java.awt.geom
Class AffineTransform

java.lang.Object
  java.awt.geom.AffineTransform

All Implemented Interfaces:

Serializable , Cloneable

public class AffineTransform
extends Object
implements Cloneable, Serializable

The AffineTransform class represents a 2D affine transform that performs a linear mapping from 2D coordinates to other 2D coordinates that preserves the "straightness" and "parallelness" of lines. Affine transformations can be constructed using sequences of translations, scales, flips, rotations, and shears.

Such a coordinate transformation can be represented by a 3 row by 3 column matrix with an implied last row of [ 0 0 1 ]. This matrix transforms source coordinates (x,y) (x, y) into destination coordinates (x',y') (x', y') by considering them to be a column vector and multiplying the coordinate vector by the matrix according to the following process:

        [ x']   [  m00  m01  m02  ] [ x ]   [ m00x + m01y + m02 ]
        [ y'] = [  m10  m11  m12  ] [ y ] = [ m10x + m11y + m12 ]
        [ 1 ]   [   0    0    1   ] [ 1 ]   [         1         ]
 

Handling 90-Degree Rotations

In some variations of the rotate methods in the AffineTransform class, a double-precision argument specifies the angle of rotation in radians. These methods have special handling for rotations of approximately 90 degrees (including multiples such as 180, 270, and 360 degrees), so that the common case of quadrant rotation is handled more efficiently. This special handling can cause angles very close to multiples of 90 degrees to be treated as if they were exact multiples of 90 degrees. For small multiples of 90 degrees the range of angles treated as a quadrant rotation is approximately 0.00000121 degrees wide. This section explains why such special care is needed and how it is implemented.

Since 90 degrees is represented as PI/2 in radians, and since PI is a transcendental (and therefore irrational) number, it is not possible to exactly represent a multiple of 90 degrees as an exact double precision value measured in radians. As a result it is theoretically impossible to describe quadrant rotations (90, 180, 270 or 360 degrees) using these values. Double precision floating point values can get very close to non-zero multiples of PI/2 but never close enough for the sine or cosine to be exactly 0.0, 1.0 or -1.0. The implementations of Math.sin() and Math.cos() correspondingly never return 0.0 for any case other than Math.sin(0.0). These same implementations do, however, return exactly 1.0 and -1.0 for some range of numbers around each multiple of 90 degrees since the correct answer is so close to 1.0 or -1.0 that the double precision significand cannot represent the difference as accurately as it can for numbers that are near 0.0.

The net result of these issues is that if the Math.sin() and Math.cos() methods are used to directly generate the values for the matrix modifications during these radian-based rotation operations then the resulting transform is never strictly classifiable as a quadrant rotation even for a simple case like rotate(Math.PI/2.0), due to minor variations in the matrix caused by the non-0.0 values obtained for the sine and cosine. If these transforms are not classified as quadrant rotations then subsequent code which attempts to optimize further operations based upon the type of the transform will be relegated to its most general implementation.

Because quadrant rotations are fairly common, this class should handle these cases reasonably quickly, both in applying the rotations to the transform and in applying the resulting transform to the coordinates. To facilitate this optimal handling, the methods which take an angle of rotation measured in radians attempt to detect angles that are intended to be quadrant rotations and treat them as such. These methods therefore treat an angle theta as a quadrant rotation if either Math.sin(theta) or Math.cos(theta) returns exactly 1.0 or -1.0. As a rule of thumb, this property holds true for a range of approximately 0.0000000211 radians (or 0.00000121 degrees) around small multiples of Math.PI/2.0.

Since:

1.2

See Also:

Serialized Form

TYPE_IDENTITY

public static final int TYPE_IDENTITY

This constant indicates that the transform defined by this object is an identity transform. An identity transform is one in which the output coordinates are always the same as the input coordinates. If this transform is anything other than the identity transform, the type will either be the constant GENERAL_TRANSFORM or a combination of the appropriate flag bits for the various coordinate conversions that this transform performs.

