/**
 * Adds the location identified by the given label
 *
 * @param  label     a label that identify the location to add.
 * @param  location  the location to add to the list of locations shown by this widget.
 * @throws FactoryException if a transformation to the display CRS can not be obtained.
 * @throws TransformException if an error occurred while transforming an envelope.
 */
public void addLocation(final String label, final AbstractLocation location) throws FactoryException, TransformException {
    final Envelope envelope = location.getEnvelope();
    final MathTransform2D tr = (MathTransform2D) CRS.findOperation(
            envelope.getCoordinateReferenceSystem(), displayCRS, null).getMathTransform();
    final Shape shape = tr.createTransformedShape(new IntervalRectangle(envelope));
    if (locations.putIfAbsent(label, shape) != null) {
        throw new IllegalArgumentException("A location is already defined for " + label);
    }
    final Rectangle2D b = shape.getBounds2D();
    if (bounds == null) {
        bounds = b;
    } else {
        bounds.add(b);
    }
}
 

/**
 * Gets the derivative of this transform at a point.
 *
 * @param  point  the coordinate point where to evaluate the derivative.
 * @return the derivative at the specified point (never {@code null}).
 * @throws TransformException if the derivative can't be evaluated at the specified point.
 */
@Override
public Matrix derivative(final Point2D point) throws TransformException {
    final MathTransform2D transform1 = (MathTransform2D) this.transform1;
    final MathTransform2D transform2 = (MathTransform2D) this.transform2;
    final Matrix matrix1 = transform1.derivative(point);
    final Matrix matrix2 = transform2.derivative(transform1.transform(point,null));
    return Matrices.multiply(matrix2, matrix1);
}
 

/**
 * Creates the inverse transform of this object.
 */
@Override
public synchronized MathTransform2D inverse() throws NoninvertibleTransformException {
    if (inverse == null) {
        inverse = new PassThroughTransform2D(firstAffectedCoordinate, subTransform.inverse(), numTrailingCoordinates);
        inverse.inverse = this;
    }
    return (MathTransform2D) inverse;
}
 

/**
 * Tests the interfaces implemented by the transforms returned by {@link MathTransforms#translation(double...)}.
 */
@Test
public void testTranslation() {
    MathTransform tr = MathTransforms.translation(4);
    assertInstanceOf("1D", MathTransform1D.class, tr);
    assertFalse("isIdentity", tr.isIdentity());

    tr = MathTransforms.translation(4, 7);
    assertInstanceOf("2D", MathTransform2D.class, tr);
    assertFalse("isIdentity", tr.isIdentity());
}
 

/**
 * Executed after every test in order to ensure that the {@linkplain #transform transform}
 * implements the {@link MathTransform1D} or {@link MathTransform2D} interface as needed.
 * In addition, all Apache SIS classes for linear transforms shall implement
 * {@link LinearTransform} and {@link Parameterized} interfaces.
 */
@After
public final void ensureImplementRightInterface() {
    if (transform instanceof TransformResultComparator) {
        transform = ((TransformResultComparator) transform).tested;
    }
    /*
     * Below is a copy of MathTransformTestCase.validate(), with minor modifications
     * due to the fact that this class does not extend MathTransformTestCase.
     */
    assertNotNull("The 'transform' field shall be assigned a value.", transform);
    Validators.validate(transform);
    final int dimension = transform.getSourceDimensions();
    if (transform.getTargetDimensions() == dimension && !skipInterfaceCheckForDimension(dimension)) {
        assertEquals("MathTransform1D", dimension == 1, (transform instanceof MathTransform1D));
        assertEquals("MathTransform2D", dimension == 2, (transform instanceof MathTransform2D));
    } else {
        assertFalse("MathTransform1D", transform instanceof MathTransform1D);
        assertFalse("MathTransform2D", transform instanceof MathTransform2D);
    }
    assertInstanceOf("Parameterized", Parameterized.class, transform);
    /*
     * End of MathTransformTestCase.validate(). Remaining is specific to LinearTransform implementations.
     */
    assertInstanceOf("Not a LinearTransform.", LinearTransform.class, transform);
    final Matrix tm = ((LinearTransform) transform).getMatrix();
    assertTrue("The matrix declared by the MathTransform is not equal to the one given at creation time.",
            Matrices.equals(matrix, tm, tolerance, false));

    assertSame("ParameterDescriptor",
            Affine.getProvider(transform.getSourceDimensions(), transform.getTargetDimensions(), true).getParameters(),
            ((Parameterized) transform).getParameterDescriptors());
}
 

/**
 * Validates the current {@linkplain #transform transform}. This method verifies that
 * the transform implements {@link MathTransform1D} or {@link MathTransform2D} if the
 * transform dimension suggests that it should. In addition, all Apache SIS transforms
 * shall implement {@link Parameterized}.
 *
 * @see Validators#validate(MathTransform)
 */
protected final void validate() {
    assertNotNull("The 'transform' field shall be assigned a value.", transform);
    Validators.validate(transform);
    final int dimension = transform.getSourceDimensions();
    if (transform.getTargetDimensions() == dimension) {
        assertEquals("transform instanceof MathTransform1D:", (transform instanceof MathTransform1D), dimension == 1);
        assertEquals("transform instanceof MathTransform2D:", (transform instanceof MathTransform2D), dimension == 2);
    } else {
        assertFalse("transform instanceof MathTransform1D:", transform instanceof MathTransform1D);
        assertFalse("transform instanceof MathTransform2D:", transform instanceof MathTransform2D);
    }
    assertInstanceOf("The transform does not implement all expected interfaces.", Parameterized.class, transform);
}
 

/**
 * Tests the transformation of an envelope or rectangle. This is a relatively simple test case
 * working in the two-dimensional space only, with a coordinate operation of type "conversion"
 * (not a "transformation") and with no need to adjust for poles.
 *
 * @throws FactoryException if an error occurred while creating the operation.
 * @throws TransformException if an error occurred while transforming the envelope.
 */
@Test
public final void testTransform() throws FactoryException, TransformException {
    final ProjectedCRS    targetCRS  = CommonCRS.WGS84.universal(10, -123.5);
    final GeographicCRS   sourceCRS  = targetCRS.getBaseCRS();
    final Conversion      conversion = targetCRS.getConversionFromBase();
    final MathTransform2D transform  = (MathTransform2D) conversion.getMathTransform();
    /*
     * Transforms envelopes using MathTransform. Geographic coordinates are in (latitude, longitude) order.
     * Opportunistically check that the transform using a CoordinateOperation object produces the same result.
     */
    final G rectλφ = createFromExtremums(sourceCRS, -20, -126, 40, -120);
    final G rectXY = transform(targetCRS, transform, rectλφ);
    assertEquals("Conversion should produce the same result.", rectXY, transform(conversion, rectλφ));
    /*
     * Expected values are determined empirically by projecting many points.
     * Those values are the same than in EnvelopesTest.testTransform().
     */
    final G expected = createFromExtremums(targetCRS, 166021.56, -2214294.03,
                                                      833978.44,  4432069.06);
    assertGeometryEquals(expected, rectXY, LINEAR_TOLERANCE, LINEAR_TOLERANCE);
    /*
     * Test the inverse conversion.
     * Final envelope should be slightly bigger than the original.
     */
    final G rectBack = transform(sourceCRS, transform.inverse(), rectXY);
    assertTrue("Transformed envelope should not be smaller than the original one.", contains(rectBack, rectλφ));
    assertGeometryEquals(rectλφ, rectBack, 0.05, 1.0);
}
 

/**
 * Adds all locations in the given area of interest.
 *
 * @param  coder           the encoder to use for computing locations and their envelopes.
 * @param  areaOfInterest  the geographic or projected area where to get locations.
 * @throws FactoryException if a transformation to the display CRS can not be obtained.
 * @throws TransformException if an error occurred while transforming an envelope.
 */
public void addLocations(final MilitaryGridReferenceSystem.Coder coder, final Envelope areaOfInterest)
        throws FactoryException, TransformException
{
    final Iterator<String> it = coder.encode(areaOfInterest);
    while (it.hasNext()) {
        final String code = it.next();
        addLocation(code, coder.decode(code));
    }
    envelope = ((MathTransform2D) CRS.findOperation(areaOfInterest.getCoordinateReferenceSystem(), displayCRS, null)
                    .getMathTransform()).createTransformedShape(new IntervalRectangle(areaOfInterest));
}
 

/**
 * Returns the inverse of this transform.
 */
@Override
public MathTransform2D inverse() {
    return inverse;
}
 

/**
 * Returns the inverse of this transform, which is the enclosing {@link SatelliteGroundTrack} transform.
 */
@Override
public MathTransform2D inverse() {
    return SatelliteGroundTrack.this;
}
 

/**
 * Returns the inverse of this math transform.
 */
@Override
public MathTransform2D inverse() {
    return forward;
}
 

/**
 * Returns the inverse of this math transform.
 */
@Override
public MathTransform2D inverse() {
    return forward;
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Constructs a concatenated transform.
 */
public ConcatenatedTransformDirect2D(final MathTransform2D transform1,
                                     final MathTransform2D transform2)
{
    super(transform1, transform2);
}
 

/**
 * Creates the inverse transform of this object.
 */
@Override
public MathTransform2D inverse() throws NoninvertibleTransformException {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Concatenates the two given transforms.
 * If the concatenation result works with two-dimensional input and output points,
 * then the returned transform will implement {@link MathTransform2D}.
 * Likewise if the concatenation result works with one-dimensional input and output points,
 * then the returned transform will implement {@link MathTransform1D}.
 *
 * <div class="note"><b>Implementation note:</b>
 * {@code ConcatenatedTransform} implementations are available in two versions: direct and non-direct.
 * The "non-direct" versions use an intermediate buffer when performing transformations; they are slower
 * and consume more memory. They are used only as a fallback when a "direct" version can not be created.</div>
 *
 * @param  tr1      the first math transform.
 * @param  tr2      the second math transform.
 * @param  factory  the factory which is (indirectly) invoking this method, or {@code null} if none.
 * @return the concatenated transform.
 *
 * @see MathTransforms#concatenate(MathTransform, MathTransform)
 */
public static MathTransform create(MathTransform tr1, MathTransform tr2, final MathTransformFactory factory)
        throws FactoryException, MismatchedDimensionException
{
    final int dim1 = tr1.getTargetDimensions();
    final int dim2 = tr2.getSourceDimensions();
    if (dim1 != dim2) {
        throw new MismatchedDimensionException(Resources.format(Resources.Keys.CanNotConcatenateTransforms_2, getName(tr1),
                getName(tr2)) + ' ' + Errors.format(Errors.Keys.MismatchedDimension_2, dim1, dim2));
    }
    MathTransform mt = createOptimized(tr1, tr2, factory);
    if (mt != null) {
        return mt;
    }
    /*
     * Can not avoid the creation of a ConcatenatedTransform object.
     * Check for the type to create (1D, 2D, general case...)
     */
    final int dimSource = tr1.getSourceDimensions();
    final int dimTarget = tr2.getTargetDimensions();
    if (dimSource == 1 && dimTarget == 1) {
        /*
         * Result needs to be a MathTransform1D.
         */
        if (tr1 instanceof MathTransform1D && tr2 instanceof MathTransform1D) {
            return new ConcatenatedTransformDirect1D((MathTransform1D) tr1,
                                                     (MathTransform1D) tr2);
        } else {
            return new ConcatenatedTransform1D(tr1, tr2);
        }
    } else if (dimSource == 2 && dimTarget == 2) {
        /*
         * Result needs to be a MathTransform2D.
         */
        if (tr1 instanceof MathTransform2D && tr2 instanceof MathTransform2D) {
            return new ConcatenatedTransformDirect2D((MathTransform2D) tr1,
                                                     (MathTransform2D) tr2);
        } else {
            return new ConcatenatedTransform2D(tr1, tr2);
        }
    } else if (dimSource == tr1.getTargetDimensions()   // dim1 = tr1.getTargetDimensions() and
            && dimTarget == tr2.getSourceDimensions())  // dim2 = tr2.getSourceDimensions() may not be true anymore.
    {
        return new ConcatenatedTransformDirect(tr1, tr2);
    } else {
        return new ConcatenatedTransform(tr1, tr2);
    }
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this transform.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this object.
 */
@Override
public MathTransform2D inverse() throws NoninvertibleTransformException {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Returns the inverse transform of this object.
 */
@Override
public MathTransform2D inverse() {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Creates the inverse transform of this object.
 */
@Override
public MathTransform2D inverse() throws NoninvertibleTransformException {
    return (MathTransform2D) super.inverse();
}
 

/**
 * Tests conversions of an envelope or rectangle over a pole using a coordinate operation.
 *
 * @throws FactoryException if an error occurred while creating the operation.
 * @throws TransformException if an error occurred while transforming the envelope.
 */
@Test
@DependsOnMethod("testTransform")
public final void testTransformOverPole() throws FactoryException, TransformException {
    final ProjectedCRS sourceCRS = (ProjectedCRS) CRS.fromWKT(
            "PROJCS[“WGS 84 / Antarctic Polar Stereographic”,\n" +
            "  GEOGCS[“WGS 84”,\n" +
            "    DATUM[“World Geodetic System 1984”,\n" +
            "      SPHEROID[“WGS 84”, 6378137.0, 298.257223563]],\n" +
            "    PRIMEM[“Greenwich”, 0.0],\n" +
            "    UNIT[“degree”, 0.017453292519943295]],\n" +
            "  PROJECTION[“Polar Stereographic (variant B)”],\n" +
            "  PARAMETER[“standard_parallel_1”, -71.0],\n" +
            "  UNIT[“m”, 1.0]]");
    final GeographicCRS   targetCRS  = sourceCRS.getBaseCRS();
    final Conversion      conversion = inverse(sourceCRS.getConversionFromBase());
    final MathTransform2D transform  = (MathTransform2D) conversion.getMathTransform();
    /*
     * The rectangle to test, which contains the South pole.
     */
    G rectangle = createFromExtremums(sourceCRS,
            -3943612.4042124213, -4078471.954436003,
             3729092.5890516187,  4033483.085688618);
    /*
     * This is what we get without special handling of singularity point.
     * Note that is does not include the South pole as we would expect.
     * The commented out values are what we get by projecting an arbitrary
     * larger amount of points.
     */
    G expected = createFromExtremums(targetCRS,
        //  -178.4935231040927  -56.61747883535035          // empirical values
            -179.8650137390031, -88.99136583196396,         // anti-regression values
        //   178.8122742080059  -40.90577500420587]         // empirical values
             137.9769431693009, -40.90577500420587);        // anti-regression values
    /*
     * Tests what we actually get. First, test using the method working on MathTransform.
     * Next, test again the same transform, but using the API on Envelope objects.
     */
    G actual = transform(targetCRS, transform, rectangle);
    assertGeometryEquals(expected, actual, ANGULAR_TOLERANCE, ANGULAR_TOLERANCE);
    /*
     * Using the transform(CoordinateOperation, …) method,
     * the singularity at South pole is taken in account.
     */
    expected = createFromExtremums(targetCRS, -180, -90, 180, -40.905775004205864);
    actual   = transform(conversion, rectangle);
    assertGeometryEquals(expected, actual, ANGULAR_TOLERANCE, ANGULAR_TOLERANCE);
    /*
     * Another rectangle containing the South pole, but this time the south
     * pole is almost in a corner of the rectangle
     */
    rectangle = createFromExtremums(sourceCRS, -4000000, -4000000, 300000, 30000);
    expected  = createFromExtremums(targetCRS, -180, -90, 180, -41.03163170198091);
    actual    = transform(conversion, rectangle);
    assertGeometryEquals(expected, actual, ANGULAR_TOLERANCE, ANGULAR_TOLERANCE);
    /*
     * Another rectangle with the South pole close to the border.
     * This test should execute the step #3 in the transform method code.
     */
    rectangle = createFromExtremums(sourceCRS, -2000000, -1000000, 200000, 2000000);
    expected  = createFromExtremums(targetCRS, -180, -90, 180, -64.3861643256928);
    actual    = transform(conversion, rectangle);
    assertGeometryEquals(expected, actual, ANGULAR_TOLERANCE, ANGULAR_TOLERANCE);
}
 

/**
 * Returns the inverse of this map projection.
 * Subclasses do not need to override this method, as they should override
 * {@link #inverseTransform(double[], int, double[], int) inverseTransform(…)} instead.
 *
 * @return the inverse of this map projection.
 */
@Override
public MathTransform2D inverse() {
    return inverse;
}
 

/**
 * Returns the inverse of this map projection.
 *
 * @return the inverse of this map projection.
 */
@Override
public MathTransform2D inverse() {
    return inverse;
}
 

/**
 * Concatenates the given two-dimensional transforms. This is a convenience methods
 * delegating to {@link #concatenate(MathTransform, MathTransform)} and casting the
 * result to a {@link MathTransform2D} instance.
 *
 * @param  tr1  the first math transform.
 * @param  tr2  the second math transform.
 * @return the concatenated transform.
 * @throws MismatchedDimensionException if the output dimension of the first transform
 *         does not match the input dimension of the second transform.
 */
public static MathTransform2D concatenate(MathTransform2D tr1, MathTransform2D tr2)
        throws MismatchedDimensionException
{
    return (MathTransform2D) concatenate((MathTransform) tr1, (MathTransform) tr2);
}
 

/**
 * Concatenates the three given two-dimensional transforms. This is a convenience methods
 * delegating to {@link #concatenate(MathTransform, MathTransform, MathTransform)} and
 * casting the result to a {@link MathTransform2D} instance.
 *
 * @param  tr1  the first math transform.
 * @param  tr2  the second math transform.
 * @param  tr3  the third math transform.
 * @return the concatenated transform.
 * @throws MismatchedDimensionException if the output dimension of a transform
 *         does not match the input dimension of next transform.
 */
public static MathTransform2D concatenate(MathTransform2D tr1, MathTransform2D tr2, MathTransform2D tr3)
        throws MismatchedDimensionException
{
    return (MathTransform2D) concatenate((MathTransform) tr1, (MathTransform) tr2, (MathTransform) tr3);
}