# Class CoordinateSystems

Object
Static
CoordinateSystems

public final class CoordinateSystems extends Static
Utility methods working on `Coordinate­System` objects and their axes. Those methods allow for example to estimate an angle between two axes or determining the change of axis directions and units between two coordinate systems.
Since:
0.4

Defined in the `sis-referencing` module

• ## Method Summary

Modifier and Type
Method
Description
`static Angle`
```angle(Axis­Direction source, Axis­Direction target)```
Returns the arithmetic (counterclockwise) angle from the first axis direction to the second direction.
`static Axis­Direction`
```direction­Along­Meridian(Axis­Direction base­Direction, double meridian)```
Returns an axis direction from a pole along a meridian.
`static Axis­Direction[]`
`get­Axis­Directions(Coordinate­System cs)`
Returns the axis directions for the specified coordinate system.
`static Integer`
```get­Epsg­Code(Class<? extends Coordinate­System> type, Coordinate­System­Axis... axes)```
Returns the EPSG code of a coordinate system using the units and directions of given axes.
`static Integer`
```get­Epsg­Code(Unit<?> unit, Axis­Direction... directions)```
Returns the EPSG code of a coordinate system using the given unit and axis directions.
`static boolean`
`is­Along­Meridian(Axis­Direction direction)`
Returns `true` if the given axis direction seems to be a direction along a meridian.
`static Axis­Direction`
`parse­Axis­Direction(String name)`
Returns an axis direction code from the given direction name.
`static Coordinate­System`
```replace­Angular­Unit(Coordinate­System cs, Unit<Angle> new­Unit)```
Returns a coordinate system derived from the given one but with all angular units replaced by the given unit.
`static Coordinate­System`
```replace­Axes(Coordinate­System cs, Axis­Filter filter)```
Returns a coordinate system derived from the given one but with a modified list of axes.
`static Coordinate­System`
```replace­Linear­Unit(Coordinate­System cs, Unit<Length> new­Unit)```
Returns a coordinate system derived from the given one but with all linear units replaced by the given unit.
`static Matrix`
```swap­And­Scale­Axes(Coordinate­System source­CS, Coordinate­System target­CS)```
Returns an affine transform between two coordinate systems.

### Methods inherited from class Object

`clone, equals, finalize, get­Class, hash­Code, notify, notify­All, to­String, wait, wait, wait`
• ## Method Details

• ### parseAxisDirection

public static AxisDirection parseAxisDirection(String name) throws IllegalArgumentException
Returns an axis direction code from the given direction name. Names are case-insensitive. They may be:
• Cardinal directions like "north" and "east".
• Inter-cardinal directions "north-east" and "south-south-east", using either `'-'`, `'_'` or spaces as separator between the cardinal points.
• Directions from a pole like "South along 180 deg" and "South along 90° East", using either the `"deg"` or `"°"` symbol. Note that the meridian is not necessarily relative to Greenwich (see `direction­Along­Meridian(…)` for more information).
Parameters:
`name` - the direction name (e.g. "north", "north-east", etc.).
Returns:
the axis direction for the given name.
Throws:
`Illegal­Argument­Exception` - if the given name is not a known axis direction.
• ### directionAlongMeridian

public static AxisDirection directionAlongMeridian(AxisDirection baseDirection, double meridian)
Returns an axis direction from a pole along a meridian. The given meridian is usually, but not necessarily, relative to the Greenwich meridian.
Example: `direction­Along­Meridian(Axis­Direction​.SOUTH, -90)` returns an axis direction for “South along 90°W”.

#### Reference meridian

The reference meridian depends on the context. It is usually the prime meridian of the geodetic datum of the geographic CRS instance that contains (through its coordinate system) the axes having those directions. This policy is consistent with WKT 2 specification §7.5.4(iv).
Parameters:
`base­Direction` - the base direction, which must be `Axis­Direction​.NORTH` or `Axis­Direction​.SOUTH`.
`meridian` - the meridian in degrees, relative to a unspecified (usually Greenwich) prime meridian. Meridians in the East hemisphere are positive and meridians in the West hemisphere are negative.
Returns:
the axis direction along the given meridian.
Since:
0.6
• ### isAlongMeridian

public static boolean isAlongMeridian(AxisDirection direction)
Returns `true` if the given axis direction seems to be a direction along a meridian.
Examples
Axis name Return value
North along 90 deg East `true`
South along 90 deg East `true`
South `false`
East `false`
Note that `true` is not a guarantee that `parse­Axis­Direction(String)` will succeed. But it means that there is reasonable chances of success based on brief inspection of axis name.
Parameters:
`direction` - the direction to test. Can be null.
Returns:
if the given direction is non-null and seems to be a direction along a meridian.
Since:
1.2
• ### angle

public static Angle angle(AxisDirection source, AxisDirection target)
Returns the arithmetic (counterclockwise) angle from the first axis direction to the second direction. This method returns a value between -180° and +180°, or `null` if no angle can be computed.

#### Horizontal directions

For any pair of compass directions which are not opposite directions, a positive angle denotes a right-handed system while a negative angle denotes a left-handed system. Examples:
Note: in the case of directions like “South along 90°W”, the caller is responsible to make sure that the meridians are relative to the same prime meridian. This is the case if the axes are part of the same `Coordinate­System` instance.

#### Horizontal and vertical directions

By convention this method defines the angle from any compass direction to the `UP` vertical direction as 90°, and the angle of any compass direction to the `DOWN` vertical direction as -90°. The sign of those angles gives no indication about whether the coordinate system is right-handed or left-handed. Those angles are returned as instances of `Elevation­Angle`.

All angles are approximations since this method does not take the Earth ellipsoidal or geoidal shape in account.

#### Invariants

For any non-null return value:
• `angle(A, A) = 0°`
• `angle(A, opposite(A)) = ±180°`
• `angle(A, B) = -angle(B, A)`
Parameters:
`source` - the source axis direction.
`target` - the target axis direction.
Returns:
the arithmetic angle (in degrees) of the rotation to apply on a line pointing toward the source direction in order to make it point toward the target direction, or `null` if this value can not be computed.
• ### swapAndScaleAxes

public static Matrix swapAndScaleAxes(CoordinateSystem sourceCS, CoordinateSystem targetCS) throws
Returns an affine transform between two coordinate systems. Only units and axes order (e.g. transforming from (North, West) to (East, North) are taken in account by this method.

#### Conditions

The two coordinate systems must implement the same GeoAPI coordinate system interface. For example if `source­CS` is a `Cartesian­CS`, then `target­CS` must be a `Cartesian­CS` too.
Example: If coordinates in `source­CS` are (x,y) tuples in metres and coordinates in `target­CS` are (-y,x) tuples in centimetres, then the transformation can be performed as below:
```┌      ┐   ┌                ┐ ┌     ┐
│-y(cm)│   │   0  -100    0 │ │ x(m)│
│ x(cm)│ = │ 100     0    0 │ │ y(m)│
│ 1    │   │   0     0    1 │ │ 1   │
└      ┘   └                ┘ └     ┘```
Parameters:
`source­CS` - the source coordinate system.
`target­CS` - the target coordinate system.
Returns:
the conversion from `source­CS` to `target­CS` as an affine transform. Only axis direction and units are taken in account.
Throws:
`Illegal­Argument­Exception` - if the CS are not of the same type, or axes do not match.
`Incommensurable­Exception` - if the units are not compatible, or the conversion is non-linear.
• ### replaceAxes

public static CoordinateSystem replaceAxes(CoordinateSystem cs, AxisFilter filter)
Returns a coordinate system derived from the given one but with a modified list of axes. The axes may be filtered (excluding some axes), reordered or have their unit and direction modified.
Example: for replacing all angular units of a coordinate system to degrees (regardless what the original angular units were) while leaving other kinds of units unchanged, one can write:
```CoordinateSystem cs = ...;
cs = CoordinateSystems.replaceAxes(cs, new AxisFilter() {
@Override
public Unit<?> getUnitReplacement(CoordinateSystemAxis axis, Unit<?> unit) {
if (Units.isAngular(unit)) {
unit = Units.DEGREE;
}
return unit;
}
});```

#### Coordinate system normalization

This method is often used together with `swap­And­Scale­Axes(…)` for normalizing the coordinate values given to a math transform.
Example:
```CoordinateSystem sourceCS = ...;
CoordinateSystem targetCS = ...;
Matrix step1 = swapAndScaleAxes(sourceCS, replaceAxes(sourceCS, AxisConvention.NORMALIZED));
Matrix step2 = ...; // some transform working on coordinates with standard axis order and unit.
Matrix step3 = swapAndScaleAxes(replaceAxes(targetCS, AxisConvention.NORMALIZED), targetCS);```
A rational for normalized axis order and units is explained in the Axis units and direction section in the description of the map projection package.
Parameters:
`cs` - the coordinate system, or `null`.
`filter` - the modifications to apply on coordinate system axes.
Returns:
the modified coordinate system as a new instance, or `cs` if the given coordinate system was null or does not need any change.
Throws:
`Illegal­Argument­Exception` - if the specified coordinate system can not be filtered. It may be because the coordinate system would contain an illegal number of axes, or because an axis would have an unexpected direction or unexpected unit of measurement.
Since:
0.6
• ### replaceLinearUnit

public static CoordinateSystem replaceLinearUnit(CoordinateSystem cs, Unit<Length> newUnit)
Returns a coordinate system derived from the given one but with all linear units replaced by the given unit. Non-linear units (e.g. angular or scale units) are left unchanged.

This convenience method is equivalent to the following code:

```return CoordinateSystems.replaceAxes(cs, new AxisFilter() {
@Override public Unit<?> getUnitReplacement(CoordinateSystemAxis axis, Unit<?> unit) {
return Units.isLinear(unit) ? newUnit : unit;
}
});```
Parameters:
`cs` - the coordinate system in which to replace linear units, or `null`.
`new­Unit` - the new linear unit.
Returns:
the modified coordinate system as a new instance, or `null` if the given `cs` was null, or `cs` if all linear units were already equal to the given one.
Since:
0.7
• ### replaceAngularUnit

public static CoordinateSystem replaceAngularUnit(CoordinateSystem cs, Unit<Angle> newUnit)
Returns a coordinate system derived from the given one but with all angular units replaced by the given unit. Non-angular units (e.g. linear or scale units) are left unchanged.

This convenience method is equivalent to the following code:

```return CoordinateSystems.replaceAxes(cs, new AxisFilter() {
@Override public Unit<?> getUnitReplacement(CoordinateSystemAxis axis, Unit<?> unit) {
return Units.isAngular(unit) ? newUnit : unit;
}
});```
Parameters:
`cs` - the coordinate system in which to replace angular units, or `null`.
`new­Unit` - the new angular unit.
Returns:
the modified coordinate system as a new instance, or `null` if the given `cs` was null, or `cs` if all angular units were already equal to the given one.
Since:
0.7
• ### getAxisDirections

public static  getAxisDirections(CoordinateSystem cs)
Returns the axis directions for the specified coordinate system. This method guarantees that the returned array is non-null and does not contain any null direction.
Parameters:
`cs` - the coordinate system.
Returns:
the axis directions for the specified coordinate system.
Throws:
`Null­Argument­Exception` - if `cs` is null, or one of its axes is null, or a value returned by `Coordinate­System­Axis​.get­Direction()` is null.
Since:
0.8
• ### getEpsgCode

public static Integer getEpsgCode(Class<? extends CoordinateSystem> type, CoordinateSystemAxis... axes)
Returns the EPSG code of a coordinate system using the units and directions of given axes. This method ignores axis metadata (names, abbreviation, identifiers, remarks, etc.). The axis minimum and maximum values are checked only if the range meaning is "wraparound". If no suitable coordinate system is known to Apache SIS, then this method returns `null`.

Current implementation uses a hard-coded list of known coordinate systems; it does not yet scan the EPSG database (this may change in future Apache SIS version). The current list of known coordinate systems is given below.

Known coordinate systems (CS)
EPSG CS type Axis directions Horizontal unit
6424 Ellipsoidal east north degree
6422 Ellipsoidal north east degree
6426 Ellipsoidal east north up degree
6423 Ellipsoidal north east up degree
6427 Ellipsoidal east north up grads
6421 Ellipsoidal north east up grads
6431 Ellipsoidal east north up radian
6430 Ellipsoidal north east up radian
4400 Cartesian east north metre
4500 Cartesian north east metre
4491 Cartesian west north metre
4501 Cartesian north west metre
6503 Cartesian west south metre
6501 Cartesian south west metre
1039 Cartesian east north foot
1029 Cartesian north east foot
4403 Cartesian east north Clarke’s foot
4502 Cartesian north east Clarke’s foot
4497 Cartesian east north US survey foot
Parameters:
`type` - the type of coordinate system for which an EPSG code is desired, as a GeoAPI interface.
`axes` - axes for which a coordinate system EPSG code is desired.
Returns:
EPSG codes for a coordinate system using the given axes (ignoring metadata), or `null` if unknown to this method. Note that a null value does not mean that a more extensive search in the EPSG database would not find a matching coordinate system.
Since:
1.0
• ### getEpsgCode

public static Integer getEpsgCode(Unit<?> unit, AxisDirection... directions)
Returns the EPSG code of a coordinate system using the given unit and axis directions. This convenience method performs the work documented in `get­Epsg­Code(Class, Coordinate­System­Axis...)`, but requiring only a frequently used subset of information. If no suitable coordinate system is known to Apache SIS, then this method returns `null`.

Current implementation uses a hard-coded list of known coordinate systems; it does not yet scan the EPSG database (this may change in future Apache SIS version). The current list of known coordinate systems is documented above.

Parameters:
`unit` - desired unit of measurement. For three-dimensional ellipsoidal coordinate system, this is the unit for the horizontal axes only; the vertical axis is in metres.
`directions` - desired axis directions.
Returns:
EPSG codes for a coordinate system using the given axis directions and unit of measurement, or `null` if unknown to this method. Note that a null value does not mean that a more extensive search in the EPSG database would not find a matching coordinate system.
Since:
0.8