Dimensions

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NOTE: This article is about the data type. For the names of a page's many dimensions, see Layout.

A dimension, in TeX, is a variable storing a length. The length is entered as a number immediately followed by two letters that indicate the unit, e.g. 12pt or 1cm. TeX recognizes 9 different units:

  • scaled points (sp), equal to 1/65536 points. This is TeX's internal unit for dimensions. One sp is so small that TeX can store dimensions as integers; at the time, this was an advantage, because floating point arithmetic was not guaranteed to be consistent across platforms.
  • points (pt) and picas (pc). One point is 1/72.27 inch; 12 points = 1 pica.
  • didot (dd) and cicero (cc). The didot is a continental counterpart of the point; 12 didot = 1 cicero.
  • big points (bp), defined by Adobe as 1/72 of an inch.
  • millimeters (mm), centimeters (cm), and, unavoidably, inches (in).

The various conversions between the units are laid out in the conversion table at the end of this article.

Defining and accessing dimensions

\newdimen is the native TeX method to initialise a dimension variable. The requirement to explicitly initialize your dimension variables is a bit clunky, but this method should still be preferred over storing dimensions as strings.

  • \newdimen is by far the more common idiom
  • Values stored in a dimension register with \newdimen can be accessed directly from Lua, which is not true for values stored in a macro with \def or \definemeasure.

The following example shows how to set and access dimensions:

\newdimen\columnA                    % initialise variable
\columnA=10mm                        % set variable

Column A is \the\columnA{} wide.     % lengths are automatically 
                                     % displayed in pt.

Column A is \number\columnA sp wide. % internally, lengths are stored
                                     % as an integer number of sp

\blackrule[width=\columnA]

Converting dimensions

Usually, you will want to express a dimension in something other than points or scaled points. For this, Lua is the way to go:

  • If you want to print, the functions number.tocentimeters, topoints, topicas, etc. are already provided. These functions return a number as a string with (by default) the unit abbreviation appended.
  • If you want to calculate, the conversion factors from standard points are stored in number.dimenfactors. For example, 65536 * number.dimenfactors["pt"] returns 1.
\newdimen\columnA                    % initialise variable
\columnA=10mm                        % set variable

\startluacode
    local A = tex.dimen.columnA      -- access a dimen value

    -- internal unit: scaled points (integer)
    context("Column A is %d scaled points", A)
    context.par()

    -- default conversion: 15 digits, unit at the end, no space
    context("Column A is %s", number.tocentimeters(A))
    context.par()

    -- expressing a dimen in cm, rounded to 0.01, no automatic unit
    context("Column A is %s cm", number.tocentimeters(A, "%.2f"))
    context.par()

    -- converting from mm to cm
    local inmm = 10
    local incm = inmm / number.dimenfactors["mm"] * number.dimenfactors["cm"]
    context("Column A is %.1f cm", incm)
\stopluacode

Calculating with dimensions

From TeX, you can compute with dimensions by writing your calculation between \dimexpr...\relax. Such an expression may only occur where a length is expected. Spaces are allowed, but never required.

\newdimen\columnA
\columnA=1cm

0.5 cm equals \the\dimexpr \columnA / 2 \relax.

\blackrule[width=\dimexpr 2 \columnA\relax]

In Lua, dimensions are a number of scaled points, and you can do all the usual things. TeX uses integers for dimens, but Lua treats them as floats; the number will only be coerced to integer when you retrieve from, or assign to, tex.dimen.somevalue. Not that half a scaled point is much to worry about.

\newdimen\columnA
\columnA=1cm

\startluacode
    local A = tex.dimen.columnA
    double_A = 2 * A
    context.blackrule({width = double_A .. "sp"})
\stopluacode

More examples
  \newdimen\AAA \AAA=100pt
  \newdimen\BBB \BBB=\AAA

  AAA is \the\AAA

  BBB is \the\BBB

Storing dimensions as strings

Because TeX expands macros, we can store a dimension string like 10pt in a macro, and insert that in any place TeX expects a dimension. You can use a plain \def; or you can define dimensions with \definemeasure[...] and retrieve them with \measure{...}.

\definemeasure[One][10mm]
\def\Two{20mm}

\definemeasure[Three][\dimexpr \measure{One} + \Two\relax]

\blackrule[width=\measure{One}]  \crlf
\blackrule[width=\Two]           \crlf
\blackrule[width=\measure{Three}]\crlf

Conversion table

Bold numbers indicate conversions that are set by definition.

unit TeX name in sp in pt in pc in dd in cc in bp in in in cm in mm
scaled point sp 1 1/65536
point pt 65536 1 1/12 0.9346 0.0779 0.9963 1/72.27 0.3516 0.0351
pica pc 786432 12 1 11.2149 0.9346 11.9552 0.1660 4.2175 0.4218
didot dd 70124.081 1.0700 0.0892 1 1/12 1.0660 0.0148 0.3761 0.0376
cicero cc 841488.98 12.8401 1.0700 12 1 12.7921 0.1777 4.5128 0.45128
big point bp 65781.76 1.0038 0.0836 0.9381 0.0782 1 1/72 0.3528 0.0353
inch in 4736286.7 72.27 6.0225 67.5415 5.6284 72 1 25.4 2.54
millimeter mm 186467.98 2.8453 0.2371 2.6591 0.2216 2.8346 0.0394 1 0.1
centimeter cm 1864679.8 28.4528 2.3711 26.5911 2.2159 28.3464 0.39370 10 1

See also