Since:

1.2

See Also:

TYPE_TRANSLATION , TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , TYPE_FLIP , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_TRANSLATION

public static final int TYPE_TRANSLATION

This flag bit indicates that the transform defined by this object performs a translation in addition to the conversions indicated by other flag bits. A translation moves the coordinates by a constant amount in x and y without changing the length or angle of vectors.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , TYPE_FLIP , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_UNIFORM_SCALE

public static final int TYPE_UNIFORM_SCALE

This flag bit indicates that the transform defined by this object performs a uniform scale in addition to the conversions indicated by other flag bits. A uniform scale multiplies the length of vectors by the same amount in both the x and y directions without changing the angle between vectors. This flag bit is mutually exclusive with the TYPE_GENERAL_SCALE flag.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_TRANSLATION , TYPE_GENERAL_SCALE , TYPE_FLIP , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_GENERAL_SCALE

public static final int TYPE_GENERAL_SCALE

This flag bit indicates that the transform defined by this object performs a general scale in addition to the conversions indicated by other flag bits. A general scale multiplies the length of vectors by different amounts in the x and y directions without changing the angle between perpendicular vectors. This flag bit is mutually exclusive with the TYPE_UNIFORM_SCALE flag.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_TRANSLATION , TYPE_UNIFORM_SCALE , TYPE_FLIP , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_MASK_SCALE

public static final int TYPE_MASK_SCALE

This constant is a bit mask for any of the scale flag bits.

Since:

1.2

See Also:

TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , Constant Field Values

TYPE_FLIP

public static final int TYPE_FLIP

This flag bit indicates that the transform defined by this object performs a mirror image flip about some axis which changes the normally right handed coordinate system into a left handed system in addition to the conversions indicated by other flag bits. A right handed coordinate system is one where the positive X axis rotates counterclockwise to overlay the positive Y axis similar to the direction that the fingers on your right hand curl when you stare end on at your thumb. A left handed coordinate system is one where the positive X axis rotates clockwise to overlay the positive Y axis similar to the direction that the fingers on your left hand curl. There is no mathematical way to determine the angle of the original flipping or mirroring transformation since all angles of flip are identical given an appropriate adjusting rotation.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_TRANSLATION , TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_QUADRANT_ROTATION

public static final int TYPE_QUADRANT_ROTATION

This flag bit indicates that the transform defined by this object performs a quadrant rotation by some multiple of 90 degrees in addition to the conversions indicated by other flag bits. A rotation changes the angles of vectors by the same amount regardless of the original direction of the vector and without changing the length of the vector. This flag bit is mutually exclusive with the TYPE_GENERAL_ROTATION flag.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_TRANSLATION , TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , TYPE_FLIP , TYPE_GENERAL_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_GENERAL_ROTATION

public static final int TYPE_GENERAL_ROTATION

This flag bit indicates that the transform defined by this object performs a rotation by an arbitrary angle in addition to the conversions indicated by other flag bits. A rotation changes the angles of vectors by the same amount regardless of the original direction of the vector and without changing the length of the vector. This flag bit is mutually exclusive with the TYPE_QUADRANT_ROTATION flag.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_TRANSLATION , TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , TYPE_FLIP , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_TRANSFORM , getType() , Constant Field Values

TYPE_MASK_ROTATION

public static final int TYPE_MASK_ROTATION

This constant is a bit mask for any of the rotation flag bits.

Since:

1.2

See Also:

TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , Constant Field Values

TYPE_GENERAL_TRANSFORM

public static final int TYPE_GENERAL_TRANSFORM

This constant indicates that the transform defined by this object performs an arbitrary conversion of the input coordinates. If this transform can be classified by any of the above constants, the type will either be the constant TYPE_IDENTITY or a combination of the appropriate flag bits for the various coordinate conversions that this transform performs.

Since:

1.2

See Also:

TYPE_IDENTITY , TYPE_TRANSLATION , TYPE_UNIFORM_SCALE , TYPE_GENERAL_SCALE , TYPE_FLIP , TYPE_QUADRANT_ROTATION , TYPE_GENERAL_ROTATION , getType() , Constant Field Values

AffineTransform

public AffineTransform()

Constructs a new AffineTransform representing the Identity transformation.

Since:

1.2

AffineTransform

public AffineTransform(AffineTransform Tx)

Constructs a new AffineTransform that is a copy of the specified AffineTransform object.

Parameters:

Tx - the AffineTransform object to copy

Since:

1.2

AffineTransform

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

Constructs a new AffineTransform from 6 floating point values representing the 6 specifiable entries of the 3x3 transformation matrix.

