Converting mEtaFoNt sources to outline fonts
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1. PK files can be imported to the background as a set of gray pixels to compare with glyph images Sometimes METAFONT with such a high resolution may fail if the author did not design the font for an arbitrary resolution Font composition We also run mftrace 10 with an appropriate encoding to make a PFB font file From this file we build a frame for the created font copy the glyph widths and glyph names and move the outlines to the background layer visible as green lines During a subsequent processing of the font with FontForge we use its internal Spline Font Database format SFD The high resolution bitmap is always huge so we import it only before a comparison But the out line contours of the font produced by mftrace are not large and we can store them in the working SFD files permanently To the foreground layer we import the outlines from the EPS files calculated in the previ ous step from the original EPS files generated by METAPOST The high resolution pixel image gives a close visual bitmap representation of the original META FONT source Of course information about contour curves intersection points corners etc virtually calculated by METAFONT has been lost The font outlines autotraced by mftrace from similar bitmaps despite the inevitable artifacts bumps holes un recognized corners give reasonably correct in formation about the glyphs Our aim is to obtain another outline representation more accu2. contain various stroked paths see figures 1 9 It is necessary to find contour curves for single strokes and then also common envelope curves for overlapping strokes The following lines from the PostScript pro duced by METAPOST correspond to fig 1 O 79 06227 dtransform truncate idtransform setlinewidth pop O setdash 1 setlinecap 1 setlinejoin 10 setmiterlimit gsave newpath 119 50958 284 54501 moveto 398 36119 284 54501 lineto 0 98387 0 98387 0 17888 0 17888 0 0 concat stroke grestore The lineto operator describes the line segment the concat operator applies the affine transformation represented by the preceding normalized matrix in brackets denoting the rotated elliptical pen and 79 06227 setlinewidth is the scale factor defin ing the stroke width Converting METAPOST products to outlines The results of METAPOST strokes are converted to primary outlines Fitting curves with the least square method is a typical approach to calculate a curve approximation This method is nothing new and may well have been used in conversion programs developed by Richard Kinch MetaFog 6 Basil Malyshev 9 George Williams FontForge 13 and others We only apply a few additional conditions We try to be more precise but our attempts are still more fragile and unstable than the programs listed above Figure 2 Primary conversion to outlines All the calculations are in the non integer value space We check ea
3. Converting METAFONT sources to outline fonts using METAPOST Karel Piska Institute of Physics Academy of Sciences 182 21 Prague Czech Republic piska fzu cz http www hep fzu cz piska Abstract The paper describes a multistep conversion process from METAFONT sources to outline fonts Adobe Type 1 format An important step finding contours is based on an accurate algorithm fitting the envelope curve of a stroke drawn by a pen along a cubic B zier curve by the least square method specially extended adapted for a rotated elliptical pen applied for instance in the Devanagari font design After converting the EPS files produced by METAPOST to the correspond ing outline representation the FontForge font editor is used for removing overlap simplification autohinting generating outline fonts and necessary manual mod ifications The conversion results the faithful Indic Type 1 fonts significantly more precise and closer to optimal than earlier attempts made by autotracing bitmaps will be released KEYWORDS font conversion bitmap fonts METAFONT METAPOST outline fonts PostScript Type 1 fonts approximation B zier curves Introduction In 2001 I experimented with approximate conversion METAFONT Indic fonts to the Type 1 format by au totracing bitmaps with the TEXtrace program 11 I was not satisfied with the results and decided to apply another analytic approach to achieve results more precise and also better opt
4. ch segment for accuracy and sub divide it if a chosen limit is exceeded insert all hori zontal and vertical extrema nodes keep all horizon tal vertical straight lines and control vectors to be exactly horizontal vertical The inner part of a con tour curve of drawing a rotated elliptical pen even along a simple B zier path without any intersections may have self intersections Therefore we try to find self intersection points as precisely as possible if it is possible at all Unfortunately sometimes this it eration does not converge A simplest conversion to outlines is shown in figure 2 For a given time of the path segment using the affine transformation matrix and its inverse matrix for a usual pen they are always regular we can cal culate the displacement corresponding to the point lying on the right parallel outline curve the left one is located symmetrically Knowing the coordinates of points on the outline curves and also on the pen boundary we can fit them by a cubic B zier approx imation But a problem is that we do not know whether the points are on the envelope curve be cause parts of the outline curves may create loops of arbitrary size being inside a closed area It de pends on complex correlations between the path and the pen We also recognize quarter circles usually rep resented in METAFONT by two segments because METAFONT tends to divide curves into octants To avoid further simplification problems we do n
