Towards An Operational (La)TEX Package Supporting Optical Scaling of Dynamic Mathematical Symbols
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1 Towards An Operational (La)TEX Package Supporting Optical Scaling of Dynamic Mathematical Symbols Abdelouahad BAYAR Cadi Ayyad University École Supérieure de Technologie de Safi (High College of Technology) July 27, 2016 A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 1
2 Introduction Handling of dynamic mathematical symbols is still a hard problem (Some)TEX and PostScript Type 3 to supply a solution A TEX (luatex) package supporting optical scaling and supplying the habitual way to format scientific documents A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 2
3 Outline 1 Mathematical formula: State and Problems 2 The Requirements to handle dynamic mathematical symbols taking care of optical scaling 3 4 Implementation A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 3
4 Mathematical formula: State and Problems Class of mathematical Symbols Static mathematical symbols Variable sized symbols (Dynamic mathematical symbols) A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 4
5 Mathematical formula: State and Problems Variable Mathematical Symbols and Variations-scaling Linear scaling a 11x 1 + a 21 x 1 + a 11x 1 + a 21 x 1 + a 31 x 1 + a11x1 + a 21 x 1 + a 31 x 1 + a 41 x 1 + A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 5
6 Mathematical formula: State and Problems Variable Mathematical Symbols and Variations-scaling Linear scaling a 11x 1 + a 21 x 1 + a 11x 1 + a 21 x 1 + a 31 x 1 + a11x1 + a 21 x 1 + a 31 x 1 + a 41 x 1 + Optical scaling a 11x 1 + a 21 x 1 + a 11x 1 + a 21 x 1 + a 31 x 1 a11x1 + + a 21 x 1 + a 31 x 1 + a 41 x 1 + A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 5
7 Mathematical formula: State and Problems Metal/Digital Typesetting and Optical Scaling Metal typesetting Digital typesetting A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 6
8 Mathematical formula: State and Problems Existing Works math-fly/grif Curext TEX/L A TEX Support of mathematical formulas witultiple variable-sized symbols ( ) ( ) a b e f c d g h ( ) i j 0 k l A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 7
9 Mathematical formula: State and Problems Existing Works TEX/L A TEX The thickness remains constant after some level Some symbols differ from corresponding ones in metal typesetting with regard to the shape after a level of size ( ) ( ) ( ) A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 8
10 Mathematical formula: State and Problems Existing Works TEX/L A TEX Some symbols differ from their corresponding in metal typesetting with regard to the shape at all sizes. { { { A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 9
11 The Requirements to handle dynamic mathematical symbols taking care of optical scaling Font requirements Document processing system requirements use Requirements by end-users Required Font for (La)\TEX: PostScript Type 3 A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 10
12 General package layout dynmath.tex. \special{!. some useful PostScript procedures /w 0 def /h 0 def /fs 0 def /dynmathfont 8 dict def dynmathfont begin /FontType 3 def /FontMatrix [ ] def /FontBBox [ ] def /Encoding 256 array def {Encoding exch /.notdef put} for A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 11
13 General package layout dynmath.tex Encoding 0 /leftpar put % Left parenthesis = 0 Encoding 1 /rightpar put % Right parenthesis = 1 Encoding 8 /leftbrace put % Left brace = 8 Encoding 9 /rightbrace put % Right brace = 9../Charprocs - individual glyph descriptions../buildglyph definition../buildchar defintion. A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 12
14 General package layout dynmath.tex currentdict end % End of font dictionary /dynmath exch definefont pop% }.. Some useful TEX defintions. % #1:left delimiter, #2:formula, #3:right delimiter \def\meleft#1#2\meright#3{. macro defintion } A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 13
15 General package layout \meleft macro The macro \meleft has to : 1 Compute the dimensions of the formula (in the correct math style): \hf, \df and \wf 2 Determine vertical and horizontal stretching amounts: \h and \w 3 Calculate the size of the font \fs in which dynmath will be used 4 Determine the dimensions of the left symbol: \symheight, \symwidth and \symdepth A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 14
