# Interface MathTransformFactory

All Superinterfaces:
`Factory`
All Known Implementing Classes:
`SimpleTransformFactory`

@UML(identifier="CT_MathTransformFactory", specification=OGC_01009) public interface MathTransformFactory extends Factory
Low level factory for creating `MathTransform` instances. Many high level GIS applications will never need to use this factory directly; they can use a coordinate operation factory instead. However, the `MathTransformFactory` interface can be used directly by applications that wish to transform other types of coordinates (e.g. color coordinates, or image pixel coordinates).

A `MathTransform` is an object that actually does the work of applying `Formula` to coordinate values. The math transform does not know or care how the coordinates relate to positions in the real world. This lack of semantics makes implementing `MathTransformFactory` significantly easier than it would be otherwise.

For example, the affine transform applies a matrix to the coordinates without knowing how what it is doing relates to the real world. So if the matrix scales z values by a factor of 1000, then it could be converting metres into millimetres, or it could be converting kilometres into metres.

Because `MathTransform`s have low semantic value (but high mathematical value), programmers who do not have much knowledge of how GIS applications use coordinate systems, or how those coordinate systems relate to the real world, can implement `MathTransformFactory`. The low semantic content of `MathTransform`s also means that they will be useful in applications that have nothing to do with GIS coordinates. For example, a math transform could be used to map color coordinates between different color spaces, such as converting (red, green, blue) colors into (hue, light, saturation) colors.

Since a `MathTransform` does not know what its source and target coordinate systems mean, it is not necessary or desirable for a math transform object to keep information on its source and target coordinate systems.

Since:
1.0
• ## Method Summary

Modifier and Type
Method
Description
`MathTransform`
`createAffineTransform(Matrix matrix)`
Creates an affine transform from a matrix.
`MathTransform`
```createBaseToDerived(CoordinateReferenceSystem baseCRS, ParameterValueGroup parameters, CoordinateSystem derivedCS)```
Creates a parameterized transform from a base CRS to a derived CS.
`MathTransform`
```createConcatenatedTransform(MathTransform transform1, MathTransform transform2)```
Creates a transform by concatenating two existing transforms.
`MathTransform`
`createFromWKT(String wkt)`
Creates a math transform object from a Well-Known Text.
`default MathTransform`
`createFromXML(String xml)`
Deprecated.
This method was defined in OGC 01-009 in anticipation for future normative specification, but no XML format for math transforms have been defined.
`MathTransform`
`createParameterizedTransform(ParameterValueGroup parameters)`
Creates a transform from a group of parameters.
`MathTransform`
```createPassThroughTransform(int firstAffectedCoordinate, MathTransform subTransform, int numTrailingCoordinates)```
Creates a transform which passes through a subset of coordinates to another transform.
`Set<OperationMethod>`
`getAvailableMethods(Class<? extends SingleOperation> type)`
Returns a set of available methods for coordinate operations of the given type.
`ParameterValueGroup`
`getDefaultParameters(String method)`
Returns the default parameter values for a math transform using the given operation method.
`OperationMethod`
`getLastMethodUsed()`
Returns the operation method used by the latest call to a `create(…)` constructor, or `null` if not applicable.

### Methods inherited from interface Factory

`getVendor`
• ## Method Details

• ### getAvailableMethods

getAvailableMethods(Class<? extends SingleOperation> type)
Returns a set of available methods for coordinate operations of the given type. For each element in this set, the operation method name must be a valid argument for `getDefaultParameters(String)`.

The `type` argument can be used for filtering the kind of operations described by the returned `OperationMethod`s. The argument is usually (but not restricted to) one of the following types:

The returned set may conservatively contain more `OperationMethod` elements than requested if this `MathTransformFactory` does not support filtering by the given type.
Parameters:
`type` - `SingleOperation.class` for fetching all operation methods, `Projection.class` for fetching only map projection methods, etc.
Returns:
methods available in this factory for coordinate operations of the given type.
Departure from OGC/ISO abstract specification:
Addition of element not in the ISO/OGC specification This method is not part of the OGC specification. It has been added as a way to publish the capabilities of a factory.
• ### getLastMethodUsed

OperationMethod getLastMethodUsed()
Returns the operation method used by the latest call to a `create(…)` constructor, or `null` if not applicable.

Implementers should document how their implementation behave in a multi-threads environment. For example, some implementations use thread local variables, while other can choose to returns `null` in all cases since `getLastMethodUsed()` is optional.

Invoking `getLastMethodUsed()` can be useful after a call to `createParameterizedTransform(…)`, or after a call to another constructor that delegates its work to `createParameterizedTransform(…)`, for example `createBaseToDerived(…)`.

Returns:
the last method used by a `create(…)` constructor, or `null` if unknown of unsupported.
Departure from OGC/ISO abstract specification:
Addition of element not in the ISO/OGC specification This method is not part of the OGC specification. It has been added because this information appears to be important in some situations. We did not defined a {`MathTransform`, `OperationMethod`} tuple in order to keep `create(…)` simpler in the common case where the operation method is not needed, and for historical reasons (conformance to OGC 01-009).
• ### getDefaultParameters

ParameterValueGroup getDefaultParameters(String method) throws NoSuchIdentifierException
Returns the default parameter values for a math transform using the given operation method. The `method` argument is the name of any `OperationMethod` instance returned by `getAvailableMethods(SingleOperation.class)`. A typical example is "Transverse Mercator").

The parameter group name shall be a method name or identifier that `createParameterizedTransform(ParameterValueGroup)` can recognize without ambiguity.

This function creates new parameter instances at every call. Parameters are intended to be modified by the user before to be given to the above-cited `createParameterizedTransform(…)` constructor.

Parameters:
`method` - the case insensitive name of the coordinate operation method to search for.
Returns:
a new group of parameter values for the `OperationMethod` identified by the given name.
Throws:
`NoSuchIdentifierException` - if there is no method registered for the given name or identifier.
Departure from OGC/ISO abstract specification:
Addition of element not in the ISO/OGC specification This method is part of the GeoAPI mechanism for defining the math transform parameters or deriving other transforms.
• ### createBaseToDerived

MathTransform createBaseToDerived(CoordinateReferenceSystem baseCRS, ParameterValueGroup parameters, CoordinateSystem derivedCS) throws
Creates a parameterized transform from a base CRS to a derived CS. This convenience constructor concatenates the parameterized transform with any other transform required for performing units changes and coordinates swapping, as described in the note on cartographic projections.

In addition, implementations are encouraged to infer the `"semi_major"` and `"semi_minor"` parameter values from the ellipsoid associated to the `baseCRS`, if those parameters are not explicitly given and if they are applicable (typically for cartographic projections). This inference is consistent with the EPSG database model.

Parameters:
`baseCRS` - the source coordinate reference system.
`parameters` - the parameter values for the transform.
`derivedCS` - the target coordinate system.
Returns:
the parameterized transform from `baseCRS` to `derivedCS`, including unit conversions and axis swapping.
Throws:
`NoSuchIdentifierException` - if there is no transform registered for the coordinate operation method.
`FactoryException` - if the object creation failed. This exception is thrown if some required parameter has not been supplied, or has illegal value.
Departure from OGC/ISO abstract specification:
Addition of element not in the ISO/OGC specification This method is part of the GeoAPI mechanism for defining the math transform parameters or deriving other transforms.
• ### createParameterizedTransform

@UML(identifier="createParameterizedTransform", obligation=MANDATORY, specification=OGC_01009) MathTransform createParameterizedTransform(ParameterValueGroup parameters) throws
Creates a transform from a group of parameters. The `OperationMethod` name is inferred from the parameter group name. Example:
``````ParameterValueGroup p = factory.getDefaultParameters("Transverse_Mercator");
p.parameter("semi_major").setValue(6378137.000);
p.parameter("semi_minor").setValue(6356752.314);
MathTransform mt = factory.createParameterizedTransform(p);
``````

#### Note on cartographic projections:

Cartographic projection transforms are used by projected coordinate reference systems to map geographic coordinates (e.g. longitude and latitude) into (x,y) coordinates. These (x,y) coordinates can be imagined to lie on a plane, such as a paper map or a screen. All cartographic projection transforms created through this constructor will have the following properties:
• Converts from (longitude,latitude) coordinates to (x,y).
• All angles are assumed to be degrees, and all distances are assumed to be meters.
• The domain shall be a subset of {[-180,180)×(-90,90)}.
• Axis directions are usually (east, north), but exceptions may exist for some operation methods like "Lambert Conic Conformal (West Orientated)" (EPSG:9826) or "Transverse Mercator (South Orientated)" (EPSG:9808).
Although all cartographic projection transforms must have the properties listed above, many projected coordinate reference systems have different properties. For example, in Europe some projected CRSs use grads instead of degrees, and often the base geographic CRS is (latitude, longitude) instead of (longitude, latitude). This means that the cartographic projected transform is often used as a single step in a series of transforms, where the other steps change units and swap coordinates.

When the change of axis directions is part of the map projection definition as in "Transverse Mercator (South Orientated)", there is a conflict with the above-cited (east, north) directions. In such cases the `createParameterizedTransform(…)` behavior is implementation specific, since different libraries may resolve this conflict in different ways. Users can invoke `createBaseToDerived(…)` instead for more determinist results.

Parameters:
`parameters` - the parameter values.
Returns:
the parameterized transform.
Throws:
`NoSuchIdentifierException` - if there is no transform registered for the coordinate operation method.
`FactoryException` - if the object creation failed. This exception is thrown if some required parameter has not been supplied, or has illegal value.
• ### createAffineTransform

@UML(identifier="createAffineTransform", obligation=MANDATORY, specification=OGC_01009) MathTransform createAffineTransform(Matrix matrix) throws FactoryException
Creates an affine transform from a matrix. If the transform's input dimension is `M`, and output dimension is `N`, then the matrix will have size `[N+1][M+1]`. The +1 in the matrix dimensions allows the matrix to do a shift, as well as a rotation. The `[M][j]` element of the matrix will be the j'th coordinate of the moved origin. The `[i][N]` element of the matrix will be 0 for i less than `M`, and 1 for i equals `M`.
Parameters:
`matrix` - the matrix used to define the affine transform.
Returns:
the affine transform.
Throws:
`FactoryException` - if the object creation failed.
• ### createConcatenatedTransform

@UML(identifier="createConcatenatedTransform", obligation=MANDATORY, specification=OGC_01009) MathTransform createConcatenatedTransform(MathTransform transform1, MathTransform transform2) throws FactoryException
Creates a transform by concatenating two existing transforms. A concatenated transform acts in the same way as applying two transforms, one after the other.

The dimension of the output space of the first transform must match the dimension of the input space in the second transform. If you wish to concatenate more than two transforms, then you can repeatedly use this constructor.

Parameters:
`transform1` - the first transform to apply to points.
`transform2` - the second transform to apply to points.
Returns:
the concatenated transform.
Throws:
`FactoryException` - if the object creation failed.
• ### createPassThroughTransform

@UML(identifier="createPassThroughTransform", obligation=MANDATORY, specification=OGC_01009) MathTransform createPassThroughTransform(int firstAffectedCoordinate, MathTransform subTransform, int numTrailingCoordinates) throws FactoryException
Creates a transform which passes through a subset of coordinates to another transform. This allows transforms to operate on a subset of coordinates. For example, giving (latitude, longitude, height) coordinates, a pass through transform can convert the height values from meters to feet without affecting the (latitude, longitude) values.
Parameters:
`firstAffectedCoordinate` - the lowest index of the affected coordinates.
`subTransform` - transform to use for affected coordinates.
`numTrailingCoordinates` - number of trailing coordinates to pass through. Affected coordinates will range from `firstAffectedCoordinate` inclusive to `dimTarget-numTrailingCoordinates` exclusive.
Returns:
a pass through transform with the following dimensions:
``` Source: firstAffectedCoordinate + subTransform.getDimSource() + numTrailingCoordinates
Target: firstAffectedCoordinate + subTransform.getDimTarget() + numTrailingCoordinates```
Throws:
`FactoryException` - if the object creation failed.
• ### createFromXML

Deprecated.
This method was defined in OGC 01-009 in anticipation for future normative specification, but no XML format for math transforms have been defined.
Creates a math transform object from a XML string.
Parameters:
`xml` - math transform encoded in XML format.
Returns:
the math transform (never `null`).
Throws:
`FactoryException` - if the object creation failed.
• ### createFromWKT

Creates a math transform object from a Well-Known Text. The definition for WKT is shown using Extended Backus Naur Form (EBNF).
Parameters:
`wkt` - math transform encoded in Well-Known Text format.
Returns:
the math transform (never `null`).
Throws:
`FactoryException` - if the Well-Known Text can't be parsed, or if the math transform creation failed from some other reason.