org.apache.sis.referencing.operation.transform

## Class InterpolatedMolodenskyTransform

- Object
- - FormattableObject
  - - AbstractMathTransform
    - - DatumShiftTransform
      - - InterpolatedMolodenskyTransform

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

      public class InterpolatedMolodenskyTransform
      extends DatumShiftTransform

  Transforms between two geographic CRS by performing geocentric translations interpolated from a grid file, but using Molodensky approximation. This transformation is conceptually defined as a translation in geocentric coordinates as performed by `InterpolatedGeocentricTransform`, but uses the Molodensy (non-abridged) approximation for performance reasons. Errors are less than 3 centimetres for the "France geocentric interpolation" (ESPG:9655). By comparison, the finest accuracy reported in the grid file for France is 5 centimetres.
  Algorithm
  This class transforms two- or three- dimensional coordinates from a geographic CRS to another geographic CRS. The changes between source and target coordinates are small (usually less than 400 metres), but vary for every position. Those changes are provided in a datum shift grid, usually loaded from one or two files.

  Many datum shift grids like NADCON and NTv2 apply the interpolated translations directly on geographic coordinates. This relatively simple case is handled by `InterpolatedTransform`. But in the `InterpolatedMolodenskyTransform` case, the interpolated translations are rather the (tX, tY, tZ) parameters of a Molodensky transformation.

  Since:
    0.7
  See Also:
    `InterpolatedGeocentricTransform`, Serialized Form

  Defined in the `sis-referencing` module

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `protected double` | `eccentricitySquared` The square of eccentricity of the source ellipsoid.
    `protected double` | `semiMajor` Semi-major axis length (a) of the source ellipsoid.
    `protected double` | `tX` Shift along the geocentric X axis (toward prime meridian) in units of the semi-major axis of the source ellipsoid.
    `protected double` | `tY` Shift along the geocentric Y axis (toward 90°E) in units of the semi-major axis of the source ellipsoid.
    `protected double` | `tZ` Shift along the geocentric Z axis (toward north pole) in units of the semi-major axis of the source ellipsoid.

  - ### Constructor Summary

    Constructors
    Modifier | Constructor and Description
    --- | ---
    `protected` | `InterpolatedMolodenskyTransform(Ellipsoid source, boolean isSource3D, Ellipsoid target, boolean isTarget3D, DatumShiftGrid<Angle,Length> grid)` Creates a transform from the specified parameters.

  - ### 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 MathTransform` | `createGeodeticTransformation(MathTransformFactory factory, Ellipsoid source, boolean isSource3D, Ellipsoid target, boolean isTarget3D, DatumShiftGrid<Angle,Length> grid)` Creates a transformation between two geographic CRS.
    `boolean` | `equals(Object object, ComparisonMode mode)` Compares the specified object with this math transform for equality.
    `ParameterDescriptorGroup` | `getParameterDescriptors()` Returns a description of the internal parameters of this `InterpolatedMolodenskyTransform` transform.
    `ParameterValueGroup` | `getParameterValues()` Returns a copy of internal parameter values of this transform.
    `int` | `getSourceDimensions()` Gets the dimension of input points.
    `int` | `getTargetDimensions()` Gets the dimension of output points.
    `MathTransform` | `inverse()` Returns the inverse of this interpolated Molodensky transform.
    `Matrix` | `transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate)` Transforms the (λ,φ) or (λ,φ,h) coordinates between two geographic CRS, and optionally returns the derivative at that location.
    `void` | `transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)` Transforms the (λ,φ) or (λ,φ,h) coordinates between two geographic CRS.

    - ### Methods inherited from class DatumShiftTransform

      `getContextualParameters`

    - ### Methods inherited from class AbstractMathTransform

      `derivative, equals, formatTo, 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`

- - ### Field Detail

    - #### tX

          protected final double tX

      Shift along the geocentric X axis (toward prime meridian) in units of the semi-major axis of the source ellipsoid.
      See Also:
        `BursaWolfParameters​.tX`

    - #### tY

          protected final double tY

      Shift along the geocentric Y axis (toward 90°E) in units of the semi-major axis of the source ellipsoid.
      See Also:
        `BursaWolfParameters​.tY`

    - #### tZ

          protected final double tZ

      Shift along the geocentric Z axis (toward north pole) in units of the semi-major axis of the source ellipsoid.
      See Also:
        `BursaWolfParameters​.tZ`

    - #### semiMajor

          protected final double semiMajor

      Semi-major axis length (a) of the source ellipsoid.

    - #### eccentricitySquared

          protected final double eccentricitySquared

      The square of eccentricity of the source ellipsoid. This can be computed by ℯ² = (a²-b²)/a² where a is the semi-major axis length and b is the semi-minor axis length.
      See Also:
        `DefaultEllipsoid​.getEccentricitySquared()`

  - ### Constructor Detail

    - #### InterpolatedMolodenskyTransform

          protected InterpolatedMolodenskyTransform(Ellipsoid source,
                                                    boolean isSource3D,
                                                    Ellipsoid target,
                                                    boolean isTarget3D,
                                                    DatumShiftGrid<Angle,Length> grid)

      Creates a transform from the specified parameters. This `InterpolatedMolodenskyTransform` class expects ordinate values in the following order and units:
      1. longitudes in radians relative to the prime meridian (usually Greenwich),
      2. latitudes in radians,
      3. optionally heights above the ellipsoid, in same units than the source ellipsoid axes.
      For converting geographic coordinates in degrees, `InterpolatedMolodenskyTransform` instances need to be concatenated with the following affine transforms:
      - Normalization before `InterpolatedMolodenskyTransform`:
        - Conversion of (λ,φ) from degrees to radians.
      - Denormalization after `InterpolatedMolodenskyTransform`:
        - Conversion of (λ,φ) from radians to degrees.
      After `InterpolatedMolodenskyTransform` construction, the full conversion chain including the above affine transforms can be created by `DatumShiftTransform​.getContextualParameters().completeTransform(factory, this)}`.
      Parameters:
        `source` - the source ellipsoid.
        `isSource3D` - `true` if the source coordinates have a height.
        `target` - the target ellipsoid.
        `isTarget3D` - `true` if the target coordinates have a height.
        `grid` - the grid of datum shifts from source to target datum. The `DatumShiftGrid​.interpolateInCell(…)` method shall compute (ΔX, ΔY, ΔZ) translations from source to target in the unit of source ellipsoid axes.
      See Also:
        `createGeodeticTransformation(MathTransformFactory, Ellipsoid, boolean, Ellipsoid, boolean, DatumShiftGrid)`

  - ### Method Detail

    - #### createGeodeticTransformation

          public static MathTransform createGeodeticTransformation(MathTransformFactory factory,
                                                                   Ellipsoid source,
                                                                   boolean isSource3D,
                                                                   Ellipsoid target,
                                                                   boolean isTarget3D,
                                                                   DatumShiftGrid<Angle,Length> grid)
                                                            throws FactoryException

      Creates a transformation between two geographic CRS. This factory method combines the `InterpolatedMolodenskyTransform` instance with the steps needed for converting values between degrees to radians. The transform works with input and output coordinates in the following units:
      1. longitudes in degrees relative to the prime meridian (usually Greenwich),
      2. latitudes in degrees,
      3. optionally heights above the ellipsoid, in same units than the source ellipsoids axes.
      Note however that the given `grid` instance shall expect geographic coordinates (λ,φ) in radians.
      Parameters:
        `factory` - the factory to use for creating the transform.
        `source` - the source ellipsoid.
        `isSource3D` - `true` if the source coordinates have a height.
        `target` - the target ellipsoid.
        `isTarget3D` - `true` if the target coordinates have a height.
        `grid` - the grid of datum shifts from source to target datum. The `DatumShiftGrid​.interpolateInCell(…)` method shall compute (ΔX, ΔY, ΔZ) translations from source to target in the unit of source ellipsoid axes.
      Returns:
        the transformation between geographic coordinates in degrees.
      Throws:
        `FactoryException` - if an error occurred while creating a transform.

    - #### transform

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

      Transforms the (λ,φ) or (λ,φ,h) coordinates between two geographic CRS, 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 the (λ,φ) or (λ,φ,h) coordinates between two geographic CRS. This method performs the same work than the above `transform(…)` method, but on an arbitrary amount of coordinates and without computing derivative.
      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 Molodensky 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.

    - #### getParameterDescriptors

          @Debug
          public ParameterDescriptorGroup getParameterDescriptors()

      Returns a description of the internal parameters of this `InterpolatedMolodenskyTransform` transform. The returned group contains parameters for the source ellipsoid semi-axis lengths and the differences between source and target ellipsoid parameters.
      Note: this method is mostly for debugging purposes since the isolation of non-linear parameters in this class is highly implementation dependent. Most GIS applications will instead be interested in the contextual parameters.
      Specified by:
        `getParameterDescriptors` in interface `Parameterized`
      Overrides:
        `getParameterDescriptors` in class `AbstractMathTransform`
      Returns:
        a description of the internal parameters.
      See Also:
        `DefaultOperationMethod​.getParameters()`

    - #### getParameterValues

          @Debug
          public ParameterValueGroup getParameterValues()

      Returns a copy of internal parameter values of this transform. The returned group contains parameters for the source ellipsoid semi-axis lengths and the differences between source and target ellipsoid parameters.
      Note: this method is mostly for debugging purposes since the isolation of non-linear parameters in this class is highly implementation dependent. Most GIS applications will instead be interested in the contextual parameters.
      Specified by:
        `getParameterValues` in interface `Parameterized`
      Overrides:
        `getParameterValues` in class `DatumShiftTransform`
      Returns:
        a copy of the internal parameter values for this transform.
      See Also:
        `AbstractMathTransform​.getContextualParameters()`, `AbstractSingleOperation​.getParameterValues()`

    - #### getSourceDimensions

          public final int getSourceDimensions()

      Gets the dimension of input points.
      Specified by:
        `getSourceDimensions` in interface `MathTransform`
      Specified by:
        `getSourceDimensions` in class `AbstractMathTransform`
      Returns:
        the input dimension, which is 2 or 3.
      See Also:
        `DefaultOperationMethod​.getSourceDimensions()`

    - #### getTargetDimensions

          public final int getTargetDimensions()

      Gets the dimension of output points.
      Specified by:
        `getTargetDimensions` in interface `MathTransform`
      Specified by:
        `getTargetDimensions` in class `AbstractMathTransform`
      Returns:
        the output dimension, which is 2 or 3.
      See Also:
        `DefaultOperationMethod​.getTargetDimensions()`

    - #### 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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