16 General package layout \meleft macro 5 Build an horizontal box \efbdel: \setbox\efbdel\hbox { \special{... /fs... store /h... store /w... store /dynmath findfont fs scalefont setfont <code of The left symbol> show } } 6 Set the dimensions of \efbdel to \symheight, \symwidth and \symdepth 7 Write the content of \efbdel A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 15
17 General package layout \meleft macro 8 Write the mathematical formula 9 Apply steps from the second to the seventh to deal with the right delimiter A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 16
18 Design of dynmath font Symbol parametrizing stretching - Concepts A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 17
19 Design of dynmath font Symbol parametrizing stretching - Concepts A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 18
20 Optical scaling support Mathematical formula characteristics Higathematical formula math axis y 1 f h Baseline h 32 y 2 f d A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 19
21 Optical scaling support Mathematical formula characteristics Deep mathematical formula math axis h 32 y 1 f h Baseline y 2 f d A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 20
22 Optical scaling support Scaling - h 32 fs = hm h 1000 h 32 y 1 y 2 hm f h f d math axis Baseline A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 21
23 Optical scaling support Scaling - h 32 fs = hm h 1000 h 32 y 1 y 2 hm f h f d math axis Baseline A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 21
24 Optical scaling support Scaling - > h 32 h 32 y 1 f h math axis Baseline y 2 f d A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 22
25 Optical scaling support Scaling - > h 32 h 32 y 1 y 2 f h f d math axis Baseline h32 hfs h y 1 y 2 f h f d math axis Baseline A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 22
26 Optical scaling support Scaling - > h 32 h p max = = A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 23
27 Optical scaling support Scaling - > h 32 ax = h p maxpt h p max = = A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 23
28 Optical scaling support Scaling - > h 32 ax = h p maxpt h p max = = ax = pt A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 23
29 Optical scaling support Scaling - > h 32 y 1 f h such that: e ( ) = c 1 + c 0 e (h 32 ) = e 32 h 32 math axis Baseline e (ax ) = λe 32 e 32 : thickness of the dynamic symbol in body 32 y 2 f d λ: a scaling factor (3.236) A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 24
30 Optical scaling support Scaling - > h 32 fs = e 1000 e A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 25
31 Optical scaling support Scaling - > h 32 fs = e 1000 e h 32 y 1 y 2 f h f d math axis Baseline A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 25
32 Optical scaling support Scaling - > h 32 fs = e 1000 e h y 1 h fs = h fs h 32 h fs f h math axis Baseline y 2 f d A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 26
33 Optical scaling support Scaling - > h 32 fs = e 1000 e h fs = h fs h 32 h fs h y 1 f h math axis Baseline y 2 f d h = h fs A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 26
34 Optical scaling support Scaling - > h 32 fs = e 1000 e h fs = h fs h 32 h fs h y 1 f h math axis Baseline y 2 f d h = h fs w =function(h) A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 26
35 Optical scaling support Scaling - > h 32 h 32 h fs h y 1 y 2 f h f d math axis Baseline A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 27
36 Optical scaling support Scaling - > h 32 h 32 h fs h y 1 y 2 f h f d math axis Baseline A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 28
37 Optical scaling support Scaling - > h 32 h 32 h fs h y 1 f h math axis Baseline y 2 f d A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 29
38 Implementation dynmath: Simple TEX source File dynmath: Mini-package dynmath for all(tex): limited and slow dynmath for LuaTEX (dviluatex and dvilual A TEX): good A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 30
39 Conclusions and Perspectives Conclusions: Support of dynamic mathematical symbols with respect to Optical Scaling is feasible. The feasibility is proved with Parentheses and Braces which are adequate representing samples. Perspectives: Support of all dynamic mathematical symbols Improvement of quality of symbols (Study of optical scaling considering the artistic viewpoint) A. BAYAR - EST-Safi/CAU TUG 2016: July 25-27, 2016 / The 37th Annual Meeting / Toronto, Canada 31
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