5. identification easier Running METAPOST Invoking METAPOST pro cesses the METAFONT sources and produces EPS files METAPOST together with a macro package mfplain 5 p 79 allows processing the original or modified to eliminate METAFONT specific com mands font sources written in METAFONT and to generate for each glyph a single file in the Encap sulated PostScript format consisting only of Post Script commands like curves strokes affine trans formations representing pens etc but no bitmap images in contrast to METAFONT s usual output Some metric data e g the glyph widths and italic angles may be lost we shall restore them later 158 TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting Converting METAFONT sources to outline fonts using METAPOST Figure 1 Result of METAPOST We also need to define a magnification factor because we have to transform the glyph images to a 1000 unit glyph coordinate system we use this usual space with the units in PostScript big points bp and the font designsize in pt units The trans formation factor from pt to bp is 1 00375 Thus in general the magnification factor will be 1000 x 1 00375 designsize For designsize 10 pt this is 1000 1 00375 10 100 375 for 8 pt it is 125 46875 for 17 28 pt 58 087384 etc So a typical command to call METAPOST is mpost amp mfplain mode localfont mag 100 375 input dvngi0 mf These files may
6. imized Conversion process Our procedure consists of studying the font defini tions in METAFONT and preparing encoding files Then the glyph strokes produced by METAPOST are converted to outlines and the font is assembled op timized and autohinted Finally it is generated as a Type 1 binary file with FontForge After verifica tion of visual proofsheet pages some steps are often repeated to correct or improve the final results Analysis of METAFONT sources We analyze the METAFONT source texts 7 of a font to select an ap propriate strategy of conversion to find the crucial parameters like the font size the italic angle and the definitions of pens and strokes Some parame ters may be also hidden inside macros Sometimes a method for efficient conversion is not apparent Therefore it is also important to know about the presence and number of METAFONT commands not available in METAPOST 5 for example using op erations with bitmap picture variables Creating encoding files Encoding files and en coding vectors define a mapping between the glyph names and their number codes METAFONT defini tions usually do not contain unique glyph names in an explicit form but only as comments The glyph names are taken from these comments to produce an unambiguous list of PostScript names i e we must find duplicated names and change them to be dif ferent Our preliminary solution inherits the META FONT comments closely to make glyph
7. l of the work is more precise outline versions of the free METAFONT Indic fonts available from CTAN Devanagari Sanskrit Gur mukhi Punjabi Bangla Sinhala Malayalam Tel ugu Kannada Tamil and Tibetan At the time of writing not all the above fonts have been converted Also the Oriya fonts are impractical because they widely use METAFONT bitmap picture commands Figures 5 6 12 13 all Devanagari and 14 for Malayalam show the results to date Chinese fonts We have also tried to convert two small single fonts with Chinese ideographs created in METAFONT the Ho ng Zi font 128 glyphs de signed by Javier Rodriguez Laguna 12 version 0 5 of 2005 03 23 shown in fig 7 and china10 a font from the china2e package 4 containing Chinese TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting 161 Karel Piska Figure 7 H ng Zi xingl of Javier Laguna calendar symbols produced by Udo Heyl 1997 in fig 8 Conclusion In this article we describe a font conversion process and briefly discuss some selected problems Creat ing precise fonts is always difficult time consuming and never ending work regardless of the approach chosen We plan to again verify all the glyphs to improve hinting and polish the outlines to remove tiny artifacts It will also be useful to make the glyph names of the Indic glyphs common for all lan guages this is not trivial because the fonts contain many variou
8. mits causes a limitcheck error and rendering fails The coordinates of the segments are rounded to integers by a more complex algorithm than a triv ial rounding of all the values First we round the node points Then we transform the control vec tors according the changes of the nodes and try to find the control points in the integer grid near the transformed control vectors Even this sophisticated rounding to integer is not without problems Some times if the change in x or y in the segment is very 160 TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting Converting METAFONT sources to outline fonts using METAPOST Figure 4 Final font in an outline form and a hinted proofsheet clip small e g about 1 unit or a segment is too short in both directions no good selection may exist and a manual adjustment is then necessary probably with the loss of closeness accuracy or symmetry of the approximation No special additional program for hinting has been developed or applied The automatic autohint ing tool in FontForge is used and any unsatisfactory results should be corrected manually Finally we generate the Type 1 binary font with FontForge rounded to integer coordinates and auto hinted as described See figure 4 Results To make font auditing and verification quicker and more efficient we have developed tools for genera tion of visual proofsheets in PDF These support a fast overview
