Typographic characters are carefullydesigned shapes incorporating type-

design tradition,1 the rules related to visual appearance,and the design ideas of a skilled character designer.2

The typographic design process is structured and sys-tematic: letterforms are visually related in weight, con-trast, space, alignment, and style. To create a new

typeface family, type designers gen-erally start by designing a few keycharacters—such as o, h, p, and v—incorporating the most importantstructure elements such as verticalstems, round parts, diagonal bars,arches, and serifs (see Figure 1).They can then use the design fea-tures embedded into these struc-ture elements (stem width,behavior of curved parts, contrastbetween thick and thin shape parts,and so on) to design the font’sremaining characters.3

Today’s industrial font descriptionstandards such as Adobe Type 1 orTrueType represent typographiccharacters by their shape outlines,because of the simplicity of digitiz-ing the contours of well-designed,large-size master characters.4 How-ever, outline characters only implic-itly incorporate the designer’s

intentions. Because their structure elements aren’texplicit, creating aesthetically appealing derived designsrequiring coherent changes in character width, weight(boldness), and contrast is difficult. Outline charactersaren’t suitable for optical scaling, which requires rela-tively fatter letter shapes at small sizes.5 Existingapproaches for creating derived designs from outlinefonts require either specifying constraints to maintainthe coherence of structure elements across differentcharacters6,7 or creating multiple master designs for theinterpolation of derived designs.8

We present a new approach for describing and syn-thesizing typographic character shapes. Instead ofdescribing characters by their outlines, we conceive eachcharacter as an assembly of structure elements (stems,bars, serifs, round parts, and arches) implemented byone or several shape components. We define the shapecomponents by typeface-category-dependent globalparameters such as the serif and junction types, by glob-al font-dependent metrics such as the location of refer-ence lines and the width of stems and curved parts, andby group and local parameters. (See the sidebar “Previ-ous Work” for background information on the field ofparameterizable fonts.)

Conceptual model and terminologyTo provide highly flexible parameterizable fonts, we

first describe a conceptual model for typographic char-acters based on shape components. A character’s basicstructure is font independent. Basic characters are made

0272-1716/01/$10.00 © 2001 IEEE

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70 May/June 2001, IEEE CG&A, Vol. 21, No. 3, 70-85

We propose a new, highly

flexible font description

method that explicitly

describes characters as

assemblies of parameter-

izable shape components.

By varying global

parameters, we can derive

fonts that vary in weight,

condensation, and shape.

Changyuan Hu and Roger D. HerschEcole Polytechnique Fédérale de Lausanne,Switzerland

ParameterizableFonts Based onShape Components

Opticalcorrection

Arch

Roundpart

Ascenderstem

Roundpart

Diagonalbar

Narrowdiagonalbar

Descenderstem

Ascenderline

x-heightline

Baseline

Descenderline

Topserif

1 Characterstructure ele-ments incorpo-rated into keytypographiccharacters.

of stem, bar, sweep, half-loop, serif, and terminal com-ponents. Figure 2 shows the set of components and theirinterconnections for the characters h and b.

By specifying the junction between components (forexample, the junction between a stem and a sweep) andby associating absolute and relative metrics to the set of

IEEE Computer Graphics and Applications 71

The earliest work known to describe typographiccharacters by parameterizable shape primitives is that ofPhilippe Coueignoux, who designed one of the first fullydigital typesetter controllers.1

The most serious published work done in the field ofparameterizable fonts is the Metafont system, a program-mable parameterizable font synthesizing system.2 TheMetafont system relies on a few basic paradigms forgenerating characters and symbols. The main characterparts such as horizontal, vertical, and diagonal strokes andround parts are specified by describing the path of a penwith given orientations and pen widths. A sequence of penpositions and directions describes the pen’s central path.From this information, Metafont computes a smoothcenterline pen trajectory. With the given pen positions,widths, and orientations and with the centerline trajectory,Metafont infers the description of the corresponding penstroke’s boundary.3 It adjusts serifs with font-dependent serifwidth, height, and depth information to the computedstroke boundary. The shape boundary resulting from theassembly of serifs and stroke can either be directly filled ortraced by a small, circular pen and then filled. In addition tostrokes defined by pen trajectories, Metafont specifiesround character parts covering one or a multiple quadrantsby superarcs, that is, scaled arcs defined within singlequadrants without outlines whose boundaries are given bysuperellipses.2

Donald Knuth used the Metafont program to create hisComputer Modern typeface family.4 He parameterized theComputer Modern typefaces so as to automaticallygenerate optically scaled fonts and to generate sans-serif,typewriter, semibold, bold, condensed, and slanted romanfonts by a simple change of parameterizations. Metafontuses separate character shape descriptions for the italic font.Since Metafont is both a complete programming languageand a flexible font design tool, using it requires bothprogramming and typographic skills. Only a few individualsuse Metafont, often for designing non-Latin characters.5,6

One of the lessons learned by Metafont users designingLatin characters is that Metafont’s pen paradigm doesn’toffer sufficient freedom to exactly generate charactershapes according to the designer’s intention. This explainswhy most Metafont designs for Latin fonts besidesComputer Modern rely heavily on outline descriptions.7

The recent Infinifont system (US Patent 5,586,241)8 is afeature-based parameterizable font description andreconstruction system. Its authors describe the basicmechanism to assemble a character such as character Efrom parameterizable vertical bars, horizontal bars, andserifs. However, most of their work isn’t published, so wedon’t know how they synthesize different typefacecategories and which paradigms they use for synthesizingcurved character shapes and serif variants.

Schneider describes a method for assembling parameter-izable pen-based strokes into typographic characters.9

Regarding Latin character shapes, the method suffers fromthe same limitations as Metafont. It seems, however, wellsuited for synthesizing Asian characters (such as Kanji andHangul).

References1. Ph. Coueignoux, “Character Generation by Computer”, Com-

puter Graphics and Image Processing, vol. 16, 1981, pp. 240-269.2. D. Knuth, The Metafont Book, Addison-Wesley, Reading, Mass.,

1986.3. J.D. Hobby, “Rasterizing Curves of Constant Width,” J. ACM, vol.

36, no. 2, Apr. 1989, pp. 209-229.4. D. Knuth, Computer Modern Typefaces (Volume E of Computers

and Typesetting), Addison-Wesley, Reading, Mass., 1986.5. Y. Haralambous, “Typesetting Khmer,” Electronic Publishing: Origi-

nation, Dissemination, and Design, vol. 7, no. 4, 1994, pp. 197-215.6. R. Southall, “Metafont in the Rockies: the Colorado Typemaking

Project,” Electronic Publishing, Artistic Imaging, and Digital Typog-

raphy, R.D. Hersch, J. André, and H. Brown, eds., LNCS 1375,Springer-Verlag, 1998, pp. 167-180.

7. N. Billawala, “Pandora, An Experience with Metafont,” Raster

Imaging and Digital Typography, J. André and R.D. Hersch, eds.,Cambridge Univ. Press, Cambridge, Mass., 1989, pp. 34-53.

8. C.D. McQueen and R.G. Beausoleil, “Infinifont, A Parametric FontGeneration System,” Electronic Publishing: Origination, Dissemi-

nation, and Design, vol. 6, no. 3, Sept. 1993, pp. 117-132.9. U. Schneider, “An Object-Oriented Model for the Hierarchical

Composition of Letterforms in Computer-Aided TypefaceDesign,” Electronic Publishing, Artistic Imaging and Digital Typog-

raphy, R.D. Hersch, J. André, and H. Brown, eds., LNCS 1375,Springer-Verlag, New York, 1998, pp. 109-125.

Previous Work

Stemconnecting

arch

Topserif

Ascenderstem

Footserif

Footserif

Stem

Topserif

Ascenderstem

Spur

Roundpart

Structureelements:

Components andinterconnections:

Structureelements:

Components andinterconnections:

(a) (b)

Topserif

Ascenderstem

Footserif

Footserif

Stem

Topserif

Ascenderstem

Spur

Halfloop

Sweep Sweep

Sweep

Sweep

2 Component-based font-independentcharactermodels.

available parameters, we can fully specify characterinstances. We associate a software object with eachcharacter. A software object incorporates different char-acter-synthesis methods that can support the genera-tion of characters of different typeface categories—thatis, of characters whose junctions between componentsconsiderably vary. We use global parameters to specifyjunction types, serif and terminal types, reference linepositions, bar and stem widths, and serif and terminalmetrics. Group parameters define the metrics associat-ed with a group of related characters—for example, thejunction depth in the characters b, d, p, and q. Localparameters are parameters describing features specificto a single character. For each font, an external filedescribes its global parameters (see Figure 3), its groupparameters, and the local parameters associated to eachcharacter. We express local and group parameters aspercentages of global parameters.

Typeface categories relate to character structure. Type-faces with strongly different structures—for example,different component junctions, different serif types, and

possibly different character round-part parameters (suchas squareness and obliqueness)—belong to differenttypeface categories. Strongly modifying a feature relat-ed to a typeface category changes the character struc-ture, or earmark.9 Modifying global width metricschanges relative weight, contrast, and certain characterfeatures (such as junctions, serifs, and terminals) with-out changing the basic character structure. Therefore,at the conceptual level, we propose two levels of designspaces: one at the structural level (typeface category)and one at the metric, boldness, and contrast level.

Regarding the terminology we use, structure elementrefers to typographic structures, and shape component(or component) refers to a set of well-defined parame-terizable geometric shapes. Metrics generally refers torelative sizes and distances.

The basic shape components we use to implementstructure elements are vertical, horizontal, and diag-onal bars; the half-loop component used for roundparts covering two quadrants; and the sweep compo-nent for connecting between two stems (see Figure 4a)and between a half-loop and a stem (see Figure 4b).We also use the sweep component to synthesize spe-cific curved parts of the characters a, g, and s. We useserifs and ellipse-like components to synthesize ter-minal elements.

We can’t synthesize some characters by simplyassembling shape components such as bars, roundparts, and ellipse-like terminal elements. Therefore,we introduce boundary correction curves, generally inthe form of cubic Bezier spline curves, to produce thedesired character outline shape (see Figure 5a) or tosmooth out the junction between two shape primitives(see Figures 5b and 5c).

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72 May/June 2001

Footserif

heightFootserif

width

Diagonalserif

width(inner)

Stemwidth

Slant serifslope

Horizonal curvewidth

Verticalcurvewidth

Narrow horizonalcurve width

Narrow diagonalstem width

Diagonal stemwidth

Diagonalserifwidth(outer)

Ascender line

x-height line

Base line

Top serif:

3 Global fontparameters.

Vericalbar

Serif

SweepSweep Top

sweep

Bottom sweep

Halfloop

(a) (b)

Verticalbar

Verticalbar

4 Description ofthe specificfeatures of theTimes charac-ters h (a) and b (b).

(b)(a) (c)

5 Application ofboundary cor-rection curvesfor synthesizingthe Times char-acters t (a), a(b), and f (c).

A further operator necessary forassembling character shape compo-nents into characters is the cut oper-ator. It enables cutting a componentinto two parts and keeping one ofthe two parts for assembling thefinal character. The cutline orienta-tion specifies the part we’ll keep (seeFigure 6a).

Describing characters bystructure elements

Traditional Latin letter shapes thatderive from Antiqua and Grotesque(sans serif) typefaces1 can be decomposed into basicstructure elements: vertical stems, round parts (alsocalled curved shape parts or bowls), arches, horizontalbars, diagonal bars, serifs, and terminals (see Figure 1).Conversely, we aim to synthesize traditional letter shapesby coherently assembling such basic structure elements.

The challenge lies in defining parameterizable geo-metric shapes (components) with which we can syn-thesize most instances of structure elements. Wepropose both components for structure elements rep-resenting straight strokes such as stems, horizontal bars,and diagonal bars and components for curved structureelements such as round parts and arches. We use simi-lar components to describe serifs and terminals. To sup-port different typeface categories, we also propose a setof standard parameterizable junctions between shapecomponents.

Parameterizable components for straightstructure elements

We describe vertical stems, horizontal bars, and diag-onal bars with one point located on their centerline,their orientation, and their respective width, which is aglobal font parameter. Vertical stems and diagonal barsare bounded by their respective reference lines (base-line, x-height line, descender line, ascender line, or caps-line). The length of horizontal bars, which are generallydefined as local parameters (for example, in the char-acters f and z) can be given as percentages of other pre-defined parameters such as serif width or letter width(see Figure 7a). Stem, horizontal bar, diagonal bar (seeFigure 7b), and curved element width are importantglobal parameters that we use to synthesize fonts of vari-able weight, contrast, and condensation.

Parameterizable shape primitives for roundstructure elements

Round structure elements are difficult to synthesize.Both external and internal boundaries need to be gen-erated to obtain the desired round-shape part. Let’s firstsee how we can synthesize round-shape parts, or loops,covering one or several quarters of an arc. Such loops,for example, appear in the lower-case characters o, c, e,g, b, d, p, and q. The definition of loops must be flexibleenough to synthesize quite different shapes, such as theround parts of the characters e, o, and b for differenttypeface families (such as Times and Bodoni).

Modeling quadrant arcs. To synthesize loops,let’s analyze the flexibility offered by cubic Bezier splineswith control polygon given by vertices B0B1B2B3 for gen-erating quadrant arcs—that is, curves that have a hori-zontal and a vertical tangent at their endpoints. Wedefine by parameters β1=—B0

—B1/—B0—A and β2=—B3

—B2 /—B3—A

the relative positions of the Bezier polygon control pointsB1 and B2 (Figure 8a, next page). By varying parametersβ1 and β2, we can obtain families of curves whose apex—the point with tangent parallel to baseline B0B3—lieswithin circumscribed triangle B0AB3. Since curvatureconveys the visual information associated with a givenarc, Figure 8b gives curvatures corresponding to the plot-ted Bezier splines. Experience shows that curves havinga high curvature at their end points and low curvatureat their central part (for example, curves with β < 0.4)aren’t visually pleasant.

We analyzed the Bezier splines (quadrant arcs) defin-ing the external and internal contours of the charactero in various font families. In most cases, β1 and β2 valuesare similar, and we can therefore merge them into a sin-

IEEE Computer Graphics and Applications 73

Contour before cutting:

Contour after cutting:

Cutting edge

Cutline

stst

sw

st

sw

l

Cut (st, l ), where cutting line l isderived fromsweep sw

Before cutting: After cutting:

(a) (b)

Cutting edge orientation and contour orientation are coherent

6 (a) Definition and (b) use of thecut operator. Figure 6b uses a cut-line to synthesize character f start-ing with a vertical bar and a topround part made of two sweepsand an ellipse-like terminal.

Narrow diagonalbar width

Diagonalbar width

Horizontalbar width

Verticalstem width

100% ofserif width

142% ofserif width

Serifwidth

(a) (b)

7 Charactersincorporatingvertical stems,horizontal, anddiagonal bars.

gle β value expressing an arc’s squareness. Even in thecase of widely different β1 and β2 values, we can com-pute an intermediate common β value by minimizing afunction giving the difference between the original Bezi-er spline and its approximation with a single β1 = β2 =β value. We minimize the sum of the squares of the dis-tances between points of the new Bezier spline Bnew(u)at parameter values u = {0.1, 0.2, 0.3, 0.4, 0.45, 0.5,0.55, 0.6, 0.7, 0.8, 0.9} and the original spline B(t) toobtain good visual results.

We have computed the single beta values for theexternal and internal contours of character o, for manydifferent typefaces.10 The distance between the originalcontour and the contour synthesized with single betavalues is negligible (less than 1/1000 of the capital let-ter height).

Modeling loops. A loop is a curved character-shapepart covering a single or several quadrants. For example,we can model the Helvetica character o with a single loopcovering four quadrants, the exterior, and respectiveinterior contours defined by four connected quadrantarcs having a common center (see Figure 9a). The Timescharacter o, however, is more complex. Although we canmodel its exterior contour—which looks like an uprightellipse—in the same manner as the Helvetica charactero’s contours, its interior contour looks like an ellipse withan oblique orientation and would require circumscribedquadrants with four different centers to describe it byquadrant arcs (see Figure 9b).

A simpler way to model oblique ellipse-like contours

is by computing their bounding box. The bounding boxcenter represents the center of symmetry of the pseu-doellipse. We can show10 that, within a single quadrant,the line VH connecting the horizontal and vertical tan-gential points is parallel to the line connecting pointsA=(±p,0)and B = (0, ±q) of the ellipse’s bounding-box(see Figure 9c). Therefore, only a single obliquenessparameter η = ∆p/p = ∆q/q giving the relative offset ofthe horizontal and vertical tangential points is neces-sary to define the four quadrant arcs making up anoblique ellipse-like contour.

We model a full loop with exterior and interior ellipse-like contours having upright or oblique orientations.Such a full loop has a single center, which is the centerof symmetry of both the exterior and the interior ellipse-like contours. However, half-loops used for synthesiz-ing the round parts of the characters b, d, p, and q mayhave disjoint centers, one for the external contour andone for the internal contour.

The characterization of loops by two parameters, βfor the squareness and η for the obliqueness of interiorand exterior arcs, offers great design freedom for creat-ing full or partial loops. It also maintains the coherenceacross characters incorporating full loops (o), half-loops(c, b, d, p, or q), and quarter-loops (e).

Modeling sweeps. We can use loops to render theround parts in the letters b, d, p, and q. When lookingat one of these characters, we can see that the curvedpart connecting the loop to the bar shows a particularbehavior. Its parameters aren’t directly related to the

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74 May/June 2001

0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1B0

B0

B3B2

B1

B3A

A

Cur

vatu

re

B1 = β1 A + (1 − β1) B0B2 = β2 A + (1 − β2) B3β = β1 = β2

β = 0.3β = 0.7

β = 0.3

β = 0.5β = 0.7

β = 1

β = 0.1

β = 0.1

β = 1

β1 = 0.25β2 = 0.9

t = 0

t = 1

Parameter t(a) (b)

8 (a) Family ofcubic Beziersplines coveringa quarter of anarc and (b) theirrespectivecurvatures,obtained byvarying parame-ters β1 and β2.

OA

B

p

ql1

l2

∆p

∆q

η = — = —∆pp

∆qq

V

H

(a) (b) (c)

9 Quadrant arcsdescribing the(a) Helveticaand (b) Timescharacter o, (c)modeled bytheir bounding-box and by theirobliqueness η.

loop’s parameters. Similarly, the arches of the charac-ters h, n, m, and u aren’t parts of loops. They’re curvedcharacter parts connecting two vertical stems and there-fore need their own shape description.

To support connecting elements made of curvedparts, we introduce the sweep-shape primitive. Tradi-tionally, sweeps were defined by a pen of a given shapeand orientation sweeping along a centerline describedby a Bezier spline.12,11 Pen width and orientation areoften given at sweep departure and arrival points andmay be interpolated according to the centerline positionparameter t. According to our observations, the sweep-ing pen paradigm isn’t always suitable for generatingLatin typographic characters. Especially if the sweepincorporates a long, flat part and strongly varying pendiameters at sweep departure and arrival positions, theresulting sweep (see Figure 10b) considerably divergesfrom an ideal sweep (see Figure 10a).

We can obtain a higher quality sweep primitive bygenerating for the left and right sweep boundaries Bezi-er splines that strongly resemble the centerline Bezierspline (see Figure 10c). We can achieve this by enforc-ing the same tangent directions at endpoints as the tan-

gent directions of the centerline spline and by using thesame β1 and β2 values. The generated control polygonsfor the left and right boundaries differ from one anoth-er by the size relationships of their respective B0A andAB3 control triangle sides. We can easily obtain elon-gated sweeps by using different β1 and β2 values for thecenterline Bezier control polygon.

The sweep component is useful for establishing theconnections between a loop and a vertical stem andbetween two vertical stems. We also use it to createcurved parts such as the tail of the character g and theround parts of the characters a, which we can’t modelwith quadrant loops.

Parameterizable terminal elementsThe shape of terminal elements such as serifs, bulbs

(see Figure 5b and 5c), and ears (top right part of thecharacter g) greatly determines a typeface’s look. Ter-minal elements at the end of straight stems and bars arestandard serifs, such as foot, top, bar, and diagonal ser-ifs. They’re composed of predefined elements whosemain metrics are given by global parameter values (seeFigure 11). To accommodate the large variety of serif

IEEE Computer Graphics and Applications 75

(a) (b) (c)

Inte

rpol

ated

bypen

orientations10 The sweep component. (a)Original sweep extracted from theTimes character, (b) sweep synthe-sized by linear interpolationbetween sweeping pen departureand arrival orientations, and (c)improved sweep obtained by syn-thesizing its boundary controlpolygons.

Foot serifwidth left

Foot serifwidth right

Footserif

height

Footserif

depth

Verticalstem

Baseline

Bar serifwidthtop

Bar serifwidthbottom

Bar serifheight

Barserif depth

Horizontalbar

Diagonalserif width

(outer)

Diagonalserif width

(inner)

Verticalserif height

Diagonalserif

depth(outer)

Diagonalstem

Baseline

Diagonalserifdepth(inner)

Connectingcurve

(a)

(c)(b)

11 Foot (a), bar(b), and diago-nal (c) serifs andtheir basicparameters.

types,9 we introduce variations in bracket styles, serifend styles and serif faces.

We can explicitly define terminals located at the endof curved strokes with a set of specific shape primitivesthat can comprise pears (ellipse-like elements) andsmall bars, as well as boundary-correction curves.

SerifsSerifs are the most important terminal elements.

Researchers have extensively described the foot and barserifs (see Figures 11a and 11b) in the literature.4,7,13 Half-serifs on each side of a stem or a bar are defined by threebasic parameters: the serif width, the serif height, andthe serif depth. In addition, serifs are characterized bytheir brackets—that is, by the way the serif slab is con-nected to the main stem or bar and by the serif ends (seeFigure 12). The serif face can also vary (see Figure 13).

Thanks to the basic serif parameters, the variationsin brackets, serif ends, and the serif face, most of theserif styles that Rockledge and Perfect9 and Bauermeis-ter14 describe can be synthesized. If required, we can

incorporate additional variations in serif ends and facesinto the serif component model.

The slant serif is designed mainly for top serifs. Wecan also use it to synthesize the shape of beaks and tipsas in the characters z and T (see Figure 14b).

We can describe a slant serif (see Figure 14a) by theintersection of its stem and of a small diagonal bar,called a slab, with orientation θ, by a certain amountof optical correction, by the curve connecting the stemto the slab (curve1), and by the equivalent of the serifface—that is, a curve connecting the slab end to theoptical correction point (curve2). In the case of theTimes character u, the slab is horizontal and doesn’trequire optical correction.

We can also apply the design variations we know fromthe foot and bar serifs—variations in stem to slab con-nection, variations in serif ends and variations in serifface (curve2) to slant serifs.

Terminal elements and dotsFor serif typefaces, terminals of curved strokes such

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76 May/June 2001

sd

sw

(a)

θ

sd

sw

(b)

sd

sw

(c)

sw

(d) Rounded end extension

(e)

(f)

12 Variations inserif brackets:(a) smoothed,(b) angled, (c) straight, and(d) none, andserif ends: (e) butt and (f) rounded.

Concavitydepth

Concavitydepth

Withangle

Withoutangle

Withoutangle

(b) Directly concave(a) Flat serif face (c) Smoothly concave

13 Variations ofthe serif face

θ

OpticalcorrectionSerif

width

Serifheight

curve2

curve1

Serifdepth

(a) (b)

l i j k h bd m u z qT Z E F

Topserif

BeakBeak

Tip

Topserif

Tail

14 (a) Descrip-tion and (b) occurrencesof slant serifs.

as bowls, arches, and tails often incorporate pears andsmall bars (see Figure 15a).

Times characters such as a, f, j, and r have bulbs thatare oblique, ellipse-like terminal elements at the end oftheir round strokes. We can obtain these terminal ele-ments by rotating pseudoellipses made up of quadrantBezier arcs and by smoothing out the junctions betweenellipse-like terminal elements and associated sweeps.Figures 5b, 5c, and 15b show terminal elements madeup of sweeps, pseudoellipses, and boundary-correctioncurves.

The junctions between ellipse-like terminal ele-ments and associated sweeps are smoothed out by aboundary-correcting curve whose departure andarrival tangents are also tangents of the two inter-secting outline segments (see Figure 15b). We give thelength of each of the correcting curve Bezier-control-polygon segments B0B1 and B2B3 as a percentage of aglobal parameter.

Sans-serif typefaces don’t generally incorporate anydecoration at the end of curved strokes. Their curvedstrokes are terminated abruptly, leaving the end squaredor pointed. An angle θ might define the orientation ofthe terminal’s end segment (see Figure 15a).

We can also model the dots on top of the characters iand j as ellipse-like elements with appropriate β valuesdefining their squareness.

Junctions between charactercomponents

We aim to synthesize traditional Latin charactersusing bar components for straight structure elementsand loop and sweep components for round structureelements. The way components are interconnectedgreatly influences a typeface’s design. We first definefeatures enabling design variations for the junctionsbetween round parts and stems (vertical bars). Then,

we introduce the parameters and geometric construc-tions enabling the synthesis of design variations forjunctions between diagonal bars and other bars.

Junctions between vertical stems and sweepsThe junctions between vertical stems and sweeps

define the interconnection between straight- and round-character structure elements. Generally, junctions areeither angled or smooth. Figure 16 shows angled andsmooth junctions for the characters h and b. The junc-tions in the character h are representative of the junc-tions in the characters n, m, and u. The angled andsmooth junctions in the character b are representativeof the junctions in the characters p, q, and d.

The sweep at the junction between straight and round-character structure elements determines the junction’svisual appearance. Besides being smooth or angled, thejunction depth parameter defines, as a proportion of thecharacter height, the vertical distance between the cor-responding horizontal reference line and the junction.The location of the control triangle’s vertex A of thesweep’s centerline Bezier spline also defines the sweep’sshape. As Figure 17a shows, we give vertex A’s horizon-tal position as a percentage of the horizontal distancebetween centerline Bezier start and end points.

The control triangle vertex A’s junction depth and rel-ative position define the connecting sweep’s shape. Byconsidering the control triangle vertex A’s junction depthand relative position as group parameters (or as valid

IEEE Computer Graphics and Applications 77

Boundarycorrecting

curve

B0B1

B2 B3

(a) (b)

θ

θ

15 (a) Repre-sentation ofcurved stroketerminals and(b) junctionbetween ellipse-like terminalelement and itsassociatedsweepcomponent.

Times Geneva Times Bodoni

AngledSmooth

16 Junctionsbetween verti-cal bar andsweep

(a) (b)

Ax-height

Junc

tion

dept

h

A

Junc

tion

dept

h

Base

x-height

Baseh17 Defining the shape of the con-necting sweep by the junctiondepth and the relative horizontalposition of centerline Bezier splinecontrol triangle vertex A.

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78 May/June 2001

Times Romanangled junction

Coronasmooth junction,thick serif slab

18 Synthesis ofcoherent Timesand Coronacharacters.

Times Flatderived fromTimes Roman,angled junction

Times Roundderived fromTimes Roman,smooth junction

19 Coherentshape modifica-tions across agroup of char-acters (Times).

s1 s1s2

l 1

l1

l 2

cut (s1, l 2)cut (s2, l 1)

Miter limit

Cut (s1, l 1)the position ofthe cut line l1is controlledby the localparameter miterlimit.

(a) (b)

20 Synthesiz-ing bar junc-tions ofcharacters v (a)and z (b).

s2

s3

s1s1

s2

s3

I1

I1 I1

I2

I2

I3

cut (s2, I1)cut (s3, I2)

After cutting:Before cutting: After cutting:Before cutting:

s1

s2

s3

s1

s2

s3

cut (s2, I3)cut (s3, I2)

s1

s2 s2́

s1

s2́

s2s2s2́ = duplicate (s2)cut (s2, I1)cut (s2, I1́ )translate (s2́ , v).

v

After correction:Before correction: Correction:

(a) (b)

(c )

21 Bar intersec-tions for thecharacters k and x.

parameters for the group of characters a, h, m, n, u, b, d,p, and q), we can generate coherent character shapemodifications across these characters. Figure 18 showscoherent Times Roman and Corona characters that wereresynthesized with components. Figure 19 shows coher-ent variants of Times Roman, generated by modifyingthe junction depth parameters. In the same way thatTimes Roman and Corona belong to different typefacecategories, our experimental Times Flat and TimesRound also belong to different typeface categories. Theyrepresent an attempt to explore a small part of the tra-ditional typeface design space.

Junctions between diagonal bars and other barsA bar is given by two points of its centerline and by its

width, which is generally a global parameter (such asVerticalBarWidth, NarrowVerticalBarWidth, and so on).To synthesize characters such as v and w, we must inter-sect two diagonal bars and appropriately reshape themwith cutlines (see Figure 20a). To synthesize the char-acter z, an additional relative parameter defines themiter junction between the diagonal and the horizon-tal bar (see Figure 20b).

Character k comprises either a single or a double junc-tion between its vertical bar and its two diagonal bars.As Figure 21a and 21b shows, we apply the cutline oper-ator differently if a single or a double junction is present.

Character x consists of the intersection of two diago-nal bars. Type creators15 know that we need an opticalcorrection: the departure of the lower part of the nar-row diagonal is displaced horizontally to the left by 15percent of its horizontal width (see Figure 21c).

Synthesis of characters withparameterizable elements

The components we described in the previous sec-tions are the basic building blocks for synthesizing char-acters. To synthesize specific characters with completelydefined metrics and shapes, the character designerneeds to supply global, group, and local parameters.

For example, consider the character b (see Figure 2b).A global lower-case stem width parameter defines theascender stem. Global parameters specifying the seriftype and the serif’s main metrics define the top serif,and a local parameter defines the spur. The round partcomprises a half-loop component and two connecting

sweeps, defined by group and local parameters.We’ll now describe how we synthesize characters

from their parameterized component description. Thefont’s horizontal reference lines (baseline, x-height,caps-height, ascender and descender lines, as well asthe corresponding optical correction lines) define exact-ly the placement of the character’s components. Thecharacter synthesizing method places the character’smain parts (the stem and half-loop) horizontally apartaccording to global spacing parameters. Secondaryparts such as serifs or connecting arches are placed soas to correctly connect to the main parts.

The font creator defines global spacing parametersfor the standard round-letter width, for the horizontalspacing between vertical stem and half-loop (the spac-ing between the stem and round parts of character b),and for the horizontal spacing of two vertical stems (seeFigure 22). These global spacing parameters are a pro-portion of the standard round-letter width parameter.

Figure 23 (next page) illustrates how the charactersynthesizing software computes the character b. We syn-thesize its vertical bar using the standard stem width andposition it at an arbitrary horizontal position. The half-loop’s center Oext is vertically in the middle of its respec-tive reference lines (xheight_o and base_o). We computethe vertical position of center Oint as a function of the ref-erence lines and the respective horizontal curve partwidths (w2 and w3). The centers’ horizontal locations aregiven by the vertical stem to half-loop spacing (dx) andby group parameters p1 and p2 specifying their relativehorizontal positions between stem midline and half-loopmidline. The half-loop’s internal and external arcs aredefined by their center positions, bounding boxes,obliqueness parameters ηint and ηext, and squarenessparameters βint and βext (according to global parameters).

After placing the half-loop component, we can placethe angled sweep components connecting the half-loopcomponent to the vertical bar. Their starting sweep posi-tion and orientation are given by the half-loop compo-nent’s extremities. The ending orientation of sweep C5

is vertical, and the junction depth group parameter p5

defines its position. The ending points of sweep C4 aregiven by group parameters p3 and p4, (parameters validfor the characters b, d, p, and q). Slant serif componentC2 is defined by the global parameters defining slant ser-ifs and is inserted at the top of the vertical bar. Compo-

IEEE Computer Graphics and Applications 79

o n b mdx_o =standard roundletter width

dx_b =standard stem toround part spacing (71% dx_o)

dx_n =standard stem to stem spacing(60.5% dx_o)

dx_n dx_n

dx_m = 200% dx_n

22 Horizontalspacing ofcharacter struc-ture elements(values forTimes Roman).

nent C3 (spur) is described by a slant serif componentwith zero width and zero height.

Font description parameters andimplementation issues

Flexible character shape descriptions, which we canmodify to create derived versions with varying width,weight, and contrast, need to incorporate their most sig-nificant features as percentages of modifiable global fontparameters. For example, the round-letter width (RLW)defined as the horizontal width of the letter o is a glob-al parameter used as a reference to describe the basicspacing of stems and curved elements (half-loops) of alllower-case characters of a font (see Figure 22).

The global width parameters specify the respectivethicknesses of vertical stems, horizontal bars, diagonalbars, vertical curved parts, and horizontal curved parts.We also use proportions of their width to describe thestarting and ending width of associated sweep primi-tives—for example, width w4 of the sweep componentc5 in the letters b (see Figure 23) and n (see Figure 24b).Since width parameters distinguish between the thick-

nesses of vertical, horizontal, and diagonal strokes aswell as between thin and thick strokes (Figure 7b), theyboth govern a character’s weight and the amount of con-trast incorporated into the font.

The global serif parameters govern the shapes of theserifs by specifying the serif type given by the selectedvariation in bracket, serif end, and serif face and by spec-ifying their width, height, depth, and slant angle (seeFigures 12 through 14).

As further examples, let’s look at the definition of theTimes characters o and n in Figure 24. Character o does-n’t need any local parameters. We can completely syn-thesize it using global font parameter information.Synthesizing the character n requires placing the first stemat an arbitrary starting position and placing the secondstem according to the given stem-to-stem spacing value.The serifs are defined according to global font parame-ters. The two sweep components are defined by global andgroup parameters. Figure 25 shows lower-case TimesRoman characters recreated with components. Figure 26shows the components and resulting characters for a fewrepresentative upper-case Times Roman characters.

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80 May/June 2001

x-height

Base

Round letter width

Opticalcorrection

Vertical curvewidth

Vertical curvewidth

Narrowhorizontalcurvewidth

x-height

Base

Opticalcorrection

Serifheight

Serifheight

Serifdepth

Stemwidth

Stemwidth

Serifwidth

Serifwidth

58%72%

72% 76%ArchdepthJunction

width

Horizontalcurvewidth

(a) (b)

Standard stemto stem spacing

(60.5% RLW)

Narrowhorizontalcurvewidth

24 Parametersneeded tosynthesize theTimes Romancharacters o (a)and n (b).

c1

c2

c0

c4

c5

dx

Ascender

x-height

Basew2

w0 w1

w3

w4

Ascender_o

x-height_o

Base_o

p1

OextOint

p7

p5

p4p3

p2

p6c3θ

Components:c0 : stem, c1 : half-loop covering quadrants IV, Ic2 : slant serif, c3 : spur (slant serif)c4, c5 : connecting sweeps

Global parameters:dx : standard vertical stem to half-loop spacingw0 : the standard vertical stem widthw1 : the standard vertical curved part widthw2 : the standard narrow horizontal curved part widthw3 : the standard horizontal curved part widthw4 : width of the junction, often equal to w2η1, η2: loop extreme corrections, external and internal

Group parameters (the group of b, d, p and q):p1 : relative h-position of loop external centerp2 : relative h-position of loop internal centerp3, p4 : relative h-position of the lower junction (c4)p5 : relative depth of the upper junction (c5)p6 : relative control point position of the sweep c4p7 : relative control point position of the sweep c5

Local parameter:θ : spur angle

23 Synthesis ofthe character bwith its parame-terizedelements.

Component-based font descriptions require global,group, and local parameters. Table 1 shows how manyparameters we need for our versions of resynthesizedlower-case Times, Helvetica, and Bodoni characters.Bodoni requires fewer parameters, because all its serifsare slab serifs (uniform height). The sans-serif font Hel-vetica further reduces the number of requiredparameters.

A 26 lower-case character font with the complexity ofTimes requires approximately 540 parameters, or 1,080bytes. Comparatively, TrueType requires approximate-ly 1,500 bytes for the global parameters and a mean of154 bytes per character for storing the outlines of lower-case characters. The grid-fitting instructions needed byTrueType for character generation at medium and lowresolution require an additional 385 bytes per charac-ter. In contrast, component-based character descriptionsalready include all information about their structure(stems, half-loops, bars, connecting sweeps, and serifs).In addition, component-based fonts let us generatederived fonts (such as condensed and semibold) bychanging the values of a few global parameters. A singlecomponent-based font can therefore replace several tra-ditional outline fonts. Thus, we expect component-based fonts to require an order of magnitude less storagespace than traditional outline fonts.

With our current software, we can synthesize char-acters by rasterizing the partly overlapping componentsand by excluding components that aren’t part of thecharacter, by using the cut operation (see Figure 6).Also, we can recover the full character outline by usinga variant of Vatti’s algorithm16 to assemble componentsmade up of straight and curved outline segments.

Synthesizing derived characters byvarying global font parameters

Here, we describe experiments showing the effectswe can obtain by varying some global font parameters.Increasing the vertical stem width and vertical curvewidth parameters and decreasing the serif width para-meters increases a font’s weight. Figure 27a (next page)shows the alphabet at different sizes, at normal weight,and at 125 percent and 150 percent weights.

High-quality horizontally condensed fonts are need-ed where space is scarce—in telephone books for exam-ple. Furthermore, condensed fonts may offer increasedflexibility for information presentation at display reso-lution—for example on Web pages.17 Reducing the char-acter width without reducing in the same proportionthe thickness of the strokes generates high-quality hor-izontally condensed fonts. Because individual charac-ter width is a function of the round letter width,

reducing the global round letter width parameter’s sizeensures the width reduction of the font’s characters. Fig-ure 27b shows text condensed to 90 percent and 80 per-cent. Condensation down to 90 percent is barelyperceptible and enables the generation of high-qualitycharacters. Eighty percent condensation considerablydistorts the original character shapes.

IEEE Computer Graphics and Applications 81

25 Lower-caseTimes Romancharactersrecreated withcomponents.

26 Resynthe-sized TimesRoman capitalletters

Table 1. Number of parameters for a font comprising the lower-case character a to z.

Times Bodoni Helvetica

Number of global parameters 110 98 63

Number of group parameters 31 31 31

Mean number of localparameters per character 15.3 16.0 14.0

Optically scaled fonts are relatively fatter and largerat small sizes.5 Their x-height and character width areslightly larger than corresponding values obtained byplain scaling. In the following optical scaling example,we use optical scaling correction factors to generatecharacters between 5 and 12 points. We experimental-ly determine maximum correction factors (maxFact) forthe various parameters (letter, stem, bar, and curvedelement widths) for the 5 point character size. Between5 and 12 points, these correction factors are interpolat-ed by the parabola giving the maximum correction at 5points and a zero correction factor at 12 points:

At 5 points, the maximum correction factor for theround letter width and for the stem-to-stem and stem-to-curved-element part spacing is between 106 and 110 per-cent. The stem, bar, and curved element width have amaximum correction factor of 125 percent. The narrowdiagonal bar, narrow horizontal bar, and narrow curvedelement width have a maximal correction factor of 150percent. Figure 28a shows characters printed at high res-

olution, with and without optical scaling. Clearly, opticalscaling improves legibility. Figure 28b shows the corre-sponding optically scaled character shapes at large sizes.

Inspired by the designs of Gerrit Nordzij, a Dutch typedesigner,18 we tried to vary the few parameters deter-mining the character e’s shape to generate deriveddesigns along three different dimensions (see Figure29). The first dimension is the character’s weight, orboldness. All horizontal and vertical width parametersare equally influenced by the boldness parameter.

The second dimension is contrast. Increasing the con-trast requires reducing the horizontal curve width para-meters. The third dimension is stress obliqueness.Characters with oblique stress derive from pen-basedmanuscript writing and were created soon after theinvention of moveable metal type—for example, thetypeface Jenson, created in 1470. Typeface designsevolved from oblique stress to vertical stress characters.Vertical stress characters became fashionable with thedesigns of the Bodoni and Didot typefaces at the end ofthe 18th century. Increasing stress obliqueness requiresincreasing the obliqueness parameter of the internalellipse-like arcs. Increased stress obliqueness alsorequires a slight increase of the horizontal curve-widthparameters determining the stroke width at the bottomof the character. Figure 30 (next page) shows the para-

corrFactor ptSize

maxFact

pt ptptSize pt pt ptSize pt

( ) =

−( )−( ) ≤ ≤

5 1212 5 12

2

2;

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82 May/June 2001

125% weight: 90% condensation:

150% weight: 80% condensation:

27 Lower-casealphabet atdifferent weight (a) andcondensationfactors (b).

(a) (b)

Opticalscaling

5 pt8 pt

12 pt

Plainscaling

5 pt8 pt

12 pt

5 pt

8 pt

12 pt

(a) (b)

28 Comparisonof optical scalingand plain scal-ing. (a) Charac-ters printed athigh resolution,with (top) andwithout (bot-tom) opticalscaling. (b)Optically scaledcharacter shapesat large sizes.

meters determining the character shapes and gives theinterpolation rules for computing these parametersfrom input parameters weight, contrast, and stressobliqueness. Figure 29 shows a volumic representationof the designs obtained by varying these three inputparameters.

Generating derived typefaces by parameter modifica-tions is a high-level process, which considerably differsfrom interpolation between character outline controlpoints.8 Direct interpolation between outline controlpoints requires the explicit design of character masters at

the extremities of the design range. Interpolationbetween character outlines may lead to inconsistenciesin stroke width and to tangential discontinuities at thejunctions between curved outline parts. On the otherhand, varying the character’s global and local parame-ters according to different design axes such as weight,contrast, and stress obliqueness is a more robust process,since loop parameters β and η ensure the coherence ofeach of the generated loops or half-loops. At the jointsbetween loops and sweeps and between consecutivesweeps, tangential continuity is ensured by construction.

IEEE Computer Graphics and Applications 83

High

Contrast

Low

Low

Weight

High

Upright

Style

Oblique

29 Variations ofthe character e’sweight, con-trast, andobliqueness.

ConclusionsUsing geometric properties as a means of enforcing

coherence across different characters of a typeface hasbeen a dream since the Renaissance. A fundamentalquestion raised by Donald Knuth and Douglas Hofs-taeder19 is whether a significant part of the design spacecan be explored by turning a few knobs.

A first requirement along that path is to reduce thenumber of parameters governing the shapes of typo-graphic characters. We’ve tried to achieve this by defin-ing loops and half-loops with the width, squareness, andobliqueness parameters and by defining categories ofterminal elements, each described with only a fewparameters. Furthermore, we’ve developed a specificgeometric construction that provides arches that havethe shape required by traditional typefaces.

Our approach is validated by the fact that we’ve beenable to recreate existing traditional Latin fonts such asTimes Roman, Helvetica, and Bodoni (see http://diwww.epfl.ch/w3lsp/research/typography/compofont/). Theexperiments we’ve made show that we can generate inter-esting derived fonts from existing component-based fontdescriptions. However, further exploration in collabora-tion with type designers is required to verify the aesthet-ic quality of the generated derived font designs.

Fonts made of shape components are flexible parame-terizable designs, which we can easily adapt to variousdisplay and printing conditions (such as condensed fontwhen lacking display space, high-quality optical scaling,adaptation of fonts to existing character metrics). Besideapplications related to typeface design, fonts based onparameterizable components may be used in portabledevices where memory is scarce. A single parameteriz-able design and its variations may allow enough flexibil-ity for providing both high-quality antialiased fonts at lowresolution and typefaces for high-resolution printing. �

AcknowledgmentWe thank André Gürtler, well-known type designer and

professor of typography at the Basel School of Design.

Thanks to his criticism and encouraging remarks, we wereable to significantly improve the quality of the characterswe resynthesized using parameterizable components.

References1. J. Tschichold, Treasurey of Alphabets and Lettering, W.W.

Norton & Company, New York, 1995.2. R. Southall, “Character Description Techniques in Type

Manufacture,” Raster Imaging and Digital Typography II, R.Morris and J. André, eds., Cambridge Univ. Press, Cam-bridge, Mass., 1991, pp. 16-27.

3. D. Adams, “abcdefg, A Better Constraint Driven Environ-ment for Font Generation,” Raster Imaging and DigitalTypography, J. André and R.D. Hersch, eds., CambridgeUniv. Press, Cambridge, Mass., 1989, pp. 54-70.

4. P. Karow, Font Technology, Description, and Tools, Springer-Verlag, New York, 1994.

5. J. André and I. Vatton, “Dynamic Optical Scaling and Vari-able-Sized Characters,” Electronic Publishing- Origination,Dissemination, and Design, vol. 7, no. 4, Dec. 1994, pp. 231-250.

6. B. Zalik, “Font Design with Incompletely Constrained FontFeatures,” Proc. Third Pacific Conf. Computer Graphics andApplications (Pacific Graphics 95), S.Y. Shin and T.L. Kunii,eds., World Scientific, Singapore, 1995, pp. 512-526

7. A. Shamir and A. Rappaport, “Feature-Based Design ofFonts Using Constraints,” Electronic Publishing, ArtisticImaging, and Digital Topography, R.D. Hersch, J. André,and H. Brown, eds., LNCS 1375, Springer-Verlag, NewYork, 1998, pp. 93-108.

8. J. Seybold, “Adobe’s MultiMasters Technology: Break-through in Type Aesthetics,” Seybold Report on Desktop Pub-lishing, vol. 7, no. 5, 1991, pp. 3-7.

9. G. Rockledge and C. Perfect, Rockledge’s International TypeFinder: The Essential Handbook of Typeface Recognition andSelection, Rizzoli Int’l Publications, New York, 1991.

10. C. Hu, Synthesis of Parameterizable Fonts by Shape Compo-nents, EPFL thesis no 1905, 1998, http://diwww.epfl.ch/

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84 May/June 2001

1. CH1 = iplt [iplt [normalCH1, maxCH1, boldness], minCH1, contrast]2. CH2 = iplt [iplt [iplt [normalCH2, maxCH2, boldness], minCH2, contrast], iplt [normalCH2, maxCH2, boldness], obliqueStress * 0.6]3. CV1 = iplt [minCV1, maxCV1, boldness]4. CV2 = iplt [minCV2, maxCV2, boldness]5. SH = iplt [iplt [normalSH, maxSH, boldness], minSH, contrast]6. ST = iplt [iplt [minCV2, maxST, boldness], minST, contrast]7. EBar = iplt [maxEBar, minEBar, boldness]8. ETail = iplt [iplt [minETail, maxETail, boldness], minETail, contrast]9. ηext = minh = 0; hint = iplt [minh, maxh, obliqueStress]10. βext = normalb; bint = iplt [iplt [normalb, maxb, (contrast + boldness) / 2], normalb, obliqueStress]

E xplanations:1: Boldness increases CH1 value, contrast decreases CH1 value.2: Boldness increases CH2 value, contrast decreases CH2 value,

stress obliqueness increases partly CH2 value.3, 4: Boldness increases CV1 and CV2 values.5, 6: Boldness increases, respectively contrast decreases SH and ST values.7: Boldness decreases EBar values.8: Boldness increases, respectively contrast decreases ETail value.9: Stress obliqueness increases obliqueness h of interior loops.10: Contrast and boldness increase, respectively obliqueness reduces squareness b.

CH1

CH2

CV2

CV1

SH

ST

ETail

EBar

iplt (a, b, percentage) = a * (1 - percentage) + b * percentage.

Definition of interpolation:

30 Parametersdetermining thecharacter e’sshape.

w3lsp/publications.11. D. Knuth, The Metafont Book, Addison-Wesley, Reading,

Mass., 1986.12. U. Schneider, “An Object-Oriented Model for the Hierar-

chical Composition of Letterforms in Computer-AidedTypeface Design,” Electronic Publishing, Artistic Imagingand Digital Typography, R.D. Hersch, J. André, and H.Brown, eds., LNCS 1375, Springer-Verlag, New York, 1998,pp. 109-125.

13. D. Knuth, Computer Modern Typefaces (Volume E of Com-puters and Typesetting), Addison-Wesley, Reading, Mass.,1986.

14. B. Bauermeister, A Manual of Comparative Typography, ThePANOSE System, Van Nostrand Reinhold Company, NewYork, 1987

15. M. Jamra, “Some Elements of Proportion and OpticalImage Support in a Typeface,” Visual & Technical Aspects ofType, R.D. Hersch, ed., Cambridge Univ. Press, Cambridge,Mass., pp. 47-55.

16. B.R. Vatti, “A Generic Solution to Polygon Clipping,”Comm. ACM, vol. 35, no. 7, pp. 56-63.

17. R.A. Morris, R.D. Hersch, and A. Coimbra, “Legibility ofCondensed Perceptually-Tuned Grayscale Fonts,” ElectronicPublishing, Artistic Imaging and Digital Typography, R.D.Hersch, J. André, and H. Brown, eds., LNCS 1375, Springer-Verlag, New York, 1998, pp. 281-291.

18. G. Nordzij, “The Shape of the Stroke,” Raster Imaging andDigital Typography II, R. Morris and J. André, eds., Cam-bridge Univ. Press, Cambridge, Mass., 1991, pp. 34-42.

19. D. Hofstaedter, “Metafont, Metamathematics, and Meta-physics: Comments on Donald Knuth’s Article ‘The Con-cept of a Meta-Font,’” Metamagical Themas, Penguin Books,London, 1985, pp. 260-296.

Changyuan Hu develops 3D Webauthoring software in Montreal,Canada. His research interests arefocused on computer graphics anddigital typography. He graduatedfrom the Department of ComputerScience, Nanjing University and

received his PhD from Ecole Polytechnique Fédérale deLausanne.

Roger D. Hersch is a professor ofcomputer science and the head of thePeripheral Systems Laboratory at theEcole Polytechnique Fédérale de Lau-sanne. He was the conference chair-man of the International Conferenceon Raster Imaging and Digital

Typography 1998. He also directs the Visible Human WebServer project, which offers advanced visualization ser-vices for exploring the Visible Human Male and Femaledatasets (see http://visiblehuman.epfl.ch). He received hisengineering degree ETH Zurich and PhD from EPFL.

Readers may contact Hersch at the Computer ScienceDept., EPFL, CH-1015 Lausanne, Switzerland, rd.hersch@epfl.ch, http://diwww.epfl.ch/w3lsp.

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