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.