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A Multiple Master based method for scaling glyphs without changing the stroke characteristics Tim Ahrens This essay was originally written as part of the MA Typeface Design programme at the University of Reading in 2006. It was later published in the academic journals Document Numérique and Digital Creativity. The method described here has been implemented as Font Remix Tools, a set of plugins for FontLab and Glyphs. Abstract This article presents methods for handling Multiple Masters (several type styles such as regular and bold joined in one font file) beyond the conventional applications such as generating semibold fonts. The “bold- ness” information in an MM font can be used to change the size of glyphs without changing the stroke weight. The method helps to create small caps, Cyrillic lowercase and – since the horizontal and vertical scale fac- tors can be chosen independently – even true condensed fonts. Comparisons to existing typefaces with designed small caps and con- densed versions show that the output generated by the model is rather close to that of the true glyphs. In contrast to “intelligent” data formats that generate glyphs, the model suggested here is a technology-independent formula for the processing of pre-existing shapes. The output has the same format as the input and can be subsequently modified, making the method a tool for the auto- mation of a specific design step rather than a stand-alone technology. A Multiple Master based method for scaling glyphs without changing the stroke characteristics Tim Ahrens 1. OBJECTIVES 2. ThE mEThOd A first simple approach More specific control over the stroke weight Anisotropic scaling Taking into account italic angles Optical sizes Scaling the bold master and enlarging Spacing and Kerning Notes on the actual scale factor Implementation Equalising the input 3. TEST Of ThE mEThOd Small caps: Meta Condensed fonts: Frutiger and Myriad Cyrillic lowercase: Gauge and Den Haag Comparison with the Ek-module 4. APPLICATIONS Generating new glyphs Width corrections Adjustments of global proportions Post-processing fonts Analysing existing typeface designs 5. CONCLuSIONS 2 1. OBJECTIVES Digital type technology has seen various innovations and advancements since its beginnings more than forty years ago. The progress is ongo- ing, with OpenType and the increasing support of Unicode being recent ground breaking improvements of the handling of glyphs. In the field of glyph shapes however, the development seems to have come to a halt years ago. The seventies, eighties and early nineties have seen more than 150 font formats (Karow 1994:22), various mathematical methods were developed and partly controversially discussed. After this phase of innovation and discussion TrueType and PostScript, both being out- line formats, “have won the competition” (Jackowski 1999:118). After the abandonment of Adobe’s Multiple Master technology it seems that static glyph shape descriptions, defined directly by the designer with- out the use of dynamic mathematics, are accepted by everyone as the only practicable system in professional print production. New ap- proaches are neither dared by mathematicians nor desired by designers and typographers. This essay resumes the discussion of mathematical models related to glyph shapes. In contrast to “intelligent” formats such as Metafont or Intellifont the model suggested here will not serve the creation of shapes. It is purely a tool for the processing of preexisting glyphs. The output has the same format as the input and can be subsequently processed, allow- ing for the manual correction of remaining deficiencies. This suggests the method to be used by typeface designers as a tool that automates a specific design step, supporting most designers’ preference of “work- ing out” as opposed to “thinking out” (Warde 1935), of making decisions as opposed to postponing them, like it would be typical for parametric design systems. However, further applications such as post-processing fonts by layout software or acting as a research tool for analysing type designs can be imagined. “TRUE SMALL CAPS ARE MORE Many glyphs used by typographers are derived from other glyphs and dif- fer only in size. However, if glyphs are scaled the stroke weight changes THAN CRUSHED CAPITALS accordingly, which leads to unacceptable alterations of the characteris- THAT LOOK LIKE THEY HAD tics (Fig. 1). BEEN WASHED AT TOO HIGH If the new glyphs are not to be designed from scratch two ways to pro- duce them are thinkable. One is to change the size by shifting portions A TEMPERATURE.” of the outline instead of applying the same scaling factor to the coordi- (Rögener et al., 1995:50, translated nates of every point. This can be done manually (Hudson 2005) or with by the author) the help of an intelligent computer programme (André and Vatton 1994). Another approach is to scale the glyph geometrically and correct the 1. Scaling changes the stroke weight stroke weight. Usually this is done manually. As will be shown in this es- say, it can also be done with the help of a mathematical model. Such a model will be developed and tested below. The stroke weight can be controlled with the help of a second master of a different weight that contains the necessary “boldness” information which can be added and subtracted as needed. The Multiple Master technology provides a numeric description of the glyph outlines and allows us to easily process the two corresponding shapes. While being obsolete as a final font format it is widely used as a production tool and its support in font editors is still improving. The model – which we will call “compensated scaling” – could be helpful to both experienced and less experienced designers. The former would 3 be enabled to save time. Less experienced designers could even improve the design, as the consistency within a font or family would be improved. Just like a circular saw that cannot build furniture by itself and maybe does not even improve the final result of the master’s work it can save a great deal of time. It performs certain aspects of the process very well and allows for subsequent refinement. This essay is organised as follows. Section 2 presents the model. Starting with a simple principle, the formulae will be refined as various aspects are taken into account. Section 3 aims to test the model. In addition to comparing it directly to the Ek-module its output will be compared to existing, well-known typefaces, for small caps, condensed versions and cyrillic lowercase letters. The comparison will show whether the output of the mathematical model is close enough to that of the true one to be able to serve as an appropriate and time-saving basis for further refine- ment by the designer. Another aim of comparing the automatic and the true shapes is not a test of the creative potential of the method but a demonstration of its analytical use. Regarding the automatically scaled glyphs as stylistically unchanged variations of their base the comparison with manually designed versions reveals modifications that the design- ers in question may have done unconsciously. Section 4 discusses in detail different applications of the method. Section 5 points out some singular properties of the approach and draws conclusions of the study. 2. ThE mEThOd If a glyph is scaled down the stoke gets thinner, too. With the help of a second, bolder master it is possible to increase the weight. The method developed here will not be a process or algorithm but only one equation for x and y coordinates each, which processes the shapes in a single step. regular semibold However, as a means of exemplification some steps will be explained as if they were performed in a certain sequence. The compensation for the loss in stroke weight is notionally done before the scaling. This means that an intermediate instance – an interpolation between regular and bold – is scaled (Fig 2). The required instance can scaled comparison be calculated. semibold Condensed versions can be created by applying only the horizontal 2. Compensation for the loss in weight changes, which is called anisotropic interpolation. The x value of each point is that of the scaled semibold while the y values remain the same as in the regular (Fig 3). A first simple approach The assumption is that a regular weight glyph should be scaled down by the factor s while the loss in stroke weight is compensated for. This is achieved by scaling an interpolation between the regular master (x ,y ) and the bold master (x ,y ), represented by the interpolation fac- r r b b tor q. y = s[qy + (1–q)y ] r b [1] 3. Anisotropic interpolation x = s[qx + (1–q)x ] r b 4 The factor q can be determined by calculating the stroke weight of the final result. The typical stroke weight of the regular may be r and the stroke weight of the bold master b·r with b as the quotient of the two weights. As the weight needs to remain unchanged the original stroke weight r is equated with the final stroke weight. r = s[qr + (1–q)br] [2] The equations can be solved for q q = (1/s – b) / (1–b) [3] The stroke width r can be cancelled straight away, which shows that the model does not rely on strokes nor does it try to recognise them. The no- tion of stroke weights is only a temporary means of exemplification. Only b, the relation between the typical bold and regular weight, is processed. The formulae [1] and [3] define the final shape. They could be united into one equation, which is not necessary here. These formulae do not depend on Bézier splines, they can be applied to any format as long as there are two corresponding sets of data.

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