Class AffineTransform

public static final int TYPE_FLIP

The transformation includes a flip about an axis, swapping between right-handed and left-handed coordinate systems. In a right-handed system, the positive x-axis rotates counter-clockwise to the positive y-axis; in a left-handed system it rotates clockwise.

Field Value:

64

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM, getType()

public static final int TYPE_GENERAL_ROTATION

The transformation includes a rotation by an arbitrary angle. Angles are rotated, but length is preserved. This is mutually exclusive with TYPE_QUADRANT_ROTATION.

Field Value:

16

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_FLIP, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_TRANSFORM, TYPE_MASK_ROTATION, getType()

public static final int TYPE_GENERAL_SCALE

The transformation includes a general scale - length is scaled in either or both the x and y directions, but by different amounts; without affecting angles. This is mutually exclusive with TYPE_UNIFORM_SCALE.

Field Value:

4

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_FLIP, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM, TYPE_MASK_SCALE, getType()

public static final int TYPE_GENERAL_TRANSFORM

The transformation is an arbitrary conversion of coordinates which could not be decomposed into the other TYPEs.

Field Value:

32

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_FLIP, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, getType()

public static final int TYPE_IDENTITY

The transformation is the identity (x' = x, y' = y). All other transforms have either a combination of the appropriate transform flag bits for their type, or the type GENERAL_TRANSFORM.

Field Value:

0

See Also:

TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_FLIP, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM, getType()

public static final int TYPE_MASK_ROTATION

This constant checks if either variety of rotation is performed.

Field Value:

24

See Also:

TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION

public static final int TYPE_MASK_SCALE

This constant checks if either variety of scale transform is performed.

Field Value:

6

See Also:

TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE

public static final int TYPE_QUADRANT_ROTATION

The transformation includes a rotation of a multiple of 90 degrees (PI/2 radians). Angles are rotated, but length is preserved. This is mutually exclusive with TYPE_GENERAL_ROTATION.

Field Value:

8

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_FLIP, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM, TYPE_MASK_ROTATION, getType()

public static final int TYPE_TRANSLATION

The transformation includes a translation - shifting in the x or y direction without changing length or angles.

Field Value:

1

See Also:

TYPE_IDENTITY, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_FLIP, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM, getType()

public static final int TYPE_UNIFORM_SCALE

The transformation includes a uniform scale - length is scaled in both the x and y directions by the same amount, without affecting angles. This is mutually exclusive with TYPE_GENERAL_SCALE.

Field Value:

2

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_GENERAL_SCALE, TYPE_FLIP, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM, TYPE_MASK_SCALE, getType()

public AffineTransform()

Construct a new identity transform:

 [ 1 0 0 ]
 [ 0 1 0 ]
 [ 0 0 1 ]
 

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

Construct a transform with the given matrix entries:

 [ m00 m01 m02 ]
 [ m10 m11 m12 ]
 [  0   0   1  ]
 

Parameters:

m00 - the x scaling component

m10 - the y shearing component

m01 - the x shearing component

m11 - the y scaling component

m02 - the x translation component

m12 - the y translation component

public AffineTransform(double[] d)

Construct a transform from a sequence of double entries. The array must have at least 4 entries, which has a translation factor of 0; or 6 entries, for specifying all parameters:

 [ d[0] d[2] (d[4]) ]
 [ d[1] d[3] (d[5]) ]
 [  0     0    1    ]
 

Parameters:

d - the matrix to copy from, with at least 4 (6) entries

Throws:

NullPointerException - if d is null

ArrayIndexOutOfBoundsException - if d is too small

public AffineTransform(float m00,
                       float m10,
                       float m01,
                       float m11,
                       float m02,
                       float m12)

Construct a transform with the given matrix entries:

 [ m00 m01 m02 ]
 [ m10 m11 m12 ]
 [  0   0   1  ]
 

Parameters:

m00 - the x scaling component

m10 - the y shearing component

m01 - the x shearing component

m11 - the y scaling component

m02 - the x translation component

m12 - the y translation component

public AffineTransform(float[] f)

Construct a transform from a sequence of float entries. The array must have at least 4 entries, which has a translation factor of 0; or 6 entries, for specifying all parameters:

 [ f[0] f[2] (f[4]) ]
 [ f[1] f[3] (f[5]) ]
 [  0     0    1    ]
 

Parameters:

f - the matrix to copy from, with at least 4 (6) entries

Throws:

NullPointerException - if f is null

ArrayIndexOutOfBoundsException - if f is too small

public AffineTransform(AffineTransform tx)

Create a new transform which copies the given one.

Parameters:

tx - the transform to copy

Throws:

NullPointerException - if tx is null

public Object clone()

Create a new transform of the same run-time type, with the same transforming properties as this one.

Overrides:

clone in interface Object

Returns:

the clone

public void concatenate(AffineTransform tx)

Set this transform to the result of performing the original version of this followed by tx. This is commonly used when chaining transformations from one space to another. In matrix form:

 [ this ] = [ this ] x [ tx ]
 

Parameters:

tx - the transform to concatenate

Throws:

NullPointerException - if tx is null

See Also:

preConcatenate(AffineTransform)

public AffineTransform createInverse()
            throws NoninvertibleTransformException

Returns a transform, which if concatenated to this one, will result in the identity transform. This is useful for undoing transformations, but is only possible if the original transform has an inverse (ie. does not map multiple points to the same line or point). A transform exists only if getDeterminant() has a non-zero value. The inverse is calculated as:

 Let A be the matrix for which we want to find the inverse:

 A = [ m00 m01 m02 ]
     [ m10 m11 m12 ]
     [ 0   0   1   ]


                 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               ]


 

Returns:

a new inverse transform

Throws:

NoninvertibleTransformException - if inversion is not possible

See Also:

getDeterminant()

public Shape createTransformedShape(Shape src)

Return a new Shape, based on the given one, where the path of the shape has been transformed by this transform. Notice that this uses GeneralPath, which only stores points in float precision.

Parameters:

src - the shape source to transform

Returns:

the shape, transformed by this, null if src is null.

See Also:

GeneralPath.transform(AffineTransform)

public void deltaTransform(double[] srcPts,
                           int srcOff,
                           double[] dstPts,
                           int dstOff,
                           int num)

Perform this transformation, less any translation, on an array of points, in (x,y) pairs, storing the results in another (possibly same) array. This will not create a destination array. All sources are copied before the transformation, so that no result will overwrite a point that has not yet been evaluated. The reduced transform is equivalent to:

 [ x' ] = [ m00 m01 ] [ x ] = [ m00 * x + m01 * y ]
 [ y' ]   [ m10 m11 ] [ y ] = [ m10 * x + m11 * y ]
 

Parameters:

srcPts - the array of source points

srcOff - the starting offset into src

dstPts - the array of destination points

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null

ArrayIndexOutOfBoundsException - if array bounds are exceeded

public Point2D deltaTransform(Point2D src,
                              Point2D dst)

Perform this transformation, less any translation, on the given source point, and store the result in the destination (creating it if necessary). It is safe for src and dst to be the same. The reduced transform is equivalent to:

 [ x' ] = [ m00 m01 ] [ x ] = [ m00 * x + m01 * y ]
 [ y' ]   [ m10 m11 ] [ y ] = [ m10 * x + m11 * y ]
 

Parameters:

src - the source point

dst - the destination, or null

Returns:

the delta transformation of src, in dst if it was non-null

Throws:

NullPointerException - if src is null

public boolean equals(Object obj)

Compares two transforms for equality. This returns true if they have the same matrix values.

Overrides:

equals in interface Object

Parameters:

obj - the transform to compare

Returns:

true if it is equal

public double getDeterminant()

Return the determinant of this transform matrix. If the determinant is non-zero, the transform is invertible; otherwise operations which require an inverse throw a NoninvertibleTransformException. A result very near zero, due to rounding errors, may indicate that inversion results do not carry enough precision to be meaningful.

If this is a uniform scale transformation, the determinant also represents the squared value of the scale. Otherwise, it carries little additional meaning. The determinant is calculated as:

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

Returns:

the determinant

See Also:

createInverse()

public void getMatrix(double[] d)

Return the matrix of values used in this transform. If the matrix has fewer than 6 entries, only the scale and shear factors are returned; otherwise the translation factors are copied as well. The resulting values are:

 [ d[0] d[2] (d[4]) ]
 [ d[1] d[3] (d[5]) ]
 [  0     0    1    ]
 

Parameters:

d - the matrix to store the results into; with 4 (6) entries

Throws:

NullPointerException - if d is null

ArrayIndexOutOfBoundsException - if d is too small

public static AffineTransform getRotateInstance(double theta)

Returns a rotation transform. A positive angle (in radians) rotates the positive x-axis to the positive y-axis:

 [ cos(theta) -sin(theta) 0 ]
 [ sin(theta)  cos(theta) 0 ]
 [     0           0      1 ]
 

Parameters:

theta - the rotation angle

Returns:

the rotating transform

public static AffineTransform getRotateInstance(double theta,
                                                double x,
                                                double y)

Returns a rotation transform about a point. A positive angle (in radians) rotates the positive x-axis to the positive y-axis. This is the same as calling:

 AffineTransform tx = new AffineTransform();
 tx.setToTranslation(x, y);
 tx.rotate(theta);
 tx.translate(-x, -y);
 

The resulting matrix is:

 [ cos(theta) -sin(theta) x-x*cos+y*sin ]
 [ sin(theta)  cos(theta) y-x*sin-y*cos ]
 [     0           0            1       ]
 

Parameters:

theta - the rotation angle

x - the x coordinate of the pivot point

y - the y coordinate of the pivot point

Returns:

the rotating transform

public static AffineTransform getScaleInstance(double sx,
                                               double sy)

Returns a scaling transform:

 [ sx 0  0 ]
 [ 0  sy 0 ]
 [ 0  0  1 ]
 

Parameters:

sx - the x scaling factor

sy - the y scaling factor

Returns:

the scaling transform

public double getScaleX()

Returns the X coordinate scaling factor of the matrix.

Returns:

m00

See Also:

getMatrix(double[])

public double getScaleY()

Returns the Y coordinate scaling factor of the matrix.

Returns:

m11

See Also:

getMatrix(double[])

public static AffineTransform getShearInstance(double shx,
                                               double shy)

Returns a shearing transform (points are shifted in the x direction based on a factor of their y coordinate, and in the y direction as a factor of their x coordinate):

 [  1  shx 0 ]
 [ shy  1  0 ]
 [  0   0  1 ]
 

Parameters:

shx - the x shearing factor

shy - the y shearing factor

Returns:

the shearing transform

public double getShearX()

Returns the X coordinate shearing factor of the matrix.

Returns:

m01

See Also:

getMatrix(double[])

public double getShearY()

Returns the Y coordinate shearing factor of the matrix.

Returns:

m10

See Also:

getMatrix(double[])

public static AffineTransform getTranslateInstance(double tx,
                                                   double ty)

Returns a translation transform:

 [ 1 0 tx ]
 [ 0 1 ty ]
 [ 0 0 1  ]
 

Parameters:

tx - the x translation distance

ty - the y translation distance

Returns:

the translating transform

public double getTranslateX()

Returns the X coordinate translation factor of the matrix.

Returns:

m02

See Also:

getMatrix(double[])

public double getTranslateY()

Returns the Y coordinate translation factor of the matrix.

Returns:

m12

See Also:

getMatrix(double[])

public int getType()

Returns the type of this transform. The result is always valid, although it may not be the simplest interpretation (in other words, there are sequences of transforms which reduce to something simpler, which this does not always detect). The result is either TYPE_GENERAL_TRANSFORM, or a bit-wise combination of TYPE_TRANSLATION, the mutually exclusive TYPE_*_ROTATIONs, and the mutually exclusive TYPE_*_SCALEs.

Returns:

The type.

See Also:

TYPE_IDENTITY, TYPE_TRANSLATION, TYPE_UNIFORM_SCALE, TYPE_GENERAL_SCALE, TYPE_QUADRANT_ROTATION, TYPE_GENERAL_ROTATION, TYPE_GENERAL_TRANSFORM

public int hashCode()

Return the hashcode for this transformation. The formula is not documented, but appears to be the same as:

 long l = Double.doubleToLongBits(getScaleX());
 l = l * 31 + Double.doubleToLongBits(getShearX());
 l = l * 31 + Double.doubleToLongBits(getTranslateX());
 l = l * 31 + Double.doubleToLongBits(getShearY());
 l = l * 31 + Double.doubleToLongBits(getScaleY());
 l = l * 31 + Double.doubleToLongBits(getTranslateY());
 return (int) ((l >> 32) ^ l);
 

Overrides:

hashCode in interface Object

Returns:

the hashcode

public void inverseTransform(double[] srcPts,
                             int srcOff,
                             double[] dstPts,
                             int dstOff,
                             int num)
            throws NoninvertibleTransformException

Perform the inverse of this transformation on an array of points, in (x,y) pairs, storing the results in another (possibly same) array. This will not create a destination array. All sources are copied before the transformation, so that no result will overwrite a point that has not yet been evaluated.

Parameters:

srcPts - the array of source points

srcOff - the starting offset into src

dstPts - the array of destination points

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null

ArrayIndexOutOfBoundsException - if array bounds are exceeded

NoninvertibleTransformException - if the inverse does not exist

See Also:

getDeterminant()

public Point2D inverseTransform(Point2D src,
                                Point2D dst)
            throws NoninvertibleTransformException

Perform the inverse of this transformation on the given source point, and store the result in the destination (creating it if necessary). It is safe for src and dst to be the same.

Parameters:

src - the source point

dst - the destination, or null

Returns:

the inverse transformation of src, in dst if it was non-null

Throws:

NullPointerException - if src is null

NoninvertibleTransformException - if the inverse does not exist

See Also:

getDeterminant()

public boolean isIdentity()

Tests if this transformation is the identity:

 [ 1 0 0 ]
 [ 0 1 0 ]
 [ 0 0 1 ]
 

Returns:

true if this is the identity transform

public void preConcatenate(AffineTransform tx)

Set this transform to the result of performing tx followed by the original version of this. This is less common than normal concatenation, but can still be used to chain transformations from one space to another. In matrix form:

 [ this ] = [ tx ] x [ this ]
 

Parameters:

tx - the transform to concatenate

Throws:

NullPointerException - if tx is null

See Also:

concatenate(AffineTransform)

public void rotate(double theta)

Concatenate a rotation onto this transform. This is equivalent, but more efficient than concatenate(AffineTransform.getRotateInstance(theta)).

Parameters:

theta - the rotation angle

See Also:

getRotateInstance(double), concatenate(AffineTransform)

public void rotate(double theta,
                   double x,
                   double y)

Concatenate a rotation about a point onto this transform. This is equivalent, but more efficient than concatenate(AffineTransform.getRotateInstance(theta, x, y)).

Parameters:

theta - the rotation angle

x - the x coordinate of the pivot point

y - the y coordinate of the pivot point

See Also:

getRotateInstance(double,double,double), concatenate(AffineTransform)

public void scale(double sx,
                  double sy)

Concatenate a scale onto this transform. This is equivalent, but more efficient than concatenate(AffineTransform.getScaleInstance(sx, sy)).

Parameters:

sx - the x scaling factor

sy - the y scaling factor

See Also:

getScaleInstance(double,double), concatenate(AffineTransform)

public void setToIdentity()

Reset this transform to the identity (no transformation):

 [ 1 0 0 ]
 [ 0 1 0 ]
 [ 0 0 1 ]
 

public void setToRotation(double theta)

Set this transform to a rotation. A positive angle (in radians) rotates the positive x-axis to the positive y-axis:

 [ cos(theta) -sin(theta) 0 ]
 [ sin(theta)  cos(theta) 0 ]
 [     0           0      1 ]
 

Parameters:

theta - the rotation angle

public void setToRotation(double theta,
                          double x,
                          double y)

Set this transform to a rotation about a point. A positive angle (in radians) rotates the positive x-axis to the positive y-axis. This is the same as calling:

 tx.setToTranslation(x, y);
 tx.rotate(theta);
 tx.translate(-x, -y);
 

The resulting matrix is:

 [ cos(theta) -sin(theta) x-x*cos+y*sin ]
 [ sin(theta)  cos(theta) y-x*sin-y*cos ]
 [     0           0            1       ]
 

Parameters:

theta - the rotation angle

x - the x coordinate of the pivot point

y - the y coordinate of the pivot point

public void setToScale(double sx,
                       double sy)

Set this transform to a scale:

 [ sx 0  0 ]
 [ 0  sy 0 ]
 [ 0  0  1 ]
 

Parameters:

sx - the x scaling factor

sy - the y scaling factor

public void setToShear(double shx,
                       double shy)

Set this transform to a shear (points are shifted in the x direction based on a factor of their y coordinate, and in the y direction as a factor of their x coordinate):

 [  1  shx 0 ]
 [ shy  1  0 ]
 [  0   0  1 ]
 

Parameters:

shx - the x shearing factor

shy - the y shearing factor

public void setToTranslation(double tx,
                             double ty)

Set this transform to a translation:

 [ 1 0 tx ]
 [ 0 1 ty ]
 [ 0 0 1  ]
 

Parameters:

tx - the x translation distance

ty - the y translation distance

public void setTransform(double m00,
                         double m10,
                         double m01,
                         double m11,
                         double m02,
                         double m12)

Set this transform to the given values:

 [ m00 m01 m02 ]
 [ m10 m11 m12 ]
 [  0   0   1  ]
 

Parameters:

m00 - the x scaling component

m10 - the y shearing component

m01 - the x shearing component

m11 - the y scaling component

m02 - the x translation component

m12 - the y translation component

public void setTransform(AffineTransform tx)

Set this transform to a copy of the given one.

Parameters:

tx - the transform to copy

Throws:

NullPointerException - if tx is null

public void shear(double shx,
                  double shy)

Concatenate a shearing onto this transform. This is equivalent, but more efficient than concatenate(AffineTransform.getShearInstance(sx, sy)).

Parameters:

shx - the x shearing factor

shy - the y shearing factor

See Also:

getShearInstance(double,double), concatenate(AffineTransform)

public String toString()

Returns a string representation of the transform, in the format: "AffineTransform[[" + m00 + ", " + m01 + ", " + m02 + "], [" + m10 + ", " + m11 + ", " + m12 + "]]".

Overrides:

toString in interface Object

Returns:

the string representation

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

Perform this transformation on an array of points, in (x,y) pairs, storing the results in another (possibly same) array. This will not create a destination array. All sources are copied before the transformation, so that no result will overwrite a point that has not yet been evaluated.

Parameters:

srcPts - the array of source points

srcOff - the starting offset into src

dstPts - the array of destination points

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null

ArrayIndexOutOfBoundsException - if array bounds are exceeded

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

Perform this transformation on an array of points, in (x,y) pairs, storing the results in another array. This will not create a destination array.

Parameters:

srcPts - the array of source points

srcOff - the starting offset into src

dstPts - the array of destination points

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null

ArrayIndexOutOfBoundsException - if array bounds are exceeded

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

Perform this transformation on an array of points, in (x,y) pairs, storing the results in another array. This will not create a destination array.

Parameters:

srcPts - the array of source points

srcOff - the starting offset into src

dstPts - the array of destination points

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null

ArrayIndexOutOfBoundsException - if array bounds are exceeded

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

Perform this transformation on an array of points, in (x,y) pairs, storing the results in another (possibly same) array. This will not create a destination array. All sources are copied before the transformation, so that no result will overwrite a point that has not yet been evaluated.

Parameters:

srcPts - the array of source points

srcOff - the starting offset into src

dstPts - the array of destination points

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null

ArrayIndexOutOfBoundsException - if array bounds are exceeded

public Point2D transform(Point2D src,
                         Point2D dst)

Perform this transformation on the given source point, and store the result in the destination (creating it if necessary). It is safe for src and dst to be the same.

Parameters:

src - the source point

dst - the destination, or null

Returns:

the transformation of src, in dst if it was non-null

Throws:

NullPointerException - if src is null

public void transform(Point2D[] src,
                      int srcOff,
                      Point2D[] dst,
                      int dstOff,
                      int num)

Perform this transformation on an array of points, storing the results in another (possibly same) array. This will not create a destination array, but will create points for the null entries of the destination. The transformation is done sequentially. While having a single source and destination point be the same is safe, you should be aware that duplicate references to the same point in the source, and having the source overlap the destination, may result in your source points changing from a previous transform before it is their turn to be evaluated.

Parameters:

src - the array of source points

srcOff - the starting offset into src

dst - the array of destination points (may have null entries)

dstOff - the starting offset into dst

num - the number of points to transform

Throws:

NullPointerException - if src or dst is null, or src has null entries

ArrayIndexOutOfBoundsException - if array bounds are exceeded

ArrayStoreException - if new points are incompatible with dst

public void translate(double tx,
                      double ty)

Concatenate a translation onto this transform. This is equivalent, but more efficient than concatenate(AffineTransform.getTranslateInstance(tx, ty)).

Parameters:

tx - the x translation distance

ty - the y translation distance

See Also:

getTranslateInstance(double,double), concatenate(AffineTransform)