Class AffineTransformation

Represents an affine transformation on the 2D Cartesian plane.

Inheritance

object

AffineTransformation

Implements

ICloneable

ICoordinateSequenceFilter

IEquatable<AffineTransformation>

Inherited Members

object.Equals(object, object)

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

Namespace: NetTopologySuite.Geometries.Utilities

Assembly: NetTopologySuite.dll

Syntax

public class AffineTransformation : ICloneable, ICoordinateSequenceFilter, IEquatable<AffineTransformation>

Remarks

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(AffineTransformation) method. Composition is computed via multiplication of the transformation matrices, and is defined as:

A.compose(B) = T_B x T_A

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

Constructors

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AffineTransformation()

Constructs a new identity transformation

Declaration

public AffineTransformation()

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AffineTransformation(Coordinate, Coordinate, Coordinate, Coordinate, Coordinate, Coordinate)

Constructs a transformation which maps the given source points into the given destination points.

Declaration

public AffineTransformation(Coordinate src0, Coordinate src1, Coordinate src2, Coordinate dest0, Coordinate dest1, Coordinate dest2)

Parameters

Type	Name	Description
Coordinate	src0	source point 0
Coordinate	src1	source point 1
Coordinate	src2	source point 2
Coordinate	dest0	the mapped point for source point 0
Coordinate	dest1	the mapped point for source point 1
Coordinate	dest2	the mapped point for source point 2

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AffineTransformation(AffineTransformation)

Constructs a transformation which is a copy of the given one.

Declaration

public AffineTransformation(AffineTransformation trans)

Parameters

Type	Name	Description
AffineTransformation	trans	the transformation to copy

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AffineTransformation(double, double, double, double, double, double)

Constructs a new transformation whose matrix has the specified values.

Declaration

public AffineTransformation(double m00, double m01, double m02, double m10, double m11, double m12)

Parameters

Type	Name	Description
double	m00	the entry for the [0, 0] element in the transformation matrix
double	m01	the entry for the [0, 1] element in the transformation matrix
double	m02	the entry for the [0, 2] element in the transformation matrix
double	m10	the entry for the [1, 0] element in the transformation matrix
double	m11	the entry for the [1, 1] element in the transformation matrix
double	m12	the entry for the [1, 2] element in the transformation matrix

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AffineTransformation(double[])

Constructs a new transformation whose matrix has the specified values.

Declaration

public AffineTransformation(double[] matrix)

Parameters

Type	Name	Description
double[]	matrix	an array containing the 6 values { m00, m01, m02, m10, m11, m12 }

Exceptions

Type	Condition
NullReferenceException	if matrix is null
IndexOutOfRangeException	if matrix is too small

Properties

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Determinant

Computes the determinant of the transformation matrix.

Declaration

public double Determinant { get; }

Property Value

Type	Description
double	the determinant of the transformation

Remarks

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 NoninvertibleTransformationException.

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Done

Reports that this filter should continue to be executed until all coordinates have been transformed.

Declaration

public bool Done { get; }

Property Value

Type	Description
bool	false

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GeometryChanged

Reports whether the execution of this filter has modified the coordinates of the geometry. If so, GeometryChanged() will be executed after this filter has finished being executed.

Declaration

public bool GeometryChanged { get; }

Property Value

Type	Description
bool

Remarks

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

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IsIdentity

Tests if this transformation is the identity transformation.

Declaration

public bool IsIdentity { get; }

Property Value

Type	Description
bool

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MatrixEntries

Gets an array containing the entries of the transformation matrix.

Declaration

public double[] MatrixEntries { get; }

Property Value

Type	Description
double[]	an array of length 6

Remarks

Only the 6 non-trivial entries are returned, in the sequence:

m00, m01, m02, m10, m11, m12

Methods

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Clone()

Clones this transformation

Declaration

public object Clone()

Returns

Type	Description
object	A copy of this transformation

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Compose(AffineTransformation)

Updates this transformation to be the composition of this transformation with the given AffineTransformation.

Declaration

public AffineTransformation Compose(AffineTransformation trans)

Parameters

Type	Name	Description
AffineTransformation	trans	an affine transformation

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

This produces a transformation whose effect is equal to applying this transformation followed by the argument transformation. Mathematically,

A.compose(B) = T_B x T_A

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ComposeBefore(AffineTransformation)

Updates this transformation to be the composition of a given AffineTransformation with this transformation.

Declaration

public AffineTransformation ComposeBefore(AffineTransformation trans)

Parameters

Type	Name	Description
AffineTransformation	trans	an affine transformation

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

This produces a transformation whose effect is equal to applying the argument transformation followed by this transformation. Mathematically,

A.composeBefore(B) = T_A x T_B

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Equals(AffineTransformation)

Declaration

public bool Equals(AffineTransformation trans)

Parameters

Type	Name	Description
AffineTransformation	trans

Returns

Type	Description
bool

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Equals(object)

Tests if an object is an AffineTransformation and has the same matrix as this transformation.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
object	obj	An object to test

Returns

Type	Description
bool	true if the given object is equal to this object

Overrides

object.Equals(object)

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Filter(CoordinateSequence, int)

Transforms the i'th coordinate in the input sequence

Declaration

public void Filter(CoordinateSequence seq, int i)

Parameters

Type	Name	Description
CoordinateSequence	seq	A `CoordinateSequence`
int	i	The index of the coordinate to transform

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GetHashCode()

Declaration

public override int GetHashCode()

Returns

Type	Description
int

Overrides

object.GetHashCode()

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GetInverse()

Computes the inverse of this transformation, if one exists.

Declaration

public AffineTransformation GetInverse()

Returns

Type	Description
AffineTransformation	A new inverse transformation

Remarks

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
            inverse(A)  =  ---   x  adjoint(A)
                           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               |</code></pre></blockquote>

Exceptions

Type	Condition
NoninvertibleTransformationException

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Reflect(double, double)

Updates the value of this transformation to that of a reflection transformation composed with the current value.

Declaration

public AffineTransformation Reflect(double x, double y)

Parameters

Type	Name	Description
double	x	the x-ordinate of the line to reflect around
double	y	the y-ordinate of the line to reflect around

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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Reflect(double, double, double, double)

Updates the value of this transformation to that of a reflection transformation composed with the current value.

Declaration

public AffineTransformation Reflect(double x0, double y0, double x1, double y1)

Parameters

Type	Name	Description
double	x0	the x-ordinate of a point on the line to reflect around
double	y0	the y-ordinate of a point on the line to reflect around
double	x1	the x-ordinate of a point on the line to reflect around
double	y1	the y-ordinate of a point on the line to reflect around

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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ReflectionInstance(double, double)

Creates a transformation for a reflection about the line (0,0) - (x,y).

Declaration

public static AffineTransformation ReflectionInstance(double x, double y)

Parameters

Type	Name	Description
double	x	the x-ordinate of a point on the reflection line
double	y	the y-ordinate of a point on the reflection line

Returns

Type	Description
AffineTransformation	a transformation for the reflection

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ReflectionInstance(double, double, double, double)

Creates a transformation for a reflection about the line (x0,y0) - (x1,y1).

Declaration

public static AffineTransformation ReflectionInstance(double x0, double y0, double x1, double y1)

Parameters

Type	Name	Description
double	x0	the x-ordinate of a point on the reflection line
double	y0	the y-ordinate of a point on the reflection line
double	x1	the x-ordinate of a another point on the reflection line
double	y1	the y-ordinate of a another point on the reflection line

Returns

Type	Description
AffineTransformation	a transformation for the reflection

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Rotate(double)

Updates the value of this transformation to that of a rotation transformation composed with the current value.

Declaration

public AffineTransformation Rotate(double theta)

Parameters

Type	Name	Description
double	theta	the angle to rotate by in radians

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

Positive angles correspond to a rotation in the counter-clockwise direction.

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Rotate(double, double)

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.

Declaration

public AffineTransformation Rotate(double sinTheta, double cosTheta)

Parameters

Type	Name	Description
double	sinTheta	the sine of the angle to rotate by
double	cosTheta	the cosine of the angle to rotate by

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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Rotate(double, double, double)

Updates the value of this transformation to that of a rotation around a given point composed with the current value.

Declaration

public AffineTransformation Rotate(double theta, double x, double y)

Parameters

Type	Name	Description
double	theta	the angle to rotate by, in radians
double	x	the x-ordinate of the rotation point
double	y	the y-ordinate of the rotation point

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

Positive angles correspond to a rotation in the counter-clockwise direction.

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Rotate(double, double, double, double)

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.

Declaration

public AffineTransformation Rotate(double sinTheta, double cosTheta, double x, double y)

Parameters

Type	Name	Description
double	sinTheta	the sine of the angle to rotate by
double	cosTheta	the cosine of the angle to rotate by
double	x	the x-ordinate of the rotation point
double	y	the y-ordinate of the rotation point

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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RotationInstance(double)

Creates a transformation for a rotation about the origin by an angle theta.

Declaration

public static AffineTransformation RotationInstance(double theta)

Parameters

Type	Name	Description
double	theta	the rotation angle, in radians

Returns

Type	Description
AffineTransformation	a transformation for the rotation

Remarks

Positive angles correspond to a rotation in the counter-clockwise direction.

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RotationInstance(double, double)

Creates a transformation for a rotation by an angle theta, specified by the sine and cosine of the angle.

Declaration

public static AffineTransformation RotationInstance(double sinTheta, double cosTheta)

Parameters

Type	Name	Description
double	sinTheta	the sine of the rotation angle
double	cosTheta	the cosine of the rotation angle

Returns

Type	Description
AffineTransformation	a transformation for the rotation

Remarks

This allows providing exact values for sin(theta) and cos(theta) for the common case of rotations of multiples of quarter-circles.

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RotationInstance(double, double, double)

Creates a transformation for a rotation about the point (x,y) by an angle theta.

Declaration

public static AffineTransformation RotationInstance(double theta, double x, double y)

Parameters

Type	Name	Description
double	theta	the rotation angle, in radians
double	x	the x-ordinate of the rotation point
double	y	the y-ordinate of the rotation point

Returns

Type	Description
AffineTransformation	a transformation for the rotation

Remarks

Positive angles correspond to a rotation in the counter-clockwise direction.

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RotationInstance(double, double, double, double)

Creates a transformation for a rotation about the point (x,y) by an angle theta, specified by the sine and cosine of the angle.

Declaration

public static AffineTransformation RotationInstance(double sinTheta, double cosTheta, double x, double y)

Parameters

Type	Name	Description
double	sinTheta	the sine of the rotation angle
double	cosTheta	the cosine of the rotation angle
double	x	the x-ordinate of the rotation point
double	y	the y-ordinate of the rotation point

Returns

Type	Description
AffineTransformation	a transformation for the rotation

Remarks

This allows providing exact values for sin(theta) and cos(theta) for the common case of rotations of multiples of quarter-circles.

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Scale(double, double)

Updates the value of this transformation to that of a scale transformation composed with the current value.

Declaration

public AffineTransformation Scale(double xScale, double yScale)

Parameters

Type	Name	Description
double	xScale	the value to scale by in the x direction
double	yScale	the value to scale by in the y direction

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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ScaleInstance(double, double)

Creates a transformation for a scaling relative to the origin.

Declaration

public static AffineTransformation ScaleInstance(double xScale, double yScale)

Parameters

Type	Name	Description
double	xScale	the value to scale by in the x direction
double	yScale	the value to scale by in the y direction

Returns

Type	Description
AffineTransformation	a transformation for the scaling

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ScaleInstance(double, double, double, double)

Creates a transformation for a scaling relative to the point (x,y).

Declaration

public static AffineTransformation ScaleInstance(double xScale, double yScale, double x, double y)

Parameters

Type	Name	Description
double	xScale	The value to scale by in the x direction
double	yScale	The value to scale by in the y direction
double	x	The x-ordinate of the point to scale around
double	y	The y-ordinate of the point to scale around

Returns

Type	Description
AffineTransformation	A transformation for the scaling

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SetToIdentity()

Sets this transformation to be the identity transformation.

Declaration

public AffineTransformation SetToIdentity()

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

The identity transformation has the matrix:

| 1 0 0 |
            | 0 1 0 |
            | 0 0 1 |

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SetToReflection(double, double)

Sets this transformation to be a reflection about the line defined by vector (x,y).

Declaration

public AffineTransformation SetToReflection(double x, double y)

Parameters

Type	Name	Description
double	x	the x-component of the reflection line vector
double	y	the y-component of the reflection line vector

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

The transformation for a reflection is computed by:

d = sqrt(x2 + y2)
            sin = x / d;
            cos = x / d;
            Tref = Trot(sin, cos) x Tscale(1, -1) x Trot(-sin, cos)

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SetToReflection(double, double, double, double)

Sets this transformation to be a reflection about the line defined by a line (x0,y0) - (x1,y1).

Declaration

public AffineTransformation SetToReflection(double x0, double y0, double x1, double y1)

Parameters

Type	Name	Description
double	x0	The x-ordinate of one point on the reflection line
double	y0	The y-ordinate of one point on the reflection line
double	x1	The x-ordinate of another point on the reflection line
double	y1	The y-ordinate of another point on the reflection line

Returns

Type	Description
AffineTransformation	This transformation with an updated matrix

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SetToReflectionBasic(double, double, double, double)

Explicitly computes the math for a reflection. May not work.

Declaration

public AffineTransformation SetToReflectionBasic(double x0, double y0, double x1, double y1)

Parameters

Type	Name	Description
double	x0	The x-ordinate of one point on the reflection line
double	y0	The y-ordinate of one point on the reflection line
double	x1	The x-ordinate of another point on the reflection line
double	y1	The y-ordinate of another point on the reflection line

Returns

Type	Description
AffineTransformation	This transformation with an updated matrix

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SetToRotation(double)

Sets this transformation to be a rotation around the orign.

Declaration

public AffineTransformation SetToRotation(double theta)

Parameters

Type	Name	Description
double	theta	the rotation angle, in radians

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

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 |

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SetToRotation(double, double)

Sets this transformation to be a rotation around the origin by specifying the sin and cos of the rotation angle directly.

Declaration

public AffineTransformation SetToRotation(double sinTheta, double cosTheta)

Parameters

Type	Name	Description
double	sinTheta	the sine of the rotation angle
double	cosTheta	the cosine of the rotation angle

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

The transformation matrix for the rotation has the value:

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

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SetToRotation(double, double, double)

Sets this transformation to be a rotation around a given point (x,y).

Declaration

public AffineTransformation SetToRotation(double theta, double x, double y)

Parameters

Type	Name	Description
double	theta	the rotation angle, in radians
double	x	the x-ordinate of the rotation point
double	y	the y-ordinate of the rotation point

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

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 |

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SetToRotation(double, double, double, double)

Sets this transformation to be a rotation around a given point (x,y) by specifying the sin and cos of the rotation angle directly.

Declaration

public AffineTransformation SetToRotation(double sinTheta, double cosTheta, double x, double y)

Parameters

Type	Name	Description
double	sinTheta	the sine of the rotation angle
double	cosTheta	the cosine of the rotation angle
double	x	the x-ordinate of the rotation point
double	y	the y-ordinate of the rotation point

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

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       |

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SetToScale(double, double)

Sets this transformation to be a scaling.

Declaration

public AffineTransformation SetToScale(double xScale, double yScale)

Parameters

Type	Name	Description
double	xScale	the amount to scale x-ordinates by
double	yScale	the amount to scale y-ordinates by

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

The transformation matrix for a scale has the value:

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

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SetToShear(double, double)

Sets this transformation to be a shear.

Declaration

public AffineTransformation SetToShear(double xShear, double yShear)

Parameters

Type	Name	Description
double	xShear	the x component to shear by
double	yShear	the y component to shear by

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

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.

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SetToTranslation(double, double)

Sets this transformation to be a translation.

Declaration

public AffineTransformation SetToTranslation(double dx, double dy)

Parameters

Type	Name	Description
double	dx	the x component to translate by
double	dy	the y component to translate by

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

Remarks

For a translation by the vector (x, y) the transformation matrix has the value:

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

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SetTransformation(AffineTransformation)

Sets this transformation to be a copy of the given one

Declaration

public AffineTransformation SetTransformation(AffineTransformation trans)

Parameters

Type	Name	Description
AffineTransformation	trans	a transformation to copy

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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SetTransformation(double, double, double, double, double, double)

Sets this transformation's matrix to have the given values.

Declaration

public AffineTransformation SetTransformation(double m00, double m01, double m02, double m10, double m11, double m12)

Parameters

Type	Name	Description
double	m00	the entry for the [0, 0] element in the transformation matrix
double	m01	the entry for the [0, 1] element in the transformation matrix
double	m02	the entry for the [0, 2] element in the transformation matrix
double	m10	the entry for the [1, 0] element in the transformation matrix
double	m11	the entry for the [1, 1] element in the transformation matrix
double	m12	the entry for the [1, 2] element in the transformation matrix

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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Shear(double, double)

Updates the value of this transformation to that of a shear transformation composed with the current value.

Declaration

public AffineTransformation Shear(double xShear, double yShear)

Parameters

Type	Name	Description
double	xShear	the value to shear by in the x direction
double	yShear	the value to shear by in the y direction

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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ShearInstance(double, double)

Creates a transformation for a shear.

Declaration

public static AffineTransformation ShearInstance(double xShear, double yShear)

Parameters

Type	Name	Description
double	xShear	the value to shear by in the x direction
double	yShear	the value to shear by in the y direction

Returns

Type	Description
AffineTransformation	a transformation for the shear

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ToString()

Gets a text representation of this transformation. The string is of the form:

AffineTransformation[[m00, m01, m02], [m10, m11, m12]]

Declaration

public override string ToString()

Returns

Type	Description
string	A string representing this transformation

Overrides

object.ToString()

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Transform(Coordinate, Coordinate)

Applies this transformation to the src coordinate and places the results in the dest coordinate (which may be the same as the source).

Declaration

public Coordinate Transform(Coordinate src, Coordinate dest)

Parameters

Type	Name	Description
Coordinate	src	the coordinate to transform
Coordinate	dest	the coordinate to accept the results

Returns

Type	Description
Coordinate	the `dest` coordinate

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Transform(CoordinateSequence, int)

Applies this transformation to the i'th coordinate in the given CoordinateSequence.

Declaration

public void Transform(CoordinateSequence seq, int i)

Parameters

Type	Name	Description
CoordinateSequence	seq	a `CoordinateSequence`
int	i	the index of the coordinate to transform

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Transform(Geometry)

Creates a new Geometry which is the result of this transformation applied to the input Geometry.

Declaration

public Geometry Transform(Geometry g)

Parameters

Type	Name	Description
Geometry	g	A `Geometry`

Returns

Type	Description
Geometry	The transformed Geometry

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Translate(double, double)

Updates the value of this transformation to that of a translation transformation composed with the current value.

Declaration

public AffineTransformation Translate(double x, double y)

Parameters

Type	Name	Description
double	x	the value to translate by in the x direction
double	y	the value to translate by in the y direction

Returns

Type	Description
AffineTransformation	this transformation, with an updated matrix

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TranslationInstance(double, double)

Creates a transformation for a translation.

Declaration

public static AffineTransformation TranslationInstance(double x, double y)

Parameters

Type	Name	Description
double	x	the value to translate by in the x direction
double	y	the value to translate by in the y direction

Returns

Type	Description
AffineTransformation	a transformation for the translation

Implements

ICloneable

ICoordinateSequenceFilter

IEquatable<T>