org.locationtech.jts:jts-core 1.18.0
org.locationtech.jts.geom.util

Class AffineTransformation

• All Implemented Interfaces:
Cloneable, CoordinateSequenceFilter

public class AffineTransformation
extends Object
implements Cloneable, CoordinateSequenceFilter
Represents an affine transformation on the 2D Cartesian plane. It can be used to transform a Coordinate or Geometry. An affine transformation is a mapping of the 2D plane into itself via a series of transformations of the following basic types:
• reflection (through a line)
• rotation (around the origin)
• scaling (relative to the origin)
• shearing (in both the X and Y directions)
• translation
In general, affine transformations preserve straightness and parallel lines, but do not preserve distance or shape.

An affine transformation can be represented by a 3x3 matrix in the following form:

T = | m00 m01 m02 |
| m10 m11 m12 |
|  0   0   1  |

A coordinate P = (x, y) can be transformed to a new coordinate P' = (x', y') by representing it as a 3x1 matrix and using matrix multiplication to compute:
| x' |  = T x | x |
| y' |        | y |
| 1  |        | 1 |

Transformation Composition

Affine transformations can be composed using the compose(org.locationtech.jts.geom.util.AffineTransformation) method. Composition is computed via multiplication of the transformation matrices, and is defined as:
A.compose(B) = TB x TA

This produces a transformation whose effect is that of A followed by B. The methods reflect(double, double, double, double), rotate(double), scale(double, double), shear(double, double), and translate(double, double) have the effect of composing a transformation of that type with the transformation they are invoked on.

The composition of transformations is in general not commutative.

Transformation Inversion

Affine transformations may be invertible or non-invertible. If a transformation is invertible, then there exists an inverse transformation which when composed produces the identity transformation. The getInverse() method computes the inverse of a transformation, if one exists.
Author:
Martin Davis
• Constructor Detail

• AffineTransformation

public AffineTransformation()
Constructs a new identity transformation
• AffineTransformation

public AffineTransformation(double[] matrix)
Constructs a new transformation whose matrix has the specified values.
Parameters:
matrix - an array containing the 6 values { m00, m01, m02, m10, m11, m12 }
Throws:
NullPointerException - if matrix is null
ArrayIndexOutOfBoundsException - if matrix is too small
• AffineTransformation

public AffineTransformation(double m00,
double m01,
double m02,
double m10,
double m11,
double m12)
Constructs a new transformation whose matrix has the specified values.
Parameters:
m00 - the entry for the [0, 0] element in the transformation matrix
m01 - the entry for the [0, 1] element in the transformation matrix
m02 - the entry for the [0, 2] element in the transformation matrix
m10 - the entry for the [1, 0] element in the transformation matrix
m11 - the entry for the [1, 1] element in the transformation matrix
m12 - the entry for the [1, 2] element in the transformation matrix
• AffineTransformation

public AffineTransformation(AffineTransformation trans)
Constructs a transformation which is a copy of the given one.
Parameters:
trans - the transformation to copy
• AffineTransformation

public AffineTransformation(Coordinate src0,
Coordinate src1,
Coordinate src2,
Coordinate dest0,
Coordinate dest1,
Coordinate dest2)
Constructs a transformation which maps the given source points into the given destination points.
Parameters:
src0 - source point 0
src1 - source point 1
src2 - source point 2
dest0 - the mapped point for source point 0
dest1 - the mapped point for source point 1
dest2 - the mapped point for source point 2
• Method Detail

• reflectionInstance

public static AffineTransformation reflectionInstance(double x0,
double y0,
double x1,
double y1)
Creates a transformation for a reflection about the line (x0,y0) - (x1,y1).
Parameters:
x0 - the x-ordinate of a point on the reflection line
y0 - the y-ordinate of a point on the reflection line
x1 - the x-ordinate of a another point on the reflection line
y1 - the y-ordinate of a another point on the reflection line
Returns:
a transformation for the reflection
• reflectionInstance

public static AffineTransformation reflectionInstance(double x,
double y)
Creates a transformation for a reflection about the line (0,0) - (x,y).
Parameters:
x - the x-ordinate of a point on the reflection line
y - the y-ordinate of a point on the reflection line
Returns:
a transformation for the reflection
• rotationInstance

public static AffineTransformation rotationInstance(double theta)
Creates a transformation for a rotation about the origin by an angle theta. Positive angles correspond to a rotation in the counter-clockwise direction.
Parameters:
theta - the rotation angle, in radians
Returns:
a transformation for the rotation
• rotationInstance

public static AffineTransformation rotationInstance(double sinTheta,
double cosTheta)
Creates a transformation for a rotation by an angle theta, specified by the sine and cosine of the angle. This allows providing exact values for sin(theta) and cos(theta) for the common case of rotations of multiples of quarter-circles.
Parameters:
sinTheta - the sine of the rotation angle
cosTheta - the cosine of the rotation angle
Returns:
a transformation for the rotation
• rotationInstance

public static AffineTransformation rotationInstance(double theta,
double x,
double y)
Creates a transformation for a rotation about the point (x,y) by an angle theta. Positive angles correspond to a rotation in the counter-clockwise direction.
Parameters:
theta - the rotation angle, in radians
x - the x-ordinate of the rotation point
y - the y-ordinate of the rotation point
Returns:
a transformation for the rotation
• rotationInstance

public static AffineTransformation rotationInstance(double sinTheta,
double cosTheta,
double x,
double y)
Creates a transformation for a rotation about the point (x,y) by an angle theta, specified by the sine and cosine of the angle. This allows providing exact values for sin(theta) and cos(theta) for the common case of rotations of multiples of quarter-circles.
Parameters:
sinTheta - the sine of the rotation angle
cosTheta - the cosine of the rotation angle
x - the x-ordinate of the rotation point
y - the y-ordinate of the rotation point
Returns:
a transformation for the rotation
• scaleInstance

public static AffineTransformation scaleInstance(double xScale,
double yScale)
Creates a transformation for a scaling relative to the origin.
Parameters:
xScale - the value to scale by in the x direction
yScale - the value to scale by in the y direction
Returns:
a transformation for the scaling
• scaleInstance

public static AffineTransformation scaleInstance(double xScale,
double yScale,
double x,
double y)
Creates a transformation for a scaling relative to the point (x,y).
Parameters:
xScale - the value to scale by in the x direction
yScale - the value to scale by in the y direction
x - the x-ordinate of the point to scale around
y - the y-ordinate of the point to scale around
Returns:
a transformation for the scaling
• shearInstance

public static AffineTransformation shearInstance(double xShear,
double yShear)
Creates a transformation for a shear.
Parameters:
xShear - the value to shear by in the x direction
yShear - the value to shear by in the y direction
Returns:
a transformation for the shear
• translationInstance

public static AffineTransformation translationInstance(double x,
double y)
Creates a transformation for a translation.
Parameters:
x - the value to translate by in the x direction
y - the value to translate by in the y direction
Returns:
a transformation for the translation
• setToIdentity

public AffineTransformation setToIdentity()
Sets this transformation to be the identity transformation. The identity transformation has the matrix:
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

Returns:
this transformation, with an updated matrix
• setTransformation

public AffineTransformation setTransformation(double m00,
double m01,
double m02,
double m10,
double m11,
double m12)
Sets this transformation's matrix to have the given values.
Parameters:
m00 - the entry for the [0, 0] element in the transformation matrix
m01 - the entry for the [0, 1] element in the transformation matrix
m02 - the entry for the [0, 2] element in the transformation matrix
m10 - the entry for the [1, 0] element in the transformation matrix
m11 - the entry for the [1, 1] element in the transformation matrix
m12 - the entry for the [1, 2] element in the transformation matrix
Returns:
this transformation, with an updated matrix
• setTransformation

public AffineTransformation setTransformation(AffineTransformation trans)
Sets this transformation to be a copy of the given one
Parameters:
trans - a transformation to copy
Returns:
this transformation, with an updated matrix
• getMatrixEntries

public double[] getMatrixEntries()
Gets an array containing the entries of the transformation matrix. Only the 6 non-trivial entries are returned, in the sequence:
m00, m01, m02, m10, m11, m12

Returns:
an array of length 6
• getDeterminant

public double getDeterminant()
Computes the determinant of the transformation matrix. The determinant is computed as:
| m00 m01 m02 |
| m10 m11 m12 | = m00 * m11 - m01 * m10
|  0   0   1  |

If the determinant is zero, the transform is singular (not invertible), and operations which attempt to compute an inverse will throw a NoninvertibleTransformException.
Returns:
the determinant of the transformation
getInverse()
• getInverse

public AffineTransformation getInverse()
throws NoninvertibleTransformationException
Computes the inverse of this transformation, if one exists. The inverse is the transformation which when composed with this one produces the identity transformation. A transformation has an inverse if and only if it is not singular (i.e. its determinant is non-zero). Geometrically, an transformation is non-invertible if it maps the plane to a line or a point. If no inverse exists this method will throw a NoninvertibleTransformationException.

The matrix of the inverse is equal to the inverse of the matrix for the transformation. It is computed as follows:

1
det

=   1       |  m11  -m01   m01*m12-m02*m11  |
---   x  | -m10   m00  -m00*m12+m10*m02  |
det      |  0     0     m00*m11-m10*m01  |

= |  m11/det  -m01/det   m01*m12-m02*m11/det |
| -m10/det   m00/det  -m00*m12+m10*m02/det |
|   0           0          1               |

Returns:
a new inverse transformation
Throws:
NoninvertibleTransformationException
getDeterminant()
• setToReflectionBasic

public AffineTransformation setToReflectionBasic(double x0,
double y0,
double x1,
double y1)
Explicitly computes the math for a reflection. May not work.
Parameters:
x0 - the X ordinate of one point on the reflection line
y0 - the Y ordinate of one point on the reflection line
x1 - the X ordinate of another point on the reflection line
y1 - the Y ordinate of another point on the reflection line
Returns:
this transformation, with an updated matrix
• setToReflection

public AffineTransformation setToReflection(double x0,
double y0,
double x1,
double y1)
Sets this transformation to be a reflection about the line defined by a line (x0,y0) - (x1,y1).
Parameters:
x0 - the X ordinate of one point on the reflection line
y0 - the Y ordinate of one point on the reflection line
x1 - the X ordinate of another point on the reflection line
y1 - the Y ordinate of another point on the reflection line
Returns:
this transformation, with an updated matrix
• setToReflection

public AffineTransformation setToReflection(double x,
double y)
Sets this transformation to be a reflection about the line defined by vector (x,y). The transformation for a reflection is computed by:
d = sqrt(x2 + y2)
sin = y / d;
cos = x / d;

Tref = Trot(sin, cos) x Tscale(1, -1) x Trot(-sin, cos)

Parameters:
x - the x-component of the reflection line vector
y - the y-component of the reflection line vector
Returns:
this transformation, with an updated matrix
• setToRotation

public AffineTransformation setToRotation(double theta)
Sets this transformation to be a rotation around the origin. A positive rotation angle corresponds to a counter-clockwise rotation. The transformation matrix for a rotation by an angle theta has the value:

|  cos(theta)  -sin(theta)   0 |
|  sin(theta)   cos(theta)   0 |
|           0            0   1 |

Parameters:
theta - the rotation angle, in radians
Returns:
this transformation, with an updated matrix
• setToRotation

public AffineTransformation setToRotation(double sinTheta,
double cosTheta)
Sets this transformation to be a rotation around the origin by specifying the sin and cos of the rotation angle directly. The transformation matrix for the rotation has the value:

|  cosTheta  -sinTheta   0 |
|  sinTheta   cosTheta   0 |
|         0          0   1 |

Parameters:
sinTheta - the sine of the rotation angle
cosTheta - the cosine of the rotation angle
Returns:
this transformation, with an updated matrix
• setToRotation

public AffineTransformation setToRotation(double theta,
double x,
double y)
Sets this transformation to be a rotation around a given point (x,y). A positive rotation angle corresponds to a counter-clockwise rotation. The transformation matrix for a rotation by an angle theta has the value:

|  cosTheta  -sinTheta   x-x*cos+y*sin |
|  sinTheta   cosTheta   y-x*sin-y*cos |
|           0            0   1 |

Parameters:
theta - the rotation angle, in radians
x - the x-ordinate of the rotation point
y - the y-ordinate of the rotation point
Returns:
this transformation, with an updated matrix
• setToRotation

public AffineTransformation setToRotation(double sinTheta,
double cosTheta,
double x,
double y)
Sets this transformation to be a rotation around a given point (x,y) by specifying the sin and cos of the rotation angle directly. The transformation matrix for the rotation has the value:

|  cosTheta  -sinTheta   x-x*cos+y*sin |
|  sinTheta   cosTheta   y-x*sin-y*cos |
|         0          0         1       |

Parameters:
sinTheta - the sine of the rotation angle
cosTheta - the cosine of the rotation angle
x - the x-ordinate of the rotation point
y - the y-ordinate of the rotation point
Returns:
this transformation, with an updated matrix
• setToScale

public AffineTransformation setToScale(double xScale,
double yScale)
Sets this transformation to be a scaling. The transformation matrix for a scale has the value:

|  xScale      0  dx |
|  1      yScale  dy |
|  0           0   1 |

Parameters:
xScale - the amount to scale x-ordinates by
yScale - the amount to scale y-ordinates by
Returns:
this transformation, with an updated matrix
• setToShear

public AffineTransformation setToShear(double xShear,
double yShear)
Sets this transformation to be a shear. The transformation matrix for a shear has the value:

|  1      xShear  0 |
|  yShear      1  0 |
|  0           0  1 |

Note that a shear of (1, 1) is not equal to shear(1, 0) composed with shear(0, 1). Instead, shear(1, 1) corresponds to a mapping onto the line x = y.
Parameters:
xShear - the x component to shear by
yShear - the y component to shear by
Returns:
this transformation, with an updated matrix
• setToTranslation

public AffineTransformation setToTranslation(double dx,
double dy)
Sets this transformation to be a translation. For a translation by the vector (x, y) the transformation matrix has the value:

|  1  0  dx |
|  1  0  dy |
|  0  0   1 |

Parameters:
dx - the x component to translate by
dy - the y component to translate by
Returns:
this transformation, with an updated matrix
• reflect

public AffineTransformation reflect(double x0,
double y0,
double x1,
double y1)
Updates the value of this transformation to that of a reflection transformation composed with the current value.
Parameters:
x0 - the x-ordinate of a point on the line to reflect around
y0 - the y-ordinate of a point on the line to reflect around
x1 - the x-ordinate of a point on the line to reflect around
y1 - the y-ordinate of a point on the line to reflect around
Returns:
this transformation, with an updated matrix
• reflect

public AffineTransformation reflect(double x,
double y)
Updates the value of this transformation to that of a reflection transformation composed with the current value.
Parameters:
x - the x-ordinate of the line to reflect around
y - the y-ordinate of the line to reflect around
Returns:
this transformation, with an updated matrix
• rotate

public AffineTransformation rotate(double theta)
Updates the value of this transformation to that of a rotation transformation composed with the current value. Positive angles correspond to a rotation in the counter-clockwise direction.
Parameters:
theta - the angle to rotate by, in radians
Returns:
this transformation, with an updated matrix
• rotate

public AffineTransformation rotate(double sinTheta,
double cosTheta)
Updates the value of this transformation to that of a rotation around the origin composed with the current value, with the sin and cos of the rotation angle specified directly.
Parameters:
sinTheta - the sine of the angle to rotate by
cosTheta - the cosine of the angle to rotate by
Returns:
this transformation, with an updated matrix
• rotate

public AffineTransformation rotate(double theta,
double x,
double y)
Updates the value of this transformation to that of a rotation around a given point composed with the current value. Positive angles correspond to a rotation in the counter-clockwise direction.
Parameters:
theta - the angle to rotate by, in radians
x - the x-ordinate of the rotation point
y - the y-ordinate of the rotation point
Returns:
this transformation, with an updated matrix
• rotate

public AffineTransformation rotate(double sinTheta,
double cosTheta,
double x,
double y)
Updates the value of this transformation to that of a rotation around a given point composed with the current value, with the sin and cos of the rotation angle specified directly.
Parameters:
sinTheta - the sine of the angle to rotate by
cosTheta - the cosine of the angle to rotate by
x - the x-ordinate of the rotation point
y - the y-ordinate of the rotation point
Returns:
this transformation, with an updated matrix
• scale

public AffineTransformation scale(double xScale,
double yScale)
Updates the value of this transformation to that of a scale transformation composed with the current value.
Parameters:
xScale - the value to scale by in the x direction
yScale - the value to scale by in the y direction
Returns:
this transformation, with an updated matrix
• shear

public AffineTransformation shear(double xShear,
double yShear)
Updates the value of this transformation to that of a shear transformation composed with the current value.
Parameters:
xShear - the value to shear by in the x direction
yShear - the value to shear by in the y direction
Returns:
this transformation, with an updated matrix
• translate

public AffineTransformation translate(double x,
double y)
Updates the value of this transformation to that of a translation transformation composed with the current value.
Parameters:
x - the value to translate by in the x direction
y - the value to translate by in the y direction
Returns:
this transformation, with an updated matrix
• compose

public AffineTransformation compose(AffineTransformation trans)
Updates this transformation to be the composition of this transformation with the given AffineTransformation. This produces a transformation whose effect is equal to applying this transformation followed by the argument transformation. Mathematically,
A.compose(B) = TB x TA

Parameters:
trans - an affine transformation
Returns:
this transformation, with an updated matrix
• composeBefore

public AffineTransformation composeBefore(AffineTransformation trans)
Updates this transformation to be the composition of a given AffineTransformation with this transformation. This produces a transformation whose effect is equal to applying the argument transformation followed by this transformation. Mathematically,
A.composeBefore(B) = TA x TB

Parameters:
trans - an affine transformation
Returns:
this transformation, with an updated matrix
• transform

public Coordinate transform(Coordinate src,
Coordinate dest)
Applies this transformation to the src coordinate and places the results in the dest coordinate (which may be the same as the source).
Parameters:
src - the coordinate to transform
dest - the coordinate to accept the results
Returns:
the dest coordinate
• transform

public Geometry transform(Geometry g)
Creates a new Geometry which is the result of this transformation applied to the input Geometry.
Parameters:
g - a Geometry
Returns:
a transformed Geometry
• transform

public void transform(CoordinateSequence seq,
int i)
Applies this transformation to the i'th coordinate in the given CoordinateSequence.
Parameters:
seq - a CoordinateSequence
i - the index of the coordinate to transform
• filter

public void filter(CoordinateSequence seq,
int i)
Transforms the i'th coordinate in the input sequence
Specified by:
filter in interface CoordinateSequenceFilter
Parameters:
seq - a CoordinateSequence
i - the index of the coordinate to transform
• isGeometryChanged

public boolean isGeometryChanged()
Description copied from interface: CoordinateSequenceFilter
Reports whether the execution of this filter has modified the coordinates of the geometry. If so, Geometry.geometryChanged() will be executed after this filter has finished being executed.

Most filters can simply return a constant value reflecting whether they are able to change the coordinates.

Specified by:
isGeometryChanged in interface CoordinateSequenceFilter
Returns:
true if this filter has changed the coordinates of the geometry
• isDone

public boolean isDone()
Reports that this filter should continue to be executed until all coordinates have been transformed.
Specified by:
isDone in interface CoordinateSequenceFilter
Returns:
false
• isIdentity

public boolean isIdentity()
Tests if this transformation is the identity transformation.
Returns:
true if this is the identity transformation
• equals

public boolean equals(Object obj)
Tests if an object is an AffineTransformation and has the same matrix as this transformation.
Overrides:
equals in class Object
Parameters:
obj - an object to test
Returns:
true if the given object is equal to this object
• toString

public String toString()
Gets a text representation of this transformation. The string is of the form:
AffineTransformation[[m00, m01, m02], [m10, m11, m12]]

Overrides:
toString in class Object
Returns:
a string representing this transformation
• clone

public Object clone()
Clones this transformation
Overrides:
clone in class Object
Returns:
a copy of this transformation