Class

`Size2DSyntax`

is an abstract base class providing the common implementation of all attributes denoting a size in two dimensions.

A two-dimensional size attribute's value consists of two items, the `X`

dimension and the `Y`

dimension. A two-dimensional size attribute may be constructed by supplying the two values and indicating the units in which the values are measured. Methods are provided to return a two-dimensional size attribute's values, indicating the units in which the values are to be returned. The two most common size units are inches (in) and millimeters (mm), and exported constants `INCH`

and `MM`

are provided for indicating those units.

Once constructed, a two-dimensional size attribute's value is immutable.

**Design**

A two-dimensional size attribute's `X`

and `Y`

dimension values are stored internally as integers in units of micrometers (µm), where 1 micrometer = 10^{-6} meter = 1/1000 millimeter = 1/25400 inch. This permits dimensions to be represented exactly to a precision of 1/1000 mm (= 1 µm) or 1/100 inch (= 254 µm). If fractional inches are expressed in negative powers of two, this permits dimensions to be represented exactly to a precision of 1/8 inch (= 3175 µm) but not 1/16 inch (because 1/16 inch does not equal an integral number of µm).

Storing the dimensions internally in common units of µm lets two size attributes be compared without regard to the units in which they were created; for example, 8.5 in will compare equal to 215.9 mm, as they both are stored as 215900 µm. For example, a lookup service can match resolution attributes based on equality of their serialized representations regardless of the units in which they were created. Using integers for internal storage allows precise equality comparisons to be done, which would not be guaranteed if an internal floating point representation were used. Note that if you're looking for `U.S. letter `

sized media in metric units, you have to search for a media size of 215.9 x 279.4 mm; rounding off to an integral 216 x 279 mm will not match.

The exported constant `INCH`

is actually the conversion factor by which to multiply a value in inches to get the value in µm. Likewise, the exported constant `MM`

is the conversion factor by which to multiply a value in mm to get the value in µm. A client can specify a resolution value in units other than inches or mm by supplying its own conversion factor. However, since the internal units of µm was chosen with supporting only the external units of inch and mm in mind, there is no guarantee that the conversion factor for the client's units will be an exact integer. If the conversion factor isn't an exact integer, resolution values in the client's units won't be stored precisely.