org.apache.sis.referencing.operation.transform

## Class InterpolatedTransform

- Object
- - FormattableObject
  - - AbstractMathTransform
    - - DatumShiftTransform
      - - InterpolatedTransform

- All Implemented Interfaces:
    Serializable, Parameterized, LenientComparable, MathTransform

      public class InterpolatedTransform
      extends DatumShiftTransform

  Transforms between two CRS by performing translations interpolated from a grid file. The source and target coordinate reference systems are typically, but not necessarily, two-dimensional geographic CRS. The actual number of dimensions is determined by `DatumShiftGrid​.getTranslationDimensions()`.
  Example: this transform is used for example with NADCON and NTv2 datum shift grids.
  Input and output coordinates
  First, "real world" input coordinates (x,y) are converted to grid coordinates (gridX, gridY), which are zero-based indices in the two-dimensional grid. This conversion is applied by an affine transform before to be passed to the `transform` methods of this `InterpolatedTransform` class.

  Translation vectors are stored in the datum shift grid at the specified grid indices. If the grid indices are non-integer values, then the translations are interpolated using a bilinear interpolation. If the grid indices are outside the grid domain ([0 … width-2] × [0 … height-2] where width and height are the number of columns and rows in the grid), then the translations are extrapolated. The translation is finally added to the input coordinates.

  The input and output coordinates can have any number of dimensions, provided that they are the same than the number of translation dimensions. However current implementation uses only the two first dimensions for interpolations in the grid.

  Since:
    0.7
  See Also:
    `DatumShiftGrid`, `LocalizationGridBuilder`, Serialized Form

  Defined in the `sis-referencing` module

- - ### Constructor Summary

    Constructors
    Modifier | Constructor and Description
    --- | ---
    `protected` | `InterpolatedTransform(DatumShiftGrid<T,T> grid)` Creates a transform for the given interpolation grid.

  - ### Method Summary

    All Methods Static Methods Instance Methods Concrete Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected int` | `computeHashCode()` Computes a hash value for this transform.
    `static <T extends Quantity<T>> MathTransform` | `createGeodeticTransformation(MathTransformFactory factory, DatumShiftGrid<T,T> grid)` Creates a transformation between two geodetic CRS.
    `boolean` | `equals(Object object, ComparisonMode mode)` Compares the specified object with this math transform for equality.
    `int` | `getSourceDimensions()` Returns the number of input dimensions.
    `int` | `getTargetDimensions()` Returns the number of target dimensions.
    `MathTransform` | `inverse()` Returns the inverse of this interpolated transform.
    `Matrix` | `transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate)` Applies the datum shift on a coordinate and optionally returns the derivative at that location.
    `void` | `transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)` Transforms an arbitrary amount of coordinates.

    - ### Methods inherited from class DatumShiftTransform

      `getContextualParameters, getParameterValues`

    - ### Methods inherited from class AbstractMathTransform

      `derivative, equals, formatTo, getParameterDescriptors, hashCode, isIdentity, transform, transform, transform, transform, tryConcatenate`

    - ### Methods inherited from class FormattableObject

      `print, toString, toString, toWKT`

    - ### Methods inherited from class Object

      `clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

    - ### Methods inherited from interface MathTransform

      `toWKT`

- - ### Constructor Detail

    - #### InterpolatedTransform

          protected InterpolatedTransform(DatumShiftGrid<T,T> grid)
                                   throws NoninvertibleMatrixException

      Creates a transform for the given interpolation grid. This `InterpolatedTransform` class works with ordinate values in units of grid cell For example input coordinate (4,5) is the position of the center of the cell at grid index (4,5). The output units are the same than the input units.

      For converting geodetic coordinates, `InterpolatedTransform` instances need to be concatenated with the following affine transforms:

      - Normalization before `InterpolatedTransform` for converting the geodetic coordinates into grid coordinates.
      - Denormalization after `InterpolatedTransform` for converting grid coordinates into geodetic coordinates.
      After `InterpolatedTransform` construction, the full conversion chain including the above affine transforms can be created by `DatumShiftTransform​.getContextualParameters().completeTransform(factory, this)}`.
      Type Parameters:
        `T` - dimension of the coordinate and the translation unit.
      Parameters:
        `grid` - the grid of datum shifts from source to target datum.
      Throws:
        `NoninvertibleMatrixException` - if the conversion from geodetic coordinates to grid indices can not be inverted.
      See Also:
        `createGeodeticTransformation(MathTransformFactory, DatumShiftGrid)`

  - ### Method Detail

    - #### createGeodeticTransformation

          public static <T extends Quantity<T>> MathTransform createGeodeticTransformation(MathTransformFactory factory,
                                                                                           DatumShiftGrid<T,T> grid)
                                                                                    throws FactoryException

      Creates a transformation between two geodetic CRS. This factory method combines the `InterpolatedTransform` instance with the steps needed for converting values between geodetic and grid coordinates.
      Unit of measurement
      The unit of measurement is determined by `DatumShiftGrid​.getCoordinateUnit()`:
      - If the datum shift unit is angular, then the transform will work with input and output coordinates in degrees of angle.
      - If the datum shift unit is linear, then the transform will work with input and output coordinates in metres.
      - If the datum shift unit is temporal, then the transform will work with input and output coordinates in seconds.
      - Generally for all units other than angular, the transform will work with input and output coordinates in the unit given by `Unit​.getSystemUnit()`.
      Type Parameters:
        `T` - dimension of the coordinate and the translation unit.
      Parameters:
        `factory` - the factory to use for creating the transform.
        `grid` - the grid of datum shifts from source to target datum. The `DatumShiftGrid​.interpolateInCell(…)` method shall compute translations from source to target as ratio of offsets divided by cell sizes.
      Returns:
        the transformation between geodetic coordinates.
      Throws:
        `FactoryException` - if an error occurred while creating a transform.

    - #### getSourceDimensions

          public final int getSourceDimensions()

      Returns the number of input dimensions. This fixed to `DatumShiftGrid​.getTranslationDimensions()`.
      Specified by:
        `getSourceDimensions` in interface `MathTransform`
      Specified by:
        `getSourceDimensions` in class `AbstractMathTransform`
      Returns:
        the dimension of input points.
      See Also:
        `DefaultOperationMethod​.getSourceDimensions()`

    - #### getTargetDimensions

          public final int getTargetDimensions()

      Returns the number of target dimensions. This fixed to `DatumShiftGrid​.getTranslationDimensions()`.
      Specified by:
        `getTargetDimensions` in interface `MathTransform`
      Specified by:
        `getTargetDimensions` in class `AbstractMathTransform`
      Returns:
        the dimension of output points.
      See Also:
        `DefaultOperationMethod​.getTargetDimensions()`

    - #### transform

          public Matrix transform(double[] srcPts,
                                  int srcOff,
                                  double[] dstPts,
                                  int dstOff,
                                  boolean derivate)
                           throws TransformException

      Applies the datum shift on a coordinate and optionally returns the derivative at that location.
      Specified by:
        `transform` in class `AbstractMathTransform`
      Parameters:
        `srcPts` - the array containing the source coordinate (can not be `null`).
        `srcOff` - the offset to the point to be transformed in the source array.
        `dstPts` - the array into which the transformed coordinate is returned. May be the same than `srcPts`. May be `null` if only the derivative matrix is desired.
        `dstOff` - the offset to the location of the transformed point that is stored in the destination array.
        `derivate` - `true` for computing the derivative, or `false` if not needed.
      Returns:
        the matrix of the transform derivative at the given source position, or `null` if the `derivate` argument is `false`.
      Throws:
        `TransformException` - if the point can not be transformed or if a problem occurred while calculating the derivative.
      See Also:
        `AbstractMathTransform​.derivative(DirectPosition)`, `AbstractMathTransform​.transform(DirectPosition, DirectPosition)`, `MathTransforms​.derivativeAndTransform(MathTransform, double[], int, double[], int)`

    - #### transform

          public void transform(double[] srcPts,
                                int srcOff,
                                double[] dstPts,
                                int dstOff,
                                int numPts)
                         throws TransformException

      Transforms an arbitrary amount of coordinates.
      Specified by:
        `transform` in interface `MathTransform`
      Overrides:
        `transform` in class `AbstractMathTransform`
      Parameters:
        `srcPts` - the array containing the source point coordinates.
        `srcOff` - the offset to the first point to be transformed in the source array.
        `dstPts` - the array into which the transformed point coordinates are returned. May be the same than `srcPts`.
        `dstOff` - the offset to the location of the first transformed point that is stored in the destination array.
        `numPts` - the number of point objects to be transformed.
      Throws:
        `TransformException` - if a point can not be transformed.

    - #### inverse

          public MathTransform inverse()

      Returns the inverse of this interpolated transform. The source ellipsoid of the returned transform will be the target ellipsoid of this transform, and conversely.
      Specified by:
        `inverse` in interface `MathTransform`
      Overrides:
        `inverse` in class `AbstractMathTransform`
      Returns:
        a transform from the target ellipsoid to the source ellipsoid of this transform.

    - #### computeHashCode

          protected int computeHashCode()

      Computes a hash value for this transform. This method is invoked by `AbstractMathTransform​.hashCode()` when first needed.
      Overrides:
        `computeHashCode` in class `DatumShiftTransform`
      Returns:
        the hash code value. This value may change between different execution of the Apache SIS library.

    - #### equals

          public boolean equals(Object object,
                                ComparisonMode mode)

      Compares the specified object with this math transform for equality.
      Specified by:
        `equals` in interface `LenientComparable`
      Overrides:
        `equals` in class `DatumShiftTransform`
      Parameters:
        `object` - the object to compare with this transform.
        `mode` - the strictness level of the comparison. Default to `STRICT`.
      Returns:
        `true` if the given object is considered equals to this math transform.
      See Also:
        `Utilities​.deepEquals(Object, Object, ComparisonMode)`

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