 All Known Subinterfaces:
MathTransform1D
,MathTransform2D
MathTransform
is an object
that actually does the work of applying a formula to coordinate values.
The math transform does not know or care how the coordinates relate to positions in the real world.
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 they have low semantic value (but high mathematical value), MathTransform
s can be used
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.
Application to coordinate operations
When used for coordinate operations, this interface transforms coordinate value for a point given in the source coordinate reference system to coordinate value for the same point in the target coordinate reference system. In a conversion, the transformation is accurate to within the limitations of the computer making the calculations.
 In a transformation, where some of the operational parameters are derived from observations, the transformation is accurate to within the limitations of those observations.
CoordinateOperation
interface,
and use the contained math transform object whenever it wishes to perform a transform. Since:
 1.0
 See Also:

Method Summary
Modifier and TypeMethodDescriptionderivative
(DirectPosition point) Gets the derivative of this transform at a point.int
Returns the number of dimensions of input points.int
Returns the number of dimensions of output points.default MathTransform
inverse()
Returns the inverse transform of this object.boolean
Tests whether this transform does not move any points.default String
toWKT()
Returns a WellKnown Text (WKT) for this object.void
transform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Transforms an array of doubleprecision coordinate tuples.void
transform
(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) Transforms an array of doubleprecision coordinate tuples, then converts to singleprecision.void
transform
(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Converts an array of singleprecision coordinate tuples to double precision, then transform.void
transform
(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) Transforms an array of singleprecision coordinate tuples.default int
transform
(DoubleBuffer srcPts, DoubleBuffer dstPts) Transforms a buffer of doubleprecision coordinate tuples.default int
transform
(DoubleBuffer srcPts, FloatBuffer dstPts) Transforms coordinate tuples and converts the result to singleprecision.default int
transform
(FloatBuffer srcPts, DoubleBuffer dstPts) Converts simpleprecision coordinate tuples to doubleprecision and transform them.default int
transform
(FloatBuffer srcPts, FloatBuffer dstPts) Transforms a buffer of singleprecision coordinate tuples.transform
(DirectPosition ptSrc, DirectPosition ptDst) Transforms the specifiedptSrc
and stores the result inptDst
.

Method Details

getSourceDimensions
Returns the number of dimensions of input points. Returns:
 the number of dimensions of input points.

getTargetDimensions
Returns the number of dimensions of output points. Returns:
 the number of dimensions of output points.

transform
@UML(identifier="transform", specification=OGC_01009) DirectPosition transform(DirectPosition ptSrc, DirectPosition ptDst) throws MismatchedDimensionException, TransformException Transforms the specifiedptSrc
and stores the result inptDst
. IfptDst
isnull
, a newDirectPosition
object is allocated and then the result of the transformation is stored in this object. In either case,ptDst
, which contains the transformed point, is returned for convenience. IfptSrc
andptDst
are the same object, the input point is correctly overwritten with the transformed point. Parameters:
ptSrc
 the specified coordinate point to be transformed.ptDst
 the specified coordinate point that stores the result of transformingptSrc
, ornull
. Returns:
 the coordinate point after transforming
ptSrc
and storing the result inptDst
, or a newly created point ifptDst
was null.  Throws:
MismatchedDimensionException
 ifptSrc
orptDst
doesn't have the expected dimension.TransformException
 if the point cannot be transformed.

transform
@UML(identifier="transformList", specification=OGC_01009) void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws TransformException Transforms an array of doubleprecision coordinate tuples. This method is provided for efficiently transforming many points. The supplied array will contain packed coordinate tuples. For example, if the source dimension is 3, then the coordinates will be packed in this order: (x₀,y₀,z₀, x₁,y₁,z₁ …). Parameters:
srcPts
 the array containing the source coordinate tuples.srcOff
 the offset to the first tuple to be transformed in the source array.dstPts
 the array into which the transformed coordinate tuples are stored. May be the same array assrcPts
.dstOff
 the offset to the first transformed coordinate that is stored in the destination array.numPts
 the number of coordinate tuples to be transformed. Throws:
TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. See Also:

transform
void transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) throws TransformException Transforms an array of singleprecision coordinate tuples. This method is provided for efficiently transforming many points. The supplied array will contain packed coordinate tuples. For example, if the source dimension is 3, then the coordinates will be packed in this order: (x₀,y₀,z₀, x₁,y₁,z₁ …).Note: while the source and destination arrays use singleprecision floating point numbers, implementation should perform intermediate calculations in doubleprecision.
 Parameters:
srcPts
 the array containing the source coordinate tuples.srcOff
 the offset to the first tuple to be transformed in the source array.dstPts
 the array into which the transformed coordinate tuples are stored. May be the same array assrcPts
.dstOff
 the offset to the first transformed coordinate that is stored in the destination array.numPts
 the number of coordinate tuples to be transformed. Throws:
TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. See Also:

transform
void transform(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws TransformException Converts an array of singleprecision coordinate tuples to double precision, then transform. This method is provided for efficiently transforming many points. The supplied array will contain packed coordinate tuples. For example, if the source dimension is 3, then the coordinates will be packed in this order: (x₀,y₀,z₀, x₁,y₁,z₁ …). Parameters:
srcPts
 the array containing the source coordinate tuples.srcOff
 the offset to the first tuple to be transformed in the source array.dstPts
 the array into which the transformed coordinate tuples are stored. May be the same array assrcPts
.dstOff
 the offset to the first transformed coordinate that is stored in the destination array.numPts
 the number of coordinate tuples to be transformed. Throws:
TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. See Also:

transform
void transform(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) throws TransformException Transforms an array of doubleprecision coordinate tuples, then converts to singleprecision. This method is provided for efficiently transforming many points. The supplied array will contain packed coordinate tuples. For example, if the source dimension is 3, then the coordinates will be packed in this order: (x₀,y₀,z₀, x₁,y₁,z₁ …). Parameters:
srcPts
 the array containing the source coordinate tuples.srcOff
 the offset to the first tuple to be transformed in the source array.dstPts
 the array into which the transformed coordinate tuples are stored. May be the same array assrcPts
.dstOff
 the offset to the first transformed coordinate that is stored in the destination array.numPts
 the number of coordinate tuples to be transformed. Throws:
TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. See Also:

transform
Transforms a buffer of doubleprecision coordinate tuples. This method is provided for efficiently transforming many points, either in Java heap or in the memory of native applications (e.g. C/C++). The supplied buffer will contain packed coordinate tuples. For example, if the source dimension is 3, then the coordinates will be packed in this order: (x₀,y₀,z₀, x₁,y₁,z₁ …).The first coordinate to transform is read at index
srcPts.position()
and the first transformed coordinate will be stored at indexdstPts.position()
. The maximal number of coordinate tuples to transform is:int numPts = Math.min(srcPts.remaining() / getSourceDimensions(), dstPts.remaining() / getTargetDimensions());
If above maximum is zero, then this method returns 0. Otherwise, this method shall transform at least one coordinate tuple. It may transform any number of coordinate tuples between 1 and the abovecited maximum, at implementation choice. On success, the position of the source and destination buffer will be set to the index after the last coordinate read and stored respectively. If an exception has been thrown, then the buffer positions are undetermined.
Default implementation
The default implementation delegates totransform(double[], int, double[], int, int)
. Therefore, the default implementation supports only buffers on Java heap. Implementations should override this method if they want to support native heaps. Parameters:
srcPts
 the buffer containing the source coordinate tuples.dstPts
 the buffer into which the transformed coordinate tuples are stored. May be the same buffer assrcPts
. Returns:
 number of coordinate tuples actually transformed.
 Throws:
UnsupportedOperationException
 if this implementation supports only buffers backed by accessible Java arrays, and at least one buffer is backed by native memory.ReadOnlyBufferException
 if the destination buffer is readonly.TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. Since:
 3.1
 See Also:

transform
Transforms a buffer of singleprecision coordinate tuples. This method follows the same contract astransform(DoubleBuffer, DoubleBuffer)
, except that the floatingpoint precision of source and destination buffers are different. See the doubleprecision variant of this method for details.Default implementation
The default implementation delegates totransform(float[], int, float[], int, int)
. Therefore, the default implementation supports only buffers on Java heap. Implementations should override this method if they want to support native heaps. Parameters:
srcPts
 the buffer containing the source coordinate tuples.dstPts
 the buffer into which the transformed coordinate tuples are stored. May be the same buffer assrcPts
. Returns:
 number of coordinate tuples actually transformed.
 Throws:
UnsupportedOperationException
 if this implementation supports only buffers backed by accessible Java arrays, and at least one buffer is backed by native memory.ReadOnlyBufferException
 if the destination buffer is readonly.TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Float.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. Since:
 3.1
 See Also:

transform
Converts simpleprecision coordinate tuples to doubleprecision and transform them. This method follows the same contract astransform(DoubleBuffer, DoubleBuffer)
, except that the floatingpoint precision of the source buffer is different. See the doubleprecision variant of this method for details.Default implementation
The default implementation delegates totransform(float[], int, double[], int, int)
. Therefore, the default implementation supports only buffers on Java heap. Implementations should override this method if they want to support native heaps. Parameters:
srcPts
 the buffer containing the source coordinate tuples.dstPts
 the buffer into which the transformed coordinate tuples are stored. May be the same buffer assrcPts
. Returns:
 number of coordinate tuples actually transformed.
 Throws:
UnsupportedOperationException
 if this implementation supports only buffers backed by accessible Java arrays, and at least one buffer is backed by native memory.ReadOnlyBufferException
 if the destination buffer is readonly.TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. Since:
 3.1
 See Also:

transform
Transforms coordinate tuples and converts the result to singleprecision. This method follows the same contract astransform(DoubleBuffer, DoubleBuffer)
, except that the floatingpoint precision of the destination buffer is different. See the doubleprecision variant of this method for details.Default implementation
The default implementation delegates totransform(double[], int, float[], int, int)
. Therefore, the default implementation supports only buffers on Java heap. Implementations should override this method if they want to support native heaps. Parameters:
srcPts
 the buffer containing the source coordinate tuples.dstPts
 the buffer into which the transformed coordinate tuples are stored. May be the same buffer assrcPts
. Returns:
 number of coordinate tuples actually transformed.
 Throws:
UnsupportedOperationException
 if this implementation supports only buffers backed by accessible Java arrays, and at least one buffer is backed by native memory.ReadOnlyBufferException
 if the destination buffer is readonly.TransformException
 if a point cannot be transformed. Some implementations may stop at the first failure, while some other implementations may fill the untransformable points with Float.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform tothis
. Since:
 3.1
 See Also:

derivative
@UML(identifier="derivative", specification=OGC_01009) Matrix derivative(DirectPosition point) throws MismatchedDimensionException, TransformException Gets the derivative of this transform at a point. The derivative is the matrix of the nontranslating portion of the approximate affine map at the point. The matrix will have dimensions corresponding to the source and target coordinate systems. If the input dimension is M, and the output dimension is N, then the matrix will have size N×M. The elements of the matrix {e_{n,m} : n=0 … (N1)} form a vector in the output space which is parallel to the displacement caused by a small change in the m'th coordinate in the input space.For example, if the input dimension is 4 and the output dimension is 3, then a small displacement (x₀, x₁, x₂, x₃) in the input space will result in a displacement (y₀, y₁, y₂) in the output space computed as below (e_{n,m} are the matrix elements):
┌ ┐ ┌ ┐ ┌ ┐ │ y₀ │ │ e₀₀ e₀₁ e₀₂ e₀₃ │ │ x₀ │ │ y₁ │ = │ e₁₀ e₁₁ e₁₂ e₁₃ │ │ x₁ │ │ y₂ │ │ e₂₀ e₂₁ e₂₂ e₂₃ │ │ x₂ │ └ ┘ └ ┘ │ x₃ │ └ ┘
 Parameters:
point
 the coordinate point where to evaluate the derivative. Null value is accepted only if the derivative is the same everywhere. For example, affine transform accept null value since they produces identical derivative no matter the coordinate value. But most map projection will requires a nonnull value. Returns:
 the derivative at the specified point (never
null
). This method never returns an internal object: changing the matrix will not change the state of this math transform.  Throws:
NullPointerException
 if the derivative depends on coordinate andpoint
isnull
.MismatchedDimensionException
 ifpoint
does not have the expected dimension.TransformException
 if the derivative cannot be evaluated at the specified point.

inverse
@UML(identifier="inverse", specification=OGC_01009) default MathTransform inverse() throws NoninvertibleTransformExceptionReturns the inverse transform of this object. The target of the inverse transform is the source of the original. The source of the inverse transform is the target of the original. Using the original transform followed by the inverse's transform will result in an identity map on the source coordinate space, when allowances for error are made. This method may fail if the transform is not one to one. However, all cartographic projections should succeed. Returns:
 the inverse transform.
 Throws:
NoninvertibleTransformException
 if the transform cannot be inverted. See Also:

isIdentity
Tests whether this transform does not move any points. Returns:
true
if thisMathTransform
is an identity transform;false
otherwise. See Also:

toWKT
Returns a WellKnown Text (WKT) for this object. Version 1 of WellKnow Text is defined in OGC 01009. This operation may fail if unsupported or if this instance contains elements that do not have WKT representation. Returns:
 the WellKnown Text (WKT) for this object.
 Throws:
UnsupportedOperationException
 if this object cannot be formatted as WKT. See Also:
