org.geotools.referencing.operation.transform

Class ProjectiveTransform

Object

Formattable

AbstractMathTransform

ProjectiveTransform

All Implemented Interfaces:

Serializable, LinearTransform, MathTransform

Direct Known Subclasses:

GeocentricTranslation

public class ProjectiveTransform
extends AbstractMathTransform
implements LinearTransform, Serializable

A usually affine, or otherwise a projective transform. A projective transform is capable of mapping an arbitrary quadrilateral into another arbitrary quadrilateral, while preserving the straightness of lines. In the special case where the transform is affine, the parallelism of lines in the source is preserved in the output.

Such a coordinate transformation can be represented by a square matrix of an arbitrary size. Point coordinates must have a dimension equals to Matrix.getNumCol()-1. For example, for square matrix of size 4×4, coordinate points are three-dimensional. The transformed points (x',y',z') are computed as below (note that this computation is similar to PerspectiveTransform in Java Advanced Imaging):

 [ u ]     [ m00  m01  m02  m03 ] [ x ]
 [ v ]  =  [ m10  m11  m12  m13 ] [ y ]
 [ w ]     [ m20  m21  m22  m23 ] [ z ]
 [ t ]     [ m30  m31  m32  m33 ] [ 1 ]

   x' = u/t
   y' = v/t
   y' = w/t
 

In the special case of an affine transform, the last row contains only zero values except in the last column, which contains 1.

Since:

2.0

Author:

Martin Desruisseaux (IRD)

See Also:

PerspectiveTransform, AffineTransform, Affine transformation on MathWorld, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ProjectiveTransform.ProviderAffine The provider for the "Affine general parametric transformation" (EPSG 9624).
static class	ProjectiveTransform.ProviderLongitudeRotation The provider for the "Longitude rotation" (EPSG 9601).

Nested classes/interfaces inherited from class AbstractMathTransform

AbstractMathTransform.Inverse

Field Summary

Fields inherited from class Formattable

SINGLE_LINE

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	ProjectiveTransform(Matrix matrix) Constructs a transform from the specified matrix.

Method Summary

Modifier and Type	Method and Description
static LinearTransform	create(AffineTransform matrix) Creates a transform for the specified matrix as a Java2D object.
static LinearTransform	create(Matrix matrix) Creates a transform for the specified matrix.
static LinearTransform	createScale(int dimension, double scale) Creates a transform that apply a uniform scale along all axis.
static Matrix	createSelectMatrix(int sourceDim, int[] toKeep) Creates a matrix that keep only a subset of the ordinate values.
static LinearTransform	createTranslation(int dimension, double offset) Creates a transform that apply the same translation along all axis.
Matrix	derivative(DirectPosition point) Gets the derivative of this transform at a point.
Matrix	derivative(Point2D point) Gets the derivative of this transform at a point.
boolean	equals(Object object) Compares the specified object with this math transform for equality.
Matrix	getMatrix() Returns a copy of the matrix.
ParameterDescriptorGroup	getParameterDescriptors() Returns the parameter descriptors for this math transform.
ParameterValueGroup	getParameterValues() Returns the matrix elements as a group of parameters values.
int	getSourceDimensions() Gets the dimension of input points.
int	getTargetDimensions() Gets the dimension of output points.
int	hashCode() Returns a hash value for this transform.
MathTransform	inverse() Creates the inverse transform of this object.
boolean	isIdentity() Tests whether this transform does not move any points.
boolean	isIdentity(double tolerance) Tests whether this transform does not move any points by using the provided tolerance.
void	transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Transforms an array of floating point coordinates by this matrix.
void	transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) Transforms an array of floating point coordinates by this matrix.

Methods inherited from class AbstractMathTransform

createTransformedShape, ensureNonNull, formatWKT, getName, needCopy, normalizeAngle, rollLongitude, transform, transform, transform, transform

Methods inherited from class Formattable

cleanupThreadLocals, toString, toWKT, toWKT, toWKT, toWKT

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface MathTransform

toWKT, transform, transform, transform

Constructor Detail

ProjectiveTransform

protected ProjectiveTransform(Matrix matrix)

Constructs a transform from the specified matrix. The matrix should be affine, but it will not be verified.

Parameters:

matrix - The matrix.

Method Detail

create

public static LinearTransform create(Matrix matrix)

Creates a transform for the specified matrix. The matrix should be affine, but it is not be verified.

Parameters:

matrix - The affine transform as a matrix.

Returns:

The transform for the given matrix.

create

public static LinearTransform create(AffineTransform matrix)

Creates a transform for the specified matrix as a Java2D object. This method is provided for interoperability with Java2D.

Parameters:

matrix - The affine transform as a matrix.

Returns:

The transform for the given matrix.

createScale

public static LinearTransform createScale(int dimension,
                                          double scale)

Creates a transform that apply a uniform scale along all axis.

Parameters:

dimension - The input and output dimensions.

scale - The scale factor.

Returns:

The scale transform.

Since:

2.3

createTranslation

public static LinearTransform createTranslation(int dimension,
                                                double offset)

Creates a transform that apply the same translation along all axis.

Parameters:

dimension - The input and output dimensions.

offset - The translation.

Returns:

The offset transform.

Since:

2.3

createSelectMatrix

public static Matrix createSelectMatrix(int sourceDim,
                                        int[] toKeep)
                                 throws IndexOutOfBoundsException

Creates a matrix that keep only a subset of the ordinate values. The dimension of source coordinates is sourceDim and the dimension of target coordinates is toKeep.length.

Parameters:

sourceDim - the dimension of source coordinates.

toKeep - the indices of ordinate values to keep.

Returns:

The matrix to give to the create(Matrix) method in order to create the transform.

Throws:

IndexOutOfBoundsException - if a value of toKeep is lower than 0 or not smaller than sourceDim.

getParameterDescriptors

public ParameterDescriptorGroup getParameterDescriptors()

Returns the parameter descriptors for this math transform.

Overrides:

getParameterDescriptors in class AbstractMathTransform

Returns:

The parameter descriptors for this math transform, or null.

See Also:

OperationMethod.getParameters()

getParameterValues

public ParameterValueGroup getParameterValues()

Returns the matrix elements as a group of parameters values. The number of parameters depends on the matrix size. Only matrix elements different from their default value will be included in this group.

Overrides:

getParameterValues in class AbstractMathTransform

Returns:

A copy of the parameter values for this math transform.

See Also:

Operation.getParameterValues()

transform

public void transform(float[] srcPts,
                      int srcOff,
                      float[] dstPts,
                      int dstOff,
                      int numPts)

Transforms an array of floating point coordinates by this matrix. Point coordinates must have a dimension equals to Matrix.getNumCol()-1. For example, for square matrix of size 4×4, coordinate points are three-dimensional and stored in the arrays starting at the specified offset (srcOff) in the order [x0, y0, z0, x1, y1, z1..., xn, yn, zn].

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.

dstOff - The offset to the location of the first transformed point that is stored in the destination array. The source and destination array sections can be overlaps.

numPts - The number of points to be transformed

transform

public void transform(double[] srcPts,
                      int srcOff,
                      double[] dstPts,
                      int dstOff,
                      int numPts)

Transforms an array of floating point coordinates by this matrix. Point coordinates must have a dimension equals to Matrix.getNumCol()-1. For example, for square matrix of size 4×4, coordinate points are three-dimensional and stored in the arrays starting at the specified offset (srcOff) in the order [x0, y0, z0, x1, y1, z1..., xn, yn, zn].

Specified by:

transform in interface MathTransform

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.

dstOff - The offset to the location of the first transformed point that is stored in the destination array. The source and destination array sections can be overlaps.

numPts - The number of points to be transformed

derivative

public Matrix derivative(Point2D point)

Gets the derivative of this transform at a point. For a matrix transform, the derivative is the same everywhere.

Overrides:

derivative in class AbstractMathTransform

Parameters:

point - The coordinate point where to evaluate the derivative.

Returns:

The derivative at the specified point as a 2×2 matrix.

See Also:

MathTransform2D.derivative(Point2D)

derivative

public Matrix derivative(DirectPosition point)

Gets the derivative of this transform at a point. For a matrix transform, the derivative is the same everywhere.

Specified by:

derivative in interface MathTransform

Overrides:

derivative in class AbstractMathTransform

Parameters:

point - The coordinate point where to evaluate the derivative.

Returns:

The derivative at the specified point (never null).

getMatrix

public Matrix getMatrix()

Returns a copy of the matrix.

Specified by:

getMatrix in interface LinearTransform

Returns:

A copy of the underlying matrix.

getSourceDimensions

public int getSourceDimensions()

Gets the dimension of input points.

Specified by:

getSourceDimensions in interface MathTransform

Specified by:

getSourceDimensions in class AbstractMathTransform

Returns:

The dimension of input points.

getTargetDimensions

public int getTargetDimensions()

Gets the dimension of output points.

Specified by:

getTargetDimensions in interface MathTransform

Specified by:

getTargetDimensions in class AbstractMathTransform

Returns:

The dimension of output points.

isIdentity

public boolean isIdentity()

Tests whether this transform does not move any points.

Specified by:

isIdentity in interface MathTransform

Overrides:

isIdentity in class AbstractMathTransform

Returns:

true if this MathTransform is an identity transform; false otherwise.

isIdentity

public boolean isIdentity(double tolerance)

Tests whether this transform does not move any points by using the provided tolerance. This method work in the same way than XMatrix.isIdentity(double).

Specified by:

isIdentity in interface LinearTransform

Parameters:

tolerance - The tolerance factor.

Returns:

true if this transform is the identity one

Since:

2.4

inverse

public MathTransform inverse()
                      throws NoninvertibleTransformException

Creates the inverse transform of this object.

Specified by:

inverse in interface MathTransform

Overrides:

inverse in class AbstractMathTransform

Returns:

The inverse transform.

Throws:

NoninvertibleTransformException - if the transform can't be inversed.

hashCode

public int hashCode()

Returns a hash value for this transform. This value need not remain consistent between different implementations of the same class.

Overrides:

hashCode in class AbstractMathTransform

equals

public boolean equals(Object object)

Compares the specified object with this math transform for equality.

Overrides:

equals in class AbstractMathTransform

Parameters:

object - The object to compare with this transform.

Returns:

true if the given object is a transform of the same class and if, given identical source position, the transformed position would be the equals.