree structure of formulae was used in batch systems such as EQN [1] and T E X [2]. At the beginning of the 80s, systems like Titus =-=[3]-=- allowed interactive formatting of formulae. Today, almost all of the commercial products offer facilities to handle high quality mathematical formulae. In this paper it is shown that problems still e... |

2 |
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Citation Context ...-200 /dy 90 def % 270x1.3-270 (L) show % figure e Such analytical computing of characters outline is possible with M E T A F O N T . It is used, for example, to compute arabic or khmer ligatures [10] =-=[11]-=- or even random fonts [12]. However, M E T A F O N T computes the shapes before bitmaps are loaded: analytical variables are not re-evaluated every time a character is used. Even here, if the followin... |

2 |
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Citation Context ...his mechanism has been exhibited some years ago [13], it does not seem that its power has been significantly understood. Indeed, drawing a character on the fly allows to take care of its context (see =-=[14]-=- for a survey on these contextual fonts). Different contexts may be involved: 1. No context: i.e. purely random. A typical example is the Scrabble font where each piece randomly stirs as if they were ... |

1 |
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Citation Context ...270 (L) show % figure e Such analytical computing of characters outline is possible with M E T A F O N T . It is used, for example, to compute arabic or khmer ligatures [10] [11] or even random fonts =-=[12]-=-. However, M E T A F O N T computes the shapes before bitmaps are loaded: analytical variables are not re-evaluated every time a character is used. Even here, if the following instructions are run: /d... |

1 |
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Citation Context .... In section 4 this mechanism is compared with other ones such as M E T A F O N T or as Adobe Master fonts. 2.2 Drawing characters on the fly Although this mechanism has been exhibited some years ago =-=[13]-=-, it does not seem that its power has been significantly understood. Indeed, drawing a character on the fly allows to take care of its context (see [14] for a survey on these contextual fonts). Differ... |

1 |
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Citation Context ...on these contextual fonts). Different contexts may be involved: 1. No context: i.e. purely random. A typical example is the Scrabble font where each piece randomly stirs as if they were an earthquake =-=[15]-=-. In [16], the Knuth's Punk font [12] has been reprogrammed in such a way that each instantiation of any letter gives a new shape (see figure 7) and, furthermore, hazard is introduced into the curve d... |

1 |
et Victor Ostromoukhov, "Punk: de METAFONT a PostScript", Cahiers GUTenberg
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Citation Context ...irst time, the bitmap of "L" is Contextual Typesetting of Mathematical Symbols 9 EP - EP - EP - EP Figure 7: This Punk poster has been printed by using a single call (EP - EP - EP - EP) show=-= -- After [16]. computed-=- then saved into a cache memory. At the second call, this cached bitmap is reused, whatever the new values of dx and dy are. (This is equivalent to a "by value" passing of parameters in prog... |

1 |
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Citation Context ...d, furthermore, hazard is introduced into the curve definitions to give the impression of inkspreading. Other fonts now use these possibilities to simulate antique fonts or to create degraded letters =-=[17]-=-, [18]. Commercial products, like PhotoShop, allow such deformations; however, they are not dynamic: every time degraded letters are reused (for example from Illustrator), the same distorsions are pro... |

1 |
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Citation Context ...e produced. Truly degraded letters require computation at any letter occurrence, like in figure 8. 2. The context of a character may be its neighbours. Ligatures may be automatically defined, like in =-=[19]. Ends of -=-lines or of words are special cases of neighbouring: a contextual font may decide to change the shape of a, say, "s" at the end of a word; or to modify the bearing of a character at the (rig... |

1 |
Is What You See Enough To Get?", Protext
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Citation Context ...information on the way symbols are extended. 3 Use of Math-fly from Grif Due to its possibility to receive parameters, a font like Math-Fly could not be fully used by editors such as T E X, Interleaf =-=[30]-=- or Framemaker [28] without modifications of the way they call formulae symbols. Due to our involvement into the Grif project, this editor was a good place to check this font. 3.1 Grif overview Grif i... |

1 | orghi, "Dynamic fonts", in raster Imaging and Digital Typography - Andr6, Bruno - 1989 |

1 | Fontes dynamiques, M6moire d'habilitation h diriger les recherches - Andr6 - 1993 |

1 | The Scrabble font", The PostScript - Andr6 - 1990 |

1 | et Victor Ostromoukhov, "Punk: de METAFONT h PostScript", Cahiers GUTenberg - Andr6 - 1989 |

1 | et Christian Delorme, "Le Delorme: un caractre modulaire et d6pendant du contexte", Communication et langage - Andr6 - 1990 |

1 | Grindration automatique de contraintes pour caractres typographiques l'aide d'un module topologique - B6trisey - 1993 |