TEI: Guidelines for Electronic Text Encoding and Interchange

TEI: Tables⚓︎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; similarly, the global style attribute coud be used to provide 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.

TEI: Formulæ and Mathematical Expressions⚓︎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 Characters, Glyphs, and Writing Modes).

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-XML 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://xml.coverpages.org/emt-ukc-index.html), 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 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 formula element provided by these Guidelines makes no attempt to represent the internal structure of formulæ.

• formula (formula) contains a mathematical or other formula.

Alternatively, if more detailed markup is desired, the content of the formula element may be redefined to include elements defined by some other XML vocabulary, such as that of ISO 12083, or to use elements from the OpenMath or MathML schemas.

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 provides a modularized version of the MathML DTD so that MathML fragments ‘embedded’ in XHTML 1.1 documents can be correctly validated.

The OpenMath (https://openmath.org/standard/) project is coordinated by the OpenMath Society (https://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 (https://openmath.org/standard/om20-2004-06-30/) consists of specifications for

1. OpenMath objects, representing the structure of formulæ (https://openmath.org/standard/om20-2004-06-30/omstd20html-2.xml#cha_obj);
2. Content Dictionaries, providing semantic context (https://openmath.org/standard/om20-2004-06-30/omstd20html-4.xml#cha_cd);
3. Encodings, both binary (https://openmath.org/standard/om20-2004-06-30/omstd20html-3.xml#sec_binary) and XML (https://openmath.org/standard/om20-2004-06-30/omstd20html-3.xml#sec_xml).

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://omdoc.org/) 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).

TEI: Notated Music in Written Text⚓︎14.3 Notated Music in Written Text

Music, like many other art forms, is often mentioned, discussed and described in writings of various kinds. This applies to both historical and contemporary documents, even though methods of notating music have changed considerably in western history. In most cases, music notation enters the text flow in a way similar to figures, images, or graphs. On other occasions, elements of music notation are treated as inline characters in running text.

notatedMusic provides a way to signal the presence of music notation in text, but defer to other representations, which are not covered by the TEI guidelines, to describe the music notation itself. In fact several commercial, academic, and standard bodies have developed digital representations of music notation. Given the topic's complexity, these representations often focus on different aspects and adopt different methodologies. Therefore, notatedMusic only defines a container element to encode the occurrence of music notation and allows linking to the data format preferred by the encoder. (Note: notatedMusic is not the same as musicNotation, a metadata element, which is used to describe musical notation that appears in a manuscript. See 10 Manuscript Description.)

The following elements can be used for encoding music notation in text:

• notatedMusic encodes the presence of music notation in a text
• ptr (pointer) defines a pointer to another location.
• desc (description) contains a short description of the purpose, function, or use of its parent element, or when the parent is a documentation element, describes or defines the object being documented.
• graphic (graphic) indicates the location of a graphic or illustration, either forming part of a text, or providing an image of it.
• binaryObject provides encoded binary data representing an inline graphic, audio, video or other object.

• notatedMusic groups elements representing or containing music notation.
• ptr can be used to indicate the location of a representation of the music notation.
  • mimeType supplies the MIME type of the data format, when available.
• desc can be used to give a prose description of the notated music.
• graphic can be used to indicate the location of a graphical representation of the music notation.
• binaryObject provides encoded binary data which constitutes another representation of the music notation (e.g. audio).

The notatedMusic element may contain a textual description and pointers to various representations of the music notation in different media. An external representation of the notated music is specified using the ptr element, whose target attribute provides its electronically-accessible location. The attribute mimeType supplies the MIME type of the data format when available. For example:

A textual description of the notation can be provided within the desc element; alternatively, a label may be supplied. For example:

It is possible to link to any kind of music notation data format. However, when a MIME type is not available, it is recommended that the format be specified in the description. See the following examples.

MIME type available:

MIME type not available:

Application format:

It is possible to specify the location of digital objects representing the notated music in other media such as images or audio-visual files. The interpretation of the correspondence between the notated music and these digital objects is not encoded explicitly. We recommend the use of graphic and binaryObject mainly as a fallback mechanism when the notated music format is not displayable by the application using the encoding. The alignment of encoded notated music, images carrying the notation, and audio files is a complex matter for which we refer the reader to other formats and specifications such as MPEG-SMR.

It is also recommended, when useful, to embed XML-based music notation formats, such as the Music Encoding Initiative format as content of notatedMusic. This must be done by means of customization.

In modern printing, music notation positioned between blocks of text for illustrative purposes is usually referred to as a ‘figure’ or ‘example’. In this cases, we recommend the inclusion of notatedMusic in figure in order to encode possible captions and headers. For example:

TEI: Specific Elements for Graphic Images⚓︎14.4 Specific Elements for Graphic Images

The following special purpose elements are used to indicate the presence of graphic images within a document:

• figure (figure) groups elements representing or containing graphic information such as an illustration, formula, or figure.
• graphic (graphic) indicates the location of a graphic or illustration, either forming part of a text, or providing an image of it.
• binaryObject provides encoded binary data representing an inline graphic, audio, video or other object.
• figDesc (description of figure) contains a brief prose description of the appearance or content of a graphic figure, for use when documenting an image without displaying it.

The graphic and binaryObject elements form part of the common core module, and are discussed in section 3.10 Graphics and Other Non-textual Components.

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.

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.

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.

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.

TEI: Overview of Basic Graphics Concepts⚓︎14.5 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.⁵⁸

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 grayscale 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.

TEI: Graphic Image Formats⚓︎14.6 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.