# Class AbstractMathTransform2D.Inverse

Object
FormattableObject
AbstractMathTransform
AbstractMathTransform.Inverse
Inverse

All Implemented Interfaces:
  `Parameterized, LenientComparable, Printable, MathTransform, MathTransform2D`

Enclosing class:
  `AbstractMathTransform2D`

protected abstract static class AbstractMathTransform2D.Inverse extends AbstractMathTransform.Inverse implements MathTransform2D
Base class for implementation of inverse math transforms. This inner class is the inverse of the enclosing `AbstractMathTransform2D`.

## Serialization

This object 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

- ## Nested Class Summary

  ### Nested classes/interfaces inherited from class AbstractMathTransform

  `AbstractMathTransform​.Inverse`

- ## Constructor Summary

  Constructors
  Modifier
  Constructor
  Description
  `protected`
  `Inverse()`
  Constructs an inverse math transform.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `Shape`
  `createTransformedShape(Shape shape)`
  Transforms the specified shape.
  `Matrix`
  `derivative(Point2D point)`
  Gets the derivative of this transform at a point.
  `abstract MathTransform2D`
  `inverse()`
  Returns the inverse of this math transform.
  `Point2D`
  `transform(Point2D ptSrc, Point2D ptDst)`
  Transforms the specified `ptSrc` and stores the result in `ptDst`.

  ### Methods inherited from class AbstractMathTransform.Inverse

  `computeHashCode, derivative, equals, formatTo, getDomain, getSourceDimensions, getTargetDimensions, isIdentity`

  ### Methods inherited from class AbstractMathTransform

  `equals, getContextualParameters, getParameterDescriptors, getParameterValues, hashCode, 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, getSourceDimensions, getTargetDimensions, isIdentity, toWKT, transform, transform, transform, transform, transform`

- ## Constructor Details

  - ### Inverse

    protected Inverse()
    Constructs an inverse math transform.

- ## Method Details

  - ### inverse

    public abstract MathTransform2D inverse()
    Returns the inverse of this math transform. The returned transform should be the enclosing math transform.
    Specified by:
      `inverse` in interface `MathTransform`
    Specified by:
      `inverse` in interface `MathTransform2D`
    Specified by:
      `inverse` in class `AbstractMathTransform​.Inverse`
    Returns:
      the inverse of this transform.

  - ### 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 tuple to be transformed.
      `ptDst` - the coordinate tuple that stores the result of transforming `ptSrc`, or `null` if a new point shall be created.
    Returns:
      the coordinate tuple after transforming `ptSrc` and storing the result in `ptDst`, or in a new point if `ptDst` was null.
    Throws:
      `TransformException` - if the point cannot 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 coordinates 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 latter method returned a non-null matrix, returns that matrix. Otherwise throws `TransformException`.
    Specified by:
      `derivative` in interface `MathTransform2D`
    Parameters:
      `point` - the coordinate tuple where to evaluate the derivative.
    Returns:
      the derivative at the specified point as a 2×2 matrix.
    Throws:
      `TransformException` - if the derivative cannot be evaluated at the specified point.