org.apache.sis.referencing.operation.transform

## Class AbstractMathTransform2D

- Object
- - FormattableObject
  - - AbstractMathTransform
    - - AbstractMathTransform2D

- All Implemented Interfaces:
    Parameterized, LenientComparable, MathTransform, MathTransform2D
  Direct Known Subclasses:
    NormalizedProjection, ZonedGridSystem

      public abstract class AbstractMathTransform2D
      extends AbstractMathTransform
      implements MathTransform2D

  Base class for math transforms that are known to be two-dimensional in all cases. Two-dimensional math transforms are not required to extend this class, however doing so may simplify their implementation.

  The simplest way to implement this abstract class is to provide an implementation for the following methods only:

  - `AbstractMathTransform​.transform(double[], int, double[], int, boolean)`
  However more performance may be gained by overriding the other `transform` methods as well.
  Immutability and thread safety
  All Apache SIS implementations of `MathTransform2D` are immutable and thread-safe. It is highly recommended that third-party implementations be immutable and thread-safe too. This means that unless otherwise noted in the javadoc, `MathTransform2D` instances can be shared by many objects and passed between threads without synchronization.
  Serialization
  `MathTransform2D` may or may not be serializable, at implementation choices. Most Apache SIS implementations are serializable, but the serialized objects are not guaranteed to be compatible with future SIS versions. Serialization should be used only for short term storage or RMI between applications running the same SIS version.
  Since:
    0.5

  Defined in the `sis-referencing` module

- - ### Nested Class Summary

    Nested Classes
    Modifier and Type | Class and Description
    --- | ---
    `protected class` | `AbstractMathTransform2D.Inverse` Base class for implementation of inverse math transforms.

  - ### Constructor Summary

    Constructors
    Modifier | Constructor and Description
    --- | ---
    `protected` | `AbstractMathTransform2D()` Constructor for subclasses.

  - ### Method Summary

    All Methods Instance Methods Concrete Methods
    Modifier and Type | Method and Description
    --- | ---
    `Shape` | `createTransformedShape(Shape shape)` Transforms the specified shape.
    `Matrix` | `derivative(Point2D point)` Gets the derivative of this transform at a point.
    `int` | `getSourceDimensions()` Returns the dimension of input points, which is always 2.
    `int` | `getTargetDimensions()` Returns the dimension of output points, which is always 2.
    `MathTransform2D` | `inverse()` Returns the inverse transform of this object.
    `Point2D` | `transform(Point2D ptSrc, Point2D ptDst)` Transforms the specified `ptSrc` and stores the result in `ptDst`.

    - ### Methods inherited from class AbstractMathTransform

      `computeHashCode, derivative, equals, equals, formatTo, getContextualParameters, getParameterDescriptors, getParameterValues, hashCode, isIdentity, transform, transform, 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

      `derivative, isIdentity, toWKT, transform, transform, transform, transform, transform`

- - ### Constructor Detail

    - #### AbstractMathTransform2D

          protected AbstractMathTransform2D()

      Constructor for subclasses.

  - ### Method Detail

    - #### getSourceDimensions

          public final int getSourceDimensions()

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

    - #### transform

          public Point2D transform(Point2D ptSrc,
                                   Point2D ptDst)
                            throws TransformException

      Transforms the specified `ptSrc` and stores the result in `ptDst`. The default implementation invokes `AbstractMathTransform​.transform(double[], int, double[], int, boolean)` using a temporary array of doubles.
      Specified by:
        `transform` in interface `MathTransform2D`
      Parameters:
        `ptSrc` - the coordinate point to be transformed.
        `ptDst` - the coordinate point that stores the result of transforming `ptSrc`, or `null` if a new point shall be created.
      Returns:
        the coordinate point after transforming `ptSrc` and storing the result in `ptDst`, or in a new point if `ptDst` was null.
      Throws:
        `TransformException` - if the point can not be transformed.
      See Also:
        `MathTransform2D​.transform(Point2D, Point2D)`

    - #### createTransformedShape

          public Shape createTransformedShape(Shape shape)
                                       throws TransformException

      Transforms the specified shape. The default implementation computes quadratic curves using three points for each line segment in the shape. The returned object is often a `Path2D`, but may also be a `Line2D` or a `QuadCurve2D` if such simplification is possible.
      Specified by:
        `createTransformedShape` in interface `MathTransform2D`
      Parameters:
        `shape` - shape to transform.
      Returns:
        transformed shape, or `shape` if this transform is the identity transform.
      Throws:
        `TransformException` - if a transform failed.

    - #### derivative

          public Matrix derivative(Point2D point)
                            throws TransformException

      Gets the derivative of this transform at a point. The default implementation performs the following steps:
      - Copy the coordinate in a temporary array and pass that array to the `AbstractMathTransform​.transform(double[], int, double[], int, boolean)` method, with the `derivate` boolean argument set to `true`.
      - If the later method returned a non-null matrix, returns that matrix. Otherwise throws `TransformException`.
      Specified by:
        `derivative` in interface `MathTransform2D`
      Parameters:
        `point` - the coordinate point where to evaluate the derivative.
      Returns:
        the derivative at the specified point as a 2×2 matrix.
      Throws:
        `TransformException` - if the derivative can not be evaluated at the specified point.

    - #### inverse

          public MathTransform2D inverse()
                                  throws NoninvertibleTransformException

      Returns the inverse transform of this object. The default implementation returns `this` if this transform is an identity transform, or throws an exception otherwise. Subclasses should override this method.
      Specified by:
        `inverse` in interface `MathTransform`
      Specified by:
        `inverse` in interface `MathTransform2D`
      Overrides:
        `inverse` in class `AbstractMathTransform`
      Throws:
        `NoninvertibleTransformException`

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