# Class InterpolatedTransform

Object
FormattableObject
AbstractMathTransform
DatumShiftTransform
InterpolatedTransform

All Implemented Interfaces:
  `Serializable, Parameterized, LenientComparable, Printable, 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()`.

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-1] × [0 … height-1] 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

- ## Constructor Summary

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

- ## Method Summary

  Modifier and Type
  Method
  Description
  `static <T extends Quantity<T>>
  MathTransform`
  `createGeodeticTransformation(MathTransformFactory factory, DatumShiftGrid<T,T> grid)`
  Creates a transformation between two geodetic CRS.
  `final DatumShiftGrid<?,?>`
  `getShiftGrid()`
  Returns the grid of datum shifts specified at construction time.
  `final int`
  `getSourceDimensions()`
  Returns the number of input dimensions.
  `final 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 tuple and optionally returns the derivative at that location.
  `void`
  `transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)`
  Transforms an arbitrary number of coordinate tuples.

  ### Methods inherited from class DatumShiftTransform

  `getContextualParameters, getParameterValues`

  ### Methods inherited from class AbstractMathTransform

  `derivative, equals, formatTo, getDomain, 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 Details

  - ### InterpolatedTransform

    protected <T extends Quantity<T>> InterpolatedTransform(DatumShiftGrid<T,T> grid) throws NoninvertibleMatrixException
    Creates a transform for the given interpolation grid. This `InterpolatedTransform` class works with coordinate values in units of grid cell For example, input coordinates (4,5) is the position of the center of the cell at grid index (4,5). The output units are the same as 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 tuples 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 cannot be inverted.
    See Also:
      - `createGeodeticTransformation(MathTransformFactory, DatumShiftGrid)`

- ## Method Details

  - ### 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 tuples 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.

  - ### getShiftGrid

    public final DatumShiftGrid<?,?> getShiftGrid()
    Returns the grid of datum shifts specified at construction time.
    Returns:
      the grid of datum shifts from source to target datum.
    Since:
      1.1

  - ### 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 tuple and optionally returns the derivative at that location.
    Specified by:
      `transform` in class `AbstractMathTransform`
    Parameters:
      `srcPts` - the array containing the source coordinates (cannot be `null`).
      `srcOff` - the offset to the point to be transformed in the source array.
      `dstPts` - the array into which the transformed coordinates is returned. May be the same as `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 cannot 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 number of coordinate tuples.
    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 as `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 cannot 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.