Parameters:

m00 - the X coordinate scaling element of the 3x3 matrix

m10 - the Y coordinate shearing element of the 3x3 matrix

m01 - the X coordinate shearing element of the 3x3 matrix

m11 - the Y coordinate scaling element of the 3x3 matrix

m02 - the X coordinate translation element of the 3x3 matrix

m12 - the Y coordinate translation element of the 3x3 matrix

Since:

1.2

m00, m01, m02, m10, m11, m12 - the 6 floating point values that compose the 3x3 transformation matrix

AffineTransform

public AffineTransform(float[] flatmatrix)

Constructs a new AffineTransform from an array of floating point values representing either the 4 non-translation enries or the 6 specifiable entries of the 3x3 transformation matrix. The values are retrieved from the array as { m00 m10 m01 m11 [m02 m12]}.

Parameters:

flatmatrix - the float array containing the values to be set in the new AffineTransform object. The length of the array is assumed to be at least 4. If the length of the array is less than 6, only the first 4 values are taken. If the length of the array is greater than 6, the first 6 values are taken.

Since:

1.2

AffineTransform

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

Constructs a new AffineTransform from 6 double precision values representing the 6 specifiable entries of the 3x3 transformation matrix.

Parameters:

m00 - the X coordinate scaling element of the 3x3 matrix

m10 - the Y coordinate shearing element of the 3x3 matrix

m01 - the X coordinate shearing element of the 3x3 matrix

m11 - the Y coordinate scaling element of the 3x3 matrix

m02 - the X coordinate translation element of the 3x3 matrix

m12 - the Y coordinate translation element of the 3x3 matrix

Since:

1.2

m00, m01, m02, m10, m11, m12 - the 6 floating point values that compose the 3x3 transformation matrix

AffineTransform

public AffineTransform(double[] flatmatrix)

Constructs a new AffineTransform from an array of double precision values representing either the 4 non-translation entries or the 6 specifiable entries of the 3x3 transformation matrix. The values are retrieved from the array as { m00 m10 m01 m11 [m02 m12]}.

Parameters:

flatmatrix - the double array containing the values to be set in the new AffineTransform object. The length of the array is assumed to be at least 4. If the length of the array is less than 6, only the first 4 values are taken. If the length of the array is greater than 6, the first 6 values are taken.

Since:

1.2

getTranslateInstance

public static AffineTransform getTranslateInstance(double tx,
                                                   double ty)

Returns a transform representing a translation transformation. The matrix representing the returned transform is:

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

Parameters:

tx - the distance by which coordinates are translated in the X axis direction

ty - the distance by which coordinates are translated in the Y axis direction

Returns:

an AffineTransform object that represents a translation transformation, created with the specified vector.

Since:

1.2

getRotateInstance

public static AffineTransform getRotateInstance(double theta)

Returns a transform representing a rotation transformation. The matrix representing the returned transform is:

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

Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.

Parameters:

theta - the angle of rotation measured in radians

Returns:

an AffineTransform object that is a rotation transformation, created with the specified angle of rotation.

Since:

1.2

getRotateInstance

public static AffineTransform getRotateInstance(double theta,
                                                double anchorx,
                                                double anchory)

Returns a transform that rotates coordinates around an anchor point. This operation is equivalent to translating the coordinates so that the anchor point is at the origin (S1), then rotating them about the new origin (S2), and finally translating so that the intermediate origin is restored to the coordinates of the original anchor point (S3).

This operation is equivalent to the following sequence of calls:

     AffineTransform Tx = new AffineTransform();
     Tx.translate(anchorx, anchory);    // S3: final translation
     Tx.rotate(theta);                // S2: rotate around anchor
     Tx.translate(-anchorx, -anchory);  // S1: translate anchor to origin
 

The matrix representing the returned transform is:

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

Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.

Parameters:

theta - the angle of rotation measured in radians

anchorx anchorx, anchory - the X coordinate coordinates of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point

Returns:

an AffineTransform object that rotates coordinates around the specified point by the specified angle of rotation.

Since:

1.2

getRotateInstance

public static AffineTransform getRotateInstance(double vecx,
                                                double vecy)

Returns a transform that rotates coordinates according to a rotation vector. All coordinates rotate about the origin by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both vecx and vecy are 0.0, an identity transform is returned. This operation is equivalent to calling:

     AffineTransform.getRotateInstance(Math.atan2(vecy, vecx));
 

Parameters:

vecx - the X coordinate of the rotation vector

vecy - the Y coordinate of the rotation vector vecx, vecy - the coordinates of the rotation vector

Returns:

an AffineTransform object that rotates coordinates according to the specified rotation vector.

Since:

1.6

getRotateInstance

public static AffineTransform getRotateInstance(double vecx,
                                                double vecy,
                                                double anchorx,
                                                double anchory)

Returns a transform that rotates coordinates around an anchor point accordinate to a rotation vector. All coordinates rotate about the specified anchor coordinates by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both vecx and vecy are 0.0, an identity transform is returned. This operation is equivalent to calling:

     AffineTransform.getRotateInstance(Math.atan2(vecy, vecx),
                                       anchorx, anchory);
 

Parameters:

vecx vecx, vecy - the X coordinate coordinates of the rotation vector

vecy - the Y coordinate of the rotation vector

anchorx - the X coordinate of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point anchorx, anchory - the coordinates of the anchor point of the rotation

Returns:

an AffineTransform object that rotates coordinates around the specified point according to the specified rotation vector.

Since:

1.6

getQuadrantRotateInstance

public static AffineTransform getQuadrantRotateInstance(int numquadrants)

Returns a transform that rotates coordinates by the specified number of quadrants. This operation is equivalent to calling:

     AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0);
 

Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.

Parameters:

numquadrants - the number of 90 degree arcs to rotate by

Returns:

an AffineTransform object that rotates coordinates by the specified number of quadrants.

Since:

1.6

getQuadrantRotateInstance

public static AffineTransform getQuadrantRotateInstance(int numquadrants,
                                                        double anchorx,
                                                        double anchory)

Returns a transform that rotates coordinates by the specified number of quadrants around the specified anchor point. This operation is equivalent to calling:

     AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0,
                                       anchorx, anchory);
 

Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.

Parameters:

numquadrants - the number of 90 degree arcs to rotate by

anchorx anchorx, anchory - the X coordinate coordinates of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point

Returns:

an AffineTransform object that rotates coordinates by the specified number of quadrants around the specified anchor point.

Since:

1.6

getScaleInstance

public static AffineTransform getScaleInstance(double sx,
                                               double sy)

Returns a transform representing a scaling transformation. The matrix representing the returned transform is:

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

Parameters:

sx - the factor by which coordinates are scaled along the X axis direction

sy - the factor by which coordinates are scaled along the Y axis direction

Returns:

an AffineTransform object that scales coordinates by the specified factors.

Since:

1.2

getShearInstance

public static AffineTransform getShearInstance(double shx,
                                               double shy)

Returns a transform representing a shearing transformation. The matrix representing the returned transform is:

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

Parameters:

shx - the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate

shy - the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate

Returns:

an AffineTransform object that shears coordinates by the specified multipliers.

Since:

1.2

getType

public int getType()

Retrieves the flag bits describing the conversion properties of this transform. The return value is either one of the constants TYPE_IDENTITY or TYPE_GENERAL_TRANSFORM, or a combination of the appriopriate flag bits. A valid combination of flag bits is an exclusive OR operation that can combine the TYPE_TRANSLATION flag bit in addition to either of the TYPE_UNIFORM_SCALE or TYPE_GENERAL_SCALE flag bits as well as either of the TYPE_QUADRANT_ROTATION or TYPE_GENERAL_ROTATION flag bits.

Returns:

the OR combination of any of the indicated flags that apply to this transform

Since:

1.2

See Also:

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

getDeterminant

public double getDeterminant()

Returns the determinant of the matrix representation of the transform. The determinant is useful both to determine if the transform can be inverted and to get a single value representing the combined X and Y scaling of the transform.

If the determinant is non-zero, then this transform is invertible and the various methods that depend on the inverse transform do not need to throw a NoninvertibleTransformException . If the determinant is zero then this transform can not be inverted since the transform maps all input coordinates onto a line or a point. If the determinant is near enough to zero then inverse transform operations might not carry enough precision to produce meaningful results.

If this transform represents a uniform scale, as indicated by the getType method then the determinant also represents the square of the uniform scale factor by which all of the points are expanded from or contracted towards the origin. If this transform represents a non-uniform scale or more general transform then the determinant is not likely to represent a value useful for any purpose other than determining if inverse transforms are possible.

Mathematically, the determinant is calculated using the formula:

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

Returns:

the determinant of the matrix used to transform the coordinates.

Since:

1.2

See Also:

getType() , createInverse() , inverseTransform(java.awt.geom.Point2D, java.awt.geom.Point2D) , TYPE_UNIFORM_SCALE

getMatrix

public void getMatrix(double[] flatmatrix)

Retrieves the 6 specifiable values in the 3x3 affine transformation matrix and places them into an array of double precisions values. The values are stored in the array as { m00 m10 m01 m11 m02 m12 }. An array of 4 doubles can also be specified, in which case only the first four elements representing the non-transform parts of the array are retrieved and the values are stored into the array as { m00 m10 m01 m11 }

Parameters:

flatmatrix - the double array used to store the returned values.

Since:

1.2

See Also:

getScaleX() , getScaleY() , getShearX() , getShearY() , getTranslateX() , getTranslateY()

getScaleX

public double getScaleX()

Returns the X coordinate scaling element (m00) of the 3x3 affine transformation matrix.

Returns:

a double value that is the X coordinate of the scaling element of the affine transformation matrix.

Since:

1.2

See Also:

getMatrix(double[])

getScaleY

public double getScaleY()

Returns the Y coordinate scaling element (m11) of the 3x3 affine transformation matrix.

Returns:

a double value that is the Y coordinate of the scaling element of the affine transformation matrix.

Since:

1.2

See Also:

getMatrix(double[])

getShearX

public double getShearX()

Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.

Returns:

a double value that is the X coordinate of the shearing element of the affine transformation matrix.

Since:

1.2

See Also:

getMatrix(double[])

getShearY

public double getShearY()

Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.

Returns:

a double value that is the Y coordinate of the shearing element of the affine transformation matrix.

Since:

1.2

See Also:

getMatrix(double[])

getTranslateX

public double getTranslateX()

Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.

Returns:

a double value that is the X coordinate of the translation element of the affine transformation matrix.

Since:

1.2

See Also:

getMatrix(double[])

getTranslateY

public double getTranslateY()

Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.

Returns:

a double value that is the Y coordinate of the translation element of the affine transformation matrix.

Since:

1.2

See Also:

getMatrix(double[])

translate

public void translate(double tx,
                      double ty)

Concatenates this transform with a translation transformation. This is equivalent to calling concatenate(T), where T is an AffineTransform represented by the following matrix:

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

Parameters:

tx - the distance by which coordinates are translated in the X axis direction

ty - the distance by which coordinates are translated in the Y axis direction

Since:

1.2

rotate

public void rotate(double theta)

Concatenates this transform with a rotation transformation. This is equivalent to calling concatenate(R), where R is an AffineTransform represented by the following matrix:

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

Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.

Parameters:

theta - the angle of rotation measured in radians

Since:

1.2

rotate

public void rotate(double theta,
                   double anchorx,
                   double anchory)

Concatenates this transform with a transform that rotates coordinates around an anchor point. This operation is equivalent to translating the coordinates so that the anchor point is at the origin (S1), then rotating them about the new origin (S2), and finally translating so that the intermediate origin is restored to the coordinates of the original anchor point (S3).

This operation is equivalent to the following sequence of calls:

     translate(anchorx, anchory);      // S3: final translation
     rotate(theta);                    // S2: rotate around anchor
     translate(-anchorx, -anchory);    // S1: translate anchor to origin
 

Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.

Parameters:

theta - the angle of rotation measured in radians

anchorx - the X coordinate of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point

Since:

1.2

anchorx, anchory - the coordinates of the anchor point of the rotation

rotate

public void rotate(double vecx,
                   double vecy)

Concatenates this transform with a transform that rotates coordinates according to a rotation vector. All coordinates rotate about the origin by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both vecx and vecy are 0.0, no additional rotation is added to this transform. This operation is equivalent to calling:

          rotate(Math.atan2(vecy, vecx));
 

Parameters:

vecx - the X coordinate of the rotation vector

vecy - the Y coordinate of the rotation vector vecx, vecy - the coordinates of the rotation vector

Since:

1.6

rotate

public void rotate(double vