14 Tables, Formulæ, and Graphics

Índice

Many documents, both historical and contemporary, include not only text, but also graphics, artwork, and other images. Although some types of images can be represented directly with markup, it is more common practice to include such information by using a reference to an external entity (typically a URL) encoded in a suitable graphical notation.

In addition to graphic images, documents often contain material presented in graphical or tabular format. In such materials, details of layout and presentation may also be of comparatively greater significance or complexity than they are for running text. Indeed, it may often be difficult to make a clear distinction between details relating purely to the rendition of information and those relating to the information itself.

Finally, documents may contain mathematical formulæ or expressions in other formulaic notations, for which no notation is defined in these Guidelines.

These areas (graphics, tabular material, and mathematical or other formulæ) have in common that they have received considerable attention from many other standards bodies or similar professional groups. In part because of this, they may frequently be most conveniently encoded and processed using some notation not defined by these Guidelines. For these reasons, and others, we consider tables, formulæ, and graphics together in this chapter.

As with text markup in general, many incompatible formats have been proposed for the representation of graphics, formulæ, and tables in electronic form. Unfortunately, no single format as effective as XML in the domain of text has yet emerged for their interchange, to some extent because of the difficulty of representing the information these data formats convey independently of the way it is rendered.

The module defined by this chapter defines special purpose ‘container’ elements that can be used to encapsulate occurrences of such data within a TEI-conformant document in a portable way. Specific recommendations for the encoding of tables are provided in section 14.1 Tables and recommendations for mathematical or other formulæ in section 14.2 Formulæ and Mathematical Expressions. Specific recommendations for the encoding of graphic figures may be found in section 14.3 Specific Elements for Graphic Images. The rest of the chapter is devoted to general problems of encoding graphic information.

There is at the time of writing no consensus on formats for graphical images, and such formats vary in many ways. We therefore provide (in section 14.4 Overview of Basic Graphics Concepts) a brief discussion of the ways in which images may be represented, and (in section 14.5 Graphic Image Formats) a list of formal names for those representations most popular at this time. Each one includes a very brief description. These Guidelines recommend a few particular representations as being the most widely supported and understood.

14.1 Tables

A table is the least ‘graphic’ of the elements discussed in this chapter. Almost any text structure can be presented as a series of rows and columns: one might, for example, choose to show a glossary or other form of list in tabular form, without necessarily regarding it as a table. In such cases, the global rend attribute is an appropriate way of indicating that some element is being presented in tabular format, for example by using an appropriate display property in CSS. When tabular presentation is regarded as of less intrinsic importance, it is correspondingly simpler to encode descriptive or functional information about the contents of the table, for example to identify one cell as containing a name and another as containing a date, though the two methods may be combined.

When, however, particular elements are required to encode the tabular arrangement itself, then one or other of the various ‘table schemas’ now available may be preferable. The schemas in common use generally view a table as a special text element, made up of row elements, themselves composed of cells. Table cells generally appear in row-major order, with the first row from left to right, then the second row, and so on. Details of appearance such as column widths, border lines, and alignment are generally encoded by numerous attributes. Beyond this, however, such schemas differ greatly. This section begins by describing a table schema of this kind; a brief summary of some other widely available table schemas is also provided in section 14.1.2 Other Table Schemas.

14.1.1 TEI Tables

For encoding tables of low to moderate complexity, these Guidelines provide the following special purpose elements:
  • table contiene texto dispuedto en forma de tabla, con filas y columnas.
    rows indica el número de filas en una tabla.
    cols (columnas) indica el número de columnas por cada fila de la tabla.
  • row contiene una fila de la tabla.
  • cell contiene una celda de una tabla.

The table element is defined as a member of the class inter; it may therefore appear both within other components (such as paragraphs), or between them, provided that the module defined in this chapter has been enabled, as described at the beginning of this chapter.

It is to a large extent arbitrary whether a table should be regarded as a series of rows or as a series of columns. For compatibility with currently available systems, however, these Guidelines require a row-by-row description of a table. It is also possible to describe a table simply as a series of cells; this may be useful for tabular material which is not presented as a simple matrix.

The attributes rows and cols may be used to indicate the size of a table, or to indicate that a particular cell or row of a table spans more than one row or column. For both tables and cells, rows and columns are always given in top-to-bottom, left-to-right order, although formatting properties such as those provided by CSS may be used to specify that they should be displayed differently. These Guidelines do not require that the size of a table be specified; for most formatting and many other applications, it will be necessary to process the whole table in two passes in any case.

Where cells span more than one column or row, the encoder must determine whether this is a purely presentational effect (in which case the rend attribute may be more appropriate), whether the part of the table affected would be better treated as a nested table, or whether to use the spanning attributes listed above.

The role attribute may be used to categorize a single cell, or set a default for all the cells in a given row. The present Guidelines distinguish the roles of label and data only, but the encoder may define other roles, such as ‘derived’, ‘numeric’, etc., as appropriate.

These three attributes are provided by the attribute class att.tableDecoration of which both cell and row are members; see further 1.3.1 Attribute Classes.

The following simple example demonstrates how the data presented as a labelled list in section 3.7 Lists might be represented by an encoder wishing to preserve its original appearance as a table:
<table rend="boxed" rows="2" cols="2">
 <head rend="it">Report of the conduct and progress
   of Ernest Pontifex. Upper Vth form — half
   term ending Midsummer 1851</head>
 <row>
  <cell role="label">Classics</cell>
  <cell>Idle listless and unimproving</cell>
 </row>
 <row>
  <cell role="label">Mathematics</cell>
  <cell>ditto</cell>
 </row>
 <row>
  <cell role="label">Divinity</cell>
  <cell>ditto</cell>
 </row>
 <row>
  <cell role="label">Conduct in house</cell>
  <cell>Orderly</cell>
 </row>
 <row>
  <cell role="label">General conduct</cell>
  <cell>Not satisfactory, on
     account of his great unpunctuality and inattention to
     duties</cell>
 </row>
</table>

Note that this encoding makes no attempt to represent the full significance of the ‘ditto’ cells above; these might be regarded as simple links between the cells containing them and that to which they refer, or as virtual copies of it. For ways of representing either interpretation, see chapter 16 Linking, Segmentation, and Alignment.

The following example demonstrates how a simple statistical table may be represented using this scheme:
<table rows="4" cols="4">
 <head>Poor Man's Lodgings in Norfolk (Mayhew, 1843)</head>
 <row role="label">
  <cell/>
  <cell>Dossing Cribs or Lodging Houses</cell>
  <cell>Beds</cell>
  <cell>Needys or Nightly Lodgers</cell>
 </row>
 <row>
  <cell role="label">Bury St Edmund's</cell>
  <cell>5</cell>
  <cell>8</cell>
  <cell>128</cell>
 </row>
 <row>
  <cell role="label">Thetford</cell>
  <cell>3</cell>
  <cell>6</cell>
  <cell>36</cell>
 </row>
 <row>
  <cell role="label">Attleboro'</cell>
  <cell>3</cell>
  <cell>5</cell>
  <cell>20</cell>
 </row>
 <row>
  <cell role="label">Wymondham</cell>
  <cell>1</cell>
  <cell>11</cell>
  <cell>22</cell>
 </row>
</table>

Note the use of a blank cell in the first row to ensure that the column labels are correctly aligned with the data. Again, this encoding does not explicitly represent the alignment between column and row labels and the data to which they apply. Where the primary emphasis of an encoding is on the semantic content of a table, a more explicit mechanism for the representation of structured information such as that provided by the feature structure mechanism described in chapter 18 Feature Structures may be preferred. Alternatively, the general purpose linkage and alignment mechanisms described in chapter 16 Linking, Segmentation, and Alignment may also be applied to individual cells of a table.

The content of a table cell need not be simply character data. It may also contain any sequence of the phrase-level elements described in chapter 3 Elements Available in All TEI Documents, thus allowing for the encoding of potentially more useful semantic information, as in the following example, where the fact that one cell contains a number and the other contains a place name has been explicitly recorded:
<table>
 <head>US State populations, 1990</head>
 <row>
  <cell>
   <name>Wyoming</name>
  </cell>
  <cell>
   <num>453,588</num>
  </cell>
 </row>
 <row>
  <cell>
   <name>Alaska</name>
  </cell>
  <cell>
   <num>550,043</num>
  </cell>
 </row>
 <row>
  <cell>
   <name>Montana</name>
  </cell>
  <cell>
   <num>799,065</num>
  </cell>
 </row>
 <row>
  <cell>
   <name>Rhode Island</name>
  </cell>
  <cell>
   <num>1,003,464</num>
  </cell>
 </row>
</table>
The role attribute provides a slightly less verbose means of conveying the same information:
<table>
 <head>US State populations, 1990</head>
 <row>
  <cell role="statename">Wyoming </cell>
  <cell role="pop">453,588 </cell>
 </row>
 <row>
  <cell role="statename">Alaska </cell>
  <cell role="pop">550,043 </cell>
 </row>
 <row>
  <cell role="statename">Montana </cell>
  <cell role="pop">799,065 </cell>
 </row>
 <row>
  <cell role="statename">Rhode Island</cell>
  <cell role="pop">1,003,464</cell>
 </row>
</table>

The use of semantically marked elements within a cell enables the encoder to convey something about the nature and significance of the information, rather than merely suggesting how to display it in rows and columns.

14.1.2 Other Table Schemas

Many authoring systems include built-in support for their own or for public table schemas. These provide an enhanced user interface and good formatting capabilities, but are often product-specific, despite their use of a XML markup language.

The DTD developed by the Association of American Publishers (AAP) and standardized in ANSI Z39.59 provided a very simple encoding for correspondingly simple tables. This has been further developed, together with the table DTD documented in ISO Technical Report 9537, and now forms part of ISO 12083. The TEI table model described above has functionality very similar to that defined by ISO 12083.

For more complex tables, the most effective publicly-available DTD is probably that developed by the US Department of Defense CALS project. This supports vertical and horizontal spanning and various kinds of text rotation and justification within cells and is also directly supported by a number of existing SGML software systems.

The CALS table model is much too complex to describe fully here; for historical background see http://www.hbingham.com/technical/tables/calstbhs.htm; for more recent simplifications of it and current implementations see http://www.oasis-open.org/specs/tablemodels.php. As with any other XML vocabulary, the XML version of the CALS model may readily be included in a TEI schema, using the techniques described in 23.2 Personalization and Customization.

The XHTML table model (XHTML™ 1.0 The Extensible HyperText Markup Language (Second Edition) (2000)) is based on the HTML table model (Ragget et al. (eds.) (1999)). Both models support arrangement of arbitrary data into rows and columns of cells. Table rows and columns may be grouped to convey additional structural information and may be rendered by user agents in ways that emphasize this structure. Support for incremental rendering of tables and for rendering on ‘non-visual’ user agents is also available. Special elements and attributes are provided to associate metadata with tables. They indicate the table's purpose, or are for the benefit of people using speech or Braille-based user agents. Tables are not recommended for use purely as a means to lay out document content, as this leads to many accessibility problems (see further http://www.w3.org/TR/WCAG10-HTML-TECHS/#tables). Stylesheets provide a far more effective means of controlling layout and other visual characteristics in both HTML and XML documents.

14.2 Formulæ and Mathematical Expressions

Mathematical and chemical formulæ pose problems similar to those posed by tables in that rendition may be of great significance and hard to disentangle from content. They also require access to a wide range of special characters, for most of which standard entity names already exist in the documented ISO entity sets (see further chapters vi. Languages and Character Sets and 5 Representation of Non-standard Characters and Glyphs).

Formulæ and tables are also similar in that well-researched and detailed DTD fragments have already been developed for them independently of the TEI. They differ in that (for mathematics at least) there also exists a richly detailed text-based but non-SGML notation which is very widely used: this is the TeX system, and the sets of descriptive macros developed for it such as LaTeX, AMS-TeX, and AMS-LaTeX.

The AAP and ISO standards mentioned in section 14.1 Tables above both provide DTDs for equations as well as for tables, which now form part of ISO 12083. The European Mathematical Trust, an organization set up specifically to enhance research support for European mathematicians, has also defined a general purpose mathematical DTD known as EuroMath (http://www.dcs.fmph.uniba.sk/~emt/), for which it provides both software and services.

Most if not all of the functionality provided by these DTDs can now be found in the OpenMath and MathML XML-based systems briefly described below.

As with tables, in all the SGML and XML solutions a tension exists between the need to encode the way a formula is written (its appearance) and the need to represent its semantics. If the object of the encoding is purely to act as an interchange format among different formatting programs, then there is no need to represent the mathematical meaning of an expression. If however the object is to use the encoding as input to an algebraic manipulation system (such as Mathematica or Maple) or a database system, clearly simply representing superscripts and subscripts will be inadequate.

The present Guidelines make no attempt to add to the number of available DTDs for representing formulæ. Instead, we recommend that the user make an informed choice from those already available. The module described in this chapter makes available only the following element, which should be used to encode any formula, no matter what notation is employed:
  • formula contiene una fórmula matemática o de otro tipo.
    notation indica el nombre de una anotación definida previamente y usada para el contenido de un elemento.
By default, a formula is assumed to contain character data which is not validated in any way:
<formula notation="TeX">$e=mc^2$</formula>
The character data must still be well-formed, of course, which means that < and & must be escaped with entity references or numeric character references, e.g.
<formula notation="TeX">$\matrix{0 &amp;amp; 1\cr&amp;lt;0&amp;amp;>1}$</formula>

If desired, the content of the formula element may be redefined to include elements defined by some other module, such as that of ISO 12083, or to use elements from the more recently defined OpenMath or MathML schemas.

When the content of a formula element is not expressed in XML the notation used should be specified using the notation attribute as above, and in the following longer example:
<p>Achilles runs ten times faster than the tortoise and
gives the animal a headstart of ten meters. Achilles runs
those ten meters, the tortoise one; Achilles runs that
meter, the tortoise runs a decimeter; Achilles runs that
decimeter, the tortoise runs a centimeter; Achilles runs
that centimeter, the tortoise, a millimeter; Fleet-footed
Achilles, the millimeter, the tortoise, a tenth of a
millimeter, and so on to infinity, without the tortoise ever
being overtaken. . . Such is the customary version.

<!-- ... -->
The problem does not change, as you can see; but I would
like to know the name of the poet who provided it with a
hero and a tortoise. To those magical competitors and to
the series
<formula notation="TeX">$$
   {1 \over 10} +
   {1 \over 100} +
   {1 \over 1000} +
   {1 \over 10,\!000} +
   \dots
   $$</formula>
the argument owes its fame.</p>
bibliography
The notation attribute supplies the name of a notation (‘TeX’), which is expected to be identified somewhere in document metadata.
Mathematical Markup Language (MathML) (Carlisle et al. (eds.) (2003)) is a vocabulary for describing mathematical notation, capturing both its structure and content. It provides two types of markup: Presentation Markup, which captures the notational structure of an expression and could be seen as the ‘TeX for the Web’ and Content Markup, which captures the mathematical structure of an expression. Most of its content elements correspond with the range of operators, relations, and named functions typically found at the high-school level of mathematics. The tortoise example given above in TeX can be re-expressed in MathML as
<m:math>
 <m:mfrac>
  <m:mrow>
   <m:mn>1</m:mn>
  </m:mrow>
  <m:mrow>
   <m:mn>10</m:mn>
  </m:mrow>
 </m:mfrac>
 <m:mo>+</m:mo>
 <m:mfrac>
  <m:mrow>
   <m:mn>1</m:mn>
  </m:mrow>
  <m:mrow>
   <m:mn>100</m:mn>
  </m:mrow>
 </m:mfrac>
 <m:mo>+</m:mo>
 <m:mfrac>
  <m:mrow>
   <m:mn>1</m:mn>
  </m:mrow>
  <m:mrow>
   <m:mn>1000</m:mn>
  </m:mrow>
 </m:mfrac>
 <m:mo>+</m:mo>
 <m:mfrac>
  <m:mrow>
   <m:mn>1</m:mn>
  </m:mrow>
  <m:mrow>
   <m:mn>10000</m:mn>
  </m:mrow>
 </m:mfrac>
 <m:mo>+</m:mo>
 <m:mo>…</m:mo>
</m:math>

MathML 2.0 provides support for a ‘Semantic Math-Web’, XML namespaces, and other current XML standards, such as XML DOM, OMG IDL, ECMAScript, and Java. It also provided a modularized version of the MathML DTD so that MathML fragments ‘embedded’ in XHTML 1.1 documents can be correctly validated.

The OpenMath (http://www.nag.co.uk/projects/OpenMath.html) project is coordinated by the OpenMath Society (http://www.openmath.org/) and funded by the European Commission under the Esprit Multimedia Standards Initiative that commenced in September 1997. It is likely to become a key standard for communicating semantically rich representations of mathematical objects both on and off the Web in a platform-independent manner.

The OpenMath Standard (http://www.openmath.org/V2/standard/index.html) consists of specifications for
  1. OpenMath objects, representing the structure of formulæ (http://www.openmath.org/V2/standard/objects.html);
  2. Content Dictionaries, providing semantic context (http://www.openmath.org/V2/standard/cd.html);
  3. Encodings, both binary (http://www.openmath.org/V2/standard/binary.html) and XML (http://www.openmath.org/V2/standard/xml.html).

OpenMath and MathML have certain common aspects. They both use prefix operators, both are XML-based and they both construct their objects by applying certain rules recursively. Such similarities facilitate mapping between the two standards. There are also some key differences between MathML and OpenMath. OpenMath does not provide support for presentation of mathematical objects and its scope of semantically-oriented elements is much broader that of MathML, with the expressive power to cover virtually all areas of computational mathematics. In fact, a particular set of Content Dictionaries, the ‘MathML CD Group’, covers the same areas of mathematics as the Content Markup elements of MathML 2.0.

Finally, OMDoc (http://www.mathweb.org/omdoc/) is an extension of the OpenMath standard that supplies markup for structures such as axioms, theorems, proofs, definitions, texts (mixing formal content with mathematical text).

In-line versus block placement for an equation can be distinguished if desired, via the global rend attribute. The global n and xml:id attributes may also be used to label or identify the formula, as in the following example:
<p>The volume of a
sphere is given by the formula:
<formula xml:id="f12" n="12" rend="inline">
  <m:math>
   <m:mi>V</m:mi>
   <m:mo>=</m:mo>
   <m:mfrac>
    <m:mrow>
     <m:mn>4</m:mn>
    </m:mrow>
    <m:mrow>
     <m:mn>3</m:mn>
    </m:mrow>
   </m:mfrac>
   <m:mi>π</m:mi>
   <m:msup>
    <m:mrow>
     <m:mi>r</m:mi>
    </m:mrow>
    <m:mrow>
     <m:mn>3</m:mn>
    </m:mrow>
   </m:msup>
  </m:math>
 </formula>
which is readily calculated.</p>
<p>As we have seen in equation
<ptr target="#f12"/>, ... </p>

14.3 Specific Elements for Graphic Images

The following special purpose elements are used to indicate the presence of graphic images within a document:
  • figure indica un bloque que contiene gráficos, ilustraciones o figuras.
  • graphic/ indica la localización de un gráfico, ilustración o figura.
  • binaryObject proporciona datos binarios codificados que representan un objeto gráfico u otro tipo de objeto inserido en el texto.
  • figDesc (descripción de una figura) contiene una breve descripción de la apariencia o del contenido de una figura gráfica, para utilizarla al documentar una imagen sin mostrarla.

The graphic and binaryObject elements form part of the common core module, and are discussed in section 3.9 Graphics and other non-textual components.

The figure element is used to contain images, captions, and textual descriptions of the pictures. The images themselves are specified using the graphic element, whose url attribute provides the location of an image. For example:
<figure>
 <graphic url="Fig1.pdf"/>
</figure>
Three kinds of content may be supplied inside a figure element: the element head may be used to transcribe (or supply) a descriptive heading or title for the graphic itself as in this example:
<figure>
 <graphic url="Fig1.pdf"/>
 <head>Figure One: The View from the
   Bridge</head>
</figure>
Figures are often accompanied not only by a title or heading, but by a paragraph or so of commentary or caption. One or more p or ab elements may be used to transcribe any caption or discussion of the figure in the source:
<figure>
 <graphic url="pullman.png"/>
 <head>Above:</head>
 <p>The drawing room of the Pullman house, the white and gold saloon
   where the magnate delighted in giving receptions for several
   hundred people.</p>
 <figDesc>The figure shows an elaborately decorated room, at least
   twenty-five feet side to side and fifty feet long, with ornate
   mouldings and Corinthian columns on the walls, overstuffed
   armchairs and loveseats arranged in several conversational
   groupings, and two large chandeliers.</figDesc>
</figure>
bibliography
Here, the paragraph ‘The drawing room ... several hundred people’ is transcribed from the source, while the description is provided by the encoder, for use by applications which cannot display the graphic directly. In documents created in electronic form with the needs of print-handicapped readers in mind, the figDesc element may be provided by the author rather than a subsequent encoder.
<figure>
 <graphic url="Fig1.jpg"/>
 <head>Figure One: The View from the Bridge</head>
 <figDesc>A Whistleresque view showing four
   or five sailing boats in the foreground, and a
   series of buoys strung out between them.</figDesc>
</figure>

Where the graphic itself contains large amounts of text, perhaps with a complex structure, and perhaps difficult to distinguish from the graphic, the encoder should choose whether to regard the graphic as containing the text (in which case, a nested floatingText element may be included within the figure element) or to regard the enclosed text as being a separate division of the text element in which the graphic appears. In this latter case, an appropriate div or div1 (etc.) element may be used for the text represented within the graphic, and the figure element embedded within it. The choice will depend to a large degree on the encoder's understanding of the relationship between the graphic and the surrounding text.

A figure which is internally divided, or contains sub-figures, may be encoded with nested figure elements, as in the following example.
<figure n="6.45">
 <figure n="a">
  <graphic url="./figs/6.45a.png"/>
  <ab type="caption">Parallel</ab>
 </figure>
 <figure n="b">
  <graphic url="./figs/6.45b.png"/>
  <ab type="caption">Perspective</ab>
 </figure>
 <ab type="caption">The two canonical view volumes, for the (a) parallel
   and (b) perspective projections. Note that -z is to the right.</ab>
</figure>
bibliography

Like any other element in the TEI scheme, figures may be given identifiers so that they can be aligned with other elements, and linked to or from them, as described in chapter 16 Linking, Segmentation, and Alignment. Some common examples are discussed briefly here; full information is provided in that chapter.

It is often desirable to maintain two versions of an image in an electronic file: one a low resolution or ‘thumbnail’ version which, when selected by the user, causes the other, high resolution, version to be accessed. In TEI terms, the thumbnail image acts as a reference to the other. Supposing that a thumbnail version of the figure discussed above is available as fig1th.png", we might embed a reference to the image using the simple ref element discussed in section 3.6 Simple Links and Cross-References:
<ref target="#IM1">Click here
<graphic url="fig1th.png"/>
for enlightenment
</ref>
<figure xml:id="IM1">
 <graphic url="fig1.jpg"/>
</figure>

Another common requirement is to associate part or the whole of an image with a textual element not necessarily contiguous to it in the text; this is sometimes known as a callout. When the module for transcription is included in a schema, specific attributes for parts of a text and parts (or all) of a digital image are available; these are discussed in 11.1 Digital Facsimiles. In addition, chapter 16 Linking, Segmentation, and Alignment may be consulted for other mechanisms available for this purpose.

The following example assumes that we wish to associate one portion of the image held as ‘fig1’ with chapter two of some text, and another portion of it with chapter three. The application may be thought of as a hypertext browser in which the user selects from a graphic image which part of a text to read next, but the mechanism is independent of this particular application.

The first requirement is some way of identifying and hence pointing to sub-parts of a graphic image. This may be done by pointing into an XML graphic representation, for example an SVG file. Thus
<ptr xml:id="PD1" target="Fig1.svg#object1"/>
<ptr xml:id="PD2" target="Fig1.svg#object2"/>
These ptr elements identify two areas within the image ‘Fig1’ by pointing at elements inside the XML file Fig1.svg, which contains the following.
<svg xmlns="http://www.w3.org/2000/svg"
 width="8cm" height="3cm" viewBox="2 1 8 3">
 <g xmlns="http://www.w3.org/2000/svg"
  id="object1">
  <ellipse xmlns="http://www.w3.org/2000/svg"
  
    style="fill: #ffffff"
    cx="3.875"
    cy="3.025"
    rx="1.175"
    ry="1.175"/>
 </g>
 <g xmlns="http://www.w3.org/2000/svg"
  id="object2">
  <rect xmlns="http://www.w3.org/2000/svg"
  
    style="fill: #a81616"
    x="7.8"
    y="1.9"
    width="2.17581"
    height="2.24833"/>
 </g>
</svg>
The next requirement is some way of identifying the parts of the document to which a link is to be made. The most obvious way of doing this is to use the global xml:id attribute:
<div1 type="chapter" xml:id="CHAP1">
<!-- ... -->
</div1>
<div1 type="chapter" xml:id="CHAP2">
<!-- ... -->
</div1>
Now, all that is needed to linking these areas to the relevant chapters is a linkGrp element, as described in section 16.1 Links:
<linkGrp type="callout">
 <link targets="#CHAP1 #PD1"/>
 <link targets="#CHAP2 #PD2"/>
</linkGrp>

In this example, the SVG representation of the graphic is stored externally to the TEI document and linked by means of a pointer. It is also possible to embed the SVG representation directly within the TEI by extending the content model of the figure element to permit an element <svg> from the SVG namespace. Like other customizations of the TEI scheme, this is carried out using the techniques documented in section 1.2 Defining a TEI Schema; further examples are provided in chapter 16 Linking, Segmentation, and Alignment.

14.4 Overview of Basic Graphics Concepts

The first major distinction in graphic representation is that between raster graphics and vector graphics. A raster image is a list of points, or dots. Scanners, fax machines and other simple devices easily produce digital raster images, and such images are therefore quite common. A vector image, in contrast, is a list of geometrical objects, such as lines, circles, arcs, or even cubes. These are much more difficult to produce, and so are mainly encountered as the output of sophisticated systems such as architectural and engineering CAD programs.

Raster images are difficult to modify because by definition they only encode single points: a line, for example, cannot grow or shrink as such, since it is not identified as such. Only its component parts are identified, and only they can be manipulated. Therefore the resolution or dot-size of a raster image is important, which is not the case with vector images. It is also far more difficult to convert raster images to vector images than to perform the opposite conversion. Raster images generally require more storage space than vector images, and a wide variety of methods exists for compressing them; the variation in these methods leads to corresponding variations in representations for storage and transmission of raster images.

Motion video usually consists of a long series of raster images. Data compression is even more effective on video than on single raster images (mainly owing to redundancy which arises from the usual similarity of adjacent frames). Notations for representing full-motion video are hotly debated at this time, and any user of these Guidelines would do well to obtain up-to-date expert advice before undertaking a project using them.

The compression methods used with any of these image types may be ‘lossy’ or ‘lossless’. Methods for lossy compression save space by discarding a small portion of the image's detail, such as fine distinctions of shading. When decompressed, therefore, such an image will be only a close approximation of the original. In contrast, lossless compression guarantees that the exact uncompressed image will be reproducible from the compressed form: only truly redundant information is removed. In general, therefore, lossless compression does not save quite so much space as lossy compression, though it does guarantee fidelity to the original uncompressed image.

Raster images may be characterized by their resolution, which is the number of dots per inch used to represent the image. Doubling the resolution will give a more precise image, but also quadruple the storage requirement (before compression), and affect processing time for any operations to be performed, such as displaying an image for a reader. Motion video also has resolution in time: the number of frames to be shown per second. Encoders should consider carefully what resolution(s) and frame rate(s) to use for particular applications; these Guidelines express no recommendation in this matter, save the universal ones of consistency and documentation.

Within any image, it is typical to refer to locations via Cartesian coordinate axes: values for x, y, and sometimes z and/or time. However, graphic notations vary in whether coordinates count from left-to-right and top-to-bottom, or another way. They also vary in whether coordinates are considered real (inches, millimeters, and so on), or virtual (dots). These Guidelines do not recommend any of these methods over another, but all decisions made should be applied consistently, and documented in the encodingDesc section of the TEI header. 44

Methods of aligning images and text are discussed in 11.1 Digital Facsimiles.

The chromatic values of an image may be rendered in many different ways. In monochrome images every displayed point is either black or white. In gray-scale images, each point is rendered in some shade of gray, the number of shades varying from system to system. In true polychrome images, points are rendered in different hues, again with varying limitations affecting the number of distinct shades and the means by which they are displayed.

14.5 Graphic Image Formats

As noted above, there exists a wide variety of different graphics formats, and the following list is in no way exhaustive. Moreover, inclusion of any format in this list should not be taken as indicating endorsement by the TEI of this format or any products associated with it. Some of the formats listed here are proprietary to a greater or lesser extent and cannot therefore be regarded as standards in any meaningful sense. They are however widely used by many different vendors.

The following formats are widely used at the present time, and likely to remain supported by more than one vendor's software:
  • BMP: Microsoft bitmap format
  • CGM: Computer Graphics Metafile
  • GIF: Graphics Interchange Format
  • JPEG: Joint Photographic Expert Group
  • PBM: Portable Bit Map
  • PCX: IBM PC raster format
  • PICT: Macintosh drawing format
  • PNG: Portable Network Graphics format
  • Photo-CD: Kodak Photo Compact Disk format
  • QuickTime: Apple real-time image system
  • SMIL: Synchronized Multimedia Integration Language format
  • SVG: Scalable Vector Graphics format
  • TIFF: Tagged Image File Format

Brief descriptions of all the above are given below. Where possible, current addresses or other contact information are shown for the originator of each format. Many formal standards, especially those promulgated by ISO and many related national organizations (ANSI, DIN, BSI, and many more), are available from those national organizations. Addresses may be found in any standard organizational directory for the country in question.

14.5.1 Vector Graphic Formats

CGM: Computer Graphics Metafile
This vector graphics format is specified by an ISO standard, ISO 8632:1987, amended in 1990. It defines binary, character, and plain-text encodings; the non-binary forms are safer for blind interchange, especially over networks. Documentation on CGM is available from ISO and from its member national bodies such as AFNOR, ANSI, BSI, DIN, JIS, etc.
SVG: Scalable Vector Graphics format
SVG is a language for describing two-dimensional vector and mixed vector or raster graphics in XML. It is defined by the Scalable Vector Graphics (SVG) 1.0 Specification, W3C Recommendation, 04 September 2001, and is available at http://www.w3.org/TR/2001/REC-SVG-20010904/.
PICT: Macintosh drawing format
This format is universally supported on Macintosh (tm) systems, and readable by a limited range of software for other systems. Documentation is available from Apple Computer Company, Cupertino, California USA.

14.5.2 Raster Graphic Formats

PNG: Portable Network Graphics format
PNG is a non-proprietary raster format currently widely available. It provides an extensible file format for the lossless, portable, well-compressed storage of raster images. Indexed-color, grayscale, and truecolor images are supported, plus an optional alpha channel. Sample depths range from 1 to 16 bits. It is defined by IETF RFC 2083, March 1997.
TIFF: Tagged Image File Format
Currently the most widely supported raster image format, especially for black and white images, TIFF is also one of the few formats commonly supported on more than one operating system. The drawback to TIFF is that it actually is a wrapper for several formats, and some TIFF-supporting software does not support all variants. TIFF files may use LZW, CCITT Group 4, or PackBits compression methods, or may use no compression at all. Also, TIFF files may be monochrome, greyscale, or polychromatic. All such options should be specified in prose at the end of the encodingDesc section of the TEI header for any document including TIFF images. TIFF is owned by Aldus Corporation. Documentation on TIFF is available from them at Craigcook Castle, Craigcook Road, Edinburgh EH4 3UH, Scotland, or 411 First Avenue South, Seattle, Washington 98104 USA.
GIF: Graphics Interchange Format
Raster images are widely available in this form, which was created by CompuServe Information Services, but has by now been implemented for many other systems as well. Documentation on GIF is copyright by, and is available from, CompuServe Incorporated, Graphics Technology Department, 5000 Arlington Center Boulevard, Columbus, Ohio 43220 USA.
PBM: Portable Bit Map
PBM files are easy to process, eschewing all compression in favor of transparency of file format. PBM files can, of course, be compressed by generic file-compression tools for storage and transfer. Public domain software exists which will convert many other formats to and from PBM. Documentation on PBM is copyright by Jeff Poskanzer, and is available widely on the Internet.
PCX: IBM PC raster format
This format is used by most IBM PC paint programs, and supports both monochrome and polychromatic images. Documentation is available from ZSoft Corporation, Technical Support Department, ATTN: Technical Reference Manual, 450 Franklin Rd. Suite 100, Marietta, GA 30067 USA.
BMP: Microsoft bitmap format
This format is the standard raster format for computer using Microsoft Windows (tm) or Presentation Manager (tm). Documentation is available from Microsoft Corporation.

14.5.3 Photographic and Motion Video Formats

JPEG: Joint Photographic Experts Group
This standard is sponsored by CCITT and by ISO. It is ISO/IEC Draft International Standard 10918-1, and CCITT T.81. It handles monochrome and polychromatic images with a variety of compression techniques. JPEG per se, like CCITT Group IV, must be encapsulated before transmission; this can be done via TIFF, or via the JPEG File Interchange Format (JFIF), as commonly done for Internet delivery.
QuickTime: Apple real-time image system
QuickTime is a proprietary method introduced by Apple Computer Company to synchronize the display of various data. The data can include frames of video, sound, lighting control mechanisms, and other things. Viewers for QuickTime productions are available for Apple and other computers. Further information is available from Apple Computer Incorporated, 10201 North de Anza Boulevard MS 23AQ, Cupertino, California 95014 USA.
Photo-CD: Kodak Photo Compact Disk format
This format was introduced by Kodak for rasterizing photographs and storing them on CD-ROMs (about one hundred 35mm file images fit on one disk), for display on televisions or CD-I systems. Information on Photo-CD is available from Kodak Limited, Research and Development, Headstone Drive, Harrow, Middlesex HA1 4TY, UK.
SMIL: Synchronized Multimedia Integration Language format
SMIL is a W3C Recommendation which supports the integration of independent multimedia objects into a synchronized multimedia presentation. It provides multimedia authors with easily-defined basic timing relationships, fine-tuned synchronization, spatial layout, direct inclusion of non-text and non-image media objects, hyperlink support for time-based media, adaptiveness to varying user and system characteristics. SMIL 1.0 (http://www.w3.org/TR/REC-smil/) became a W3C Recommendation on June 15, 1998, and was further developed in SMIL 2.0. SMIL 2.0 adds native support for transitions, animation, event-based interaction, extended layout facilities, and more sophisticated timing and synchronization primitives to the SMIL 1.0 language. It also allows reuse of SMIL syntax and semantics in other XML-based languages, in particular those who need to represent timing and synchronization. For example, SMIL 2.0 components are used for integrating timing into XHTML Document Types and into SVG. SMIL 2.0 also provides recommendations for Document Types based on SMIL 2.0 Modules (http://www.w3.org/TR/smil20/smil-modules.html). One such Document Type is the SMIL 2.0 Language Profile (http://www.w3.org/TR/smil20/smil20-profile.html). It contains support for all of the major SMIL 2.0 features including animation, content control, layout, linking, media object, meta-information, structure, timing, and transition effects and is designed for Web clients that support direct playback from SMIL 2.0 markup. SMIL 2.0 (http://www.w3.org/TR/smil20/) became a W3C Recommendation on August 7, 2001, becoming the first vocabulary to provide XML Schema support and to have reached such status.

As noted above, the reader will encounter many, many other graphics formats.

14.6 Module for Tables, Formulæ, and Graphics

The module described in this chapter provides the following features:
Módulo figures: Tables, formulæ, and figures
The selection and combination of modules to form a TEI schema is described in 1.2 Defining a TEI Schema.

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Notas
44.
Since no special purpose element is provided for this purpose by the current version of the Guidelines, such information should be provided as one or more distinct paragraphs at the end of the encodingDesc element described in section 2.3 The Encoding Description.
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