9. of all glyph images display of out line curves with node and control points and vectors and hinting zones They can also produce warnings about undesirable situations such as missing nodes at extrema presence of inflection inside a segment a non smooth transition between segments etc Our aim is to fulfill the Type 1 conventions 1 Therefore we include the extrema nodes they may be omitted if they are really redundant exclude other unnecessary node points and preserve smooth connections between the adjacent segments We also keep the straight lines corners and arcs after con version and avoid any false bumps holes or steps absent in the original METAFONT sources In this paper some selected figures have the node points squares the control points bullets and the control vectors enlarged for readability In a real working process they are colored and small as in other proofsheets when we zoom in on interesting details only if we need to check them The principal and auxiliary algorithms are still under development and adaptation for new fonts Figure 5 dvng10 tta of Frans Velthuis Figure 6 dvngbi10 lla of Frans Velthuis The programs are written in awk or gawk 3 For Type 1 font handling the t1utils 8 are used Several pictures illustrate the intermediate and final results in the conversion of METAFONT fonts to the Type 1 format figures 2 4 10 11 15 and 16 Indic fonts A basic goa
10. ot pre serve the 45 degree middle nodes and change the quarter circles to the accurate single segment Post Script representation with relative lengths of con trol vectors 4 3 2 1 0 552285 cf R Kinch 6 p 236 and Luc Devroye 2 For an example of our circle approximation see figure 3 To summarize in the primary approximation straight lines and circles are represented by the min imal number of segments because other nodes are unnecessary and on the other hand other outline curves have redundant node points to preserve a maximal starting accuracy These intermediate re sults of the primary conversion to outline are demon strated in figures 2 and 10 TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting 159 Karel Piska Figure 3 Representation of circles Creating a font with FontForge FontForge is a powerful open source font editor Among its wide range of useful abilities is a background layer which may contain bitmap images and line drawings So we generate with METAFONT high resolution bitmaps for the font under study either 2400 dpi supre mode or 7254dpi The 7254dpi device corresponds to the relation 1 pixel in the PK bitmap 1 unit in the PostScript glyph space for a 10 pt design size 72 27 1000 375 10dpi 7254 1 mode_param pixels_per_inch 4000 3254 1 mode_param blacker 0 mode_param fillin 0 mode_param o_correction 1 The resulting GF or
11. rate and closer to optimal minimizing the number of defects Having the font in SFD format built from the mftrace output our next step with FontForge is re moving overlap and optimization simplifica tion We continue processing in the non integer space to keep accuracy in particular not changing the slopes of the neighboring control vectors so as to preserve a smooth transition between segments Rounding to integer hinting and Type 1 font generation FontForge allows for generating PostScript fonts with non integer point coordinates and PostScript RIP devices usually render these fonts properly But we have three significant reasons to round coordinates to integers and to generate the Type 1 fonts in integer representation e Non integer values in the PostScript charstring occupy 3 items Therefore the integer rep resentation saves storage and the PFB files are smaller e The final Type 1 fonts do not need such accu racy after removing overlap and simplification e For hinting it would be inconvenient and im practical to use any discrete grid other than in tegers For example the non integer Type 1 command occupies 19 items 18153 100 div 212 100 div 14437 100 div 407 100 div 7208 100 div 243 100 div rrcurveto and after rounding only 7 items 182 2 144 4 72 2 rrcurveto It is desirable to minimize the number of items because PostScript interpreters have internal mem ory limits per glyph Exceeding these li
12. s ligatures special signs or variants not covered in the Unicode standards Acknowledgements I would like to thank all the authors of the free con version programs the authors of the public META FONT fonts for Indic languages other sources and program packages used in this work References 1 Adobe Systems Inc Adobe Type 1 Font Format Addison Wesley 1990 2 Luc Devroye Formatting Font Formats TUGboat 24 3 pp 588 596 2003 10 11 12 13 Figure 8 chinai0 yeu of Udo Heyl Free Software Foundation GNU awk http www gnu org software gawk Udo Heyl china2e CTAN macros latex contrib china2e 1997 John D Hobby A user s manual for META POST AT amp T Bell Laboratories Computing Science Technical Report 162 1994 Richard J Kinch MetaFog METAFONT Shapes to Contours 16 3 pp 233 243 1995 Donald E Knuth The METAFONTbook Addison Wesley 1986 Volume C of Computers and Typesetting Eddie Kohler tlutils Type 1 font utilities http freshmeat net projects tiutils Basil K Malyshev Problems of the conver sion of METAFONT fonts to PostScript Type 1 TUGboat 16 1 pp 60 68 1995 Han Wen Nienhuys mftrace http www cs uu nl hanwen mftrace Converting TUGboat Karel Piska A conversion of public Indic fonts from METAFONT into Type 1 format with TEX trace TUGboat 23 1 pp 70 73 2002 Javier Rodriguez Laguna Hong Zi a Chine
13. se METAFONT http hongzi sourceforge net 2005 George Williams FontForge an outline font editor http fontforge sourceforge net 162 TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting Converting METAFONT sources to outline fonts using METAPOST Figure 9 dvngi0 lh METAPOST output Figure 12 dvng10 om of Frans Velthuis T N O X A AX DN we AN NN E O Ye o ee Sr a a N eS a Ne R WS N Y C Bs RSX Ss NY Eag Ss Ww ae N MQ SX Figure 10 dvng10 l h primary outlines Figure 13 dvngbi10 om of Frans Velthuis Figure 11 dvngi0 l h Type 1 font proofsheet Figure 14 mm10 a of Jeroen Hellingman TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting 163 Karel P ka a 3 G AK ei F AAM MA Sa C eee KD SO i aT ZT 7 A NO Figure 15 mm10 j_juu METAPOST output converted to primary outlines Figure 16 mm10 j_juu Type 1 font proofsheet with hints 164 TUGboat Volume 26 2005 No 2 Proceedings of the 2005 Annual Meeting
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