Absolute quantities¶

An absolute quantity contains a value measured from a given reference point. Examples are time with a reference point 1-1-1970 (UNIX epoch) or a reference point 1-1-0000 (Gregorian calendar time). As an other example, a geographical direction can be defined relative to North or East as a reference point. Therefore, an absolute quantity is a quantity relative to a defined reference point. Every absolute quantity has its own type of reference point: a Time has a Time.Reference, a Position has a Position.Reference. Multiple instances of reference points can be defined (such as EAST and NORTH in the Direction example). References can be defined relative to each other: NORTH is defined as having an Angle difference of π/2 relative to the EAST reference point.

Absolute quantities therefore have three fields as compared to two fields for a relative quantity:

the reference point of the correct type (e.g., Direction.Reference.EAST).
the relative value in SI or BASE units relative to the reference point (e.g., an Angle of π/4).
the display unit to use (e.g., Angle.Unit.deg).

The above example results in a north-easterly direction, since Angle is defined clockwise.

The relation between relative and absolute quantities is sketched in the class diagram below:

Operations on absolute quantities¶

Adding two absolute values together makes no sense. Subtracting one absolute value from another does make sense (and results in a relative value). Subtracting East from North should result in an angle of ±90° or ±π/2 (depending on the unit used to express the result). An absolute quantity always needs a reference to be useful. Values subtracted from each other need to know their reference to be able to carry out the subtraction. Therefore, the reference is explicitly stored with an absolute quantity.

A relative value expresses the difference between two (absolute or relative) values. The angle in the example above is a relative value. Relative values can be added together and subtracted from each other (resulting in relative values). Adding a relative value to an absolute value results in an absolute value. Subtracting a relative value from an absolute value also results in an absolute value.

In the geographical example, directions are absolute and angles are relative. Similarly, when applied to lengths, positions are absolute and distances are relative.

Generally, if adding a value to itself makes no sense, the value is absolute; otherwise it is relative.

Operation	Operands	Result
+ (plus)	Absolute + Absolute	Not allowed
+ (plus)	Absolute + Relative	Absolute
+ (plus)	Relative + Absolute	Absolute
+ (plus)	Relative + Relative	Relative
- (minus)	Absolute - Absolute	Relative (corresponding quantity)
- (minus)	Absolute - Relative	Absolute
- (minus)	Relative - Absolute	Not allowed
- (minus)	Relative - Relative	Relative
* (times)	Absolute * Absolute	Not allowed
* (times)	Absolute * Relative	Not allowed
* (times)	Relative * Absolute	Not allowed
* (times)	Relative * Relative	Relative (different quantity)
/ (divide)	Absolute / Absolute	Not allowed
/ (divide)	Absolute / Relative	Not allowed
/ (divide)	Relative / Absolute	Not allowed
/ (divide)	Relative / Relative	Relative (different quantity)

Attempts to perform operations that are marked not allowed are caught at compile time.

Available absolute quantities¶

All quantities make sense as relative values. The four quantities that also make sense as absolute values are listed in the table below.

Quantity	Absolute interpretation	Absolute class and Unit	Relative interpretation	Relative class and Unit
Length	Position	Position Length.Unit	Distance	Length Length.Unit
Angle	Direction or Slope	Direction Angle.Unit	Angle (direction or slope difference)	Angle Angle.Unit
Temperature	Temperature	Temperature Temperature.Unit	Temperature difference	TemperatureDifference Temperature.Unit
Time	Time (instant)	Time Duration.Unit	Duration	Duration Duration.Unit

Examples¶

The Temperature absolute quantity assumes the reference Temperature.Reference.KELVIN as the default when it is not mentioned in the constructor.

Temperature t = new Temperature(0.0, Temperature.Unit.degF);
System.out.println("Temperature t  = " + t + ", si = " + t.si());
System.out.println("t in Kelvin    = " + t.toString(Temperature.Unit.K));
System.out.println("t in Celsius   = " + t.toString(Temperature.Unit.degC));

// add 32 degrees Fahrenheit - should be 0 Celsius
System.out.println("\nadd 32 degrees Fahrenheit - should be 0 Celsius");
TemperatureDifference t32 = new TemperatureDifference(32.0, Temperature.Unit.degF);
Temperature t2 = t.add(t32);
System.out.println("Temperature t2 = " + t2);
System.out.println("t2 in Kelvin   = "
    + t2.relativeTo(Temperature.Reference.KELVIN).toString(Temperature.Unit.K));
System.out.println("t2 in Celsius  = " 
    + t2.relativeTo(Temperature.Reference.CELSIUS).toString(Temperature.Unit.degC));

This prints:

Temperature t  = 0.00000000 °F (FAHRENHEIT), si = 0.0
t in Kelvin    = 0.00000000 K (FAHRENHEIT)
t in Celsius   = 0.00000000 °C (FAHRENHEIT)

add 32 degrees Fahrenheit - should be 0 Celsius
Temperature t2 = 32.0000000 °F (FAHRENHEIT)
t2 in Kelvin   = 491.670000 K (KELVIN)
t2 in Celsius  = 0.00000000 °C (CELSIUS)

Note that a Celsius temperature difference can be defined relative to 0 degrees Fahrenheit. Of course, this is typically not done; an absolute temperature in degrees Celsius will typically be defined relative to 0 °C, and similarly, kelvin and degrees Fahrenheit will be defined relative to their 'own' natural reference point. But it is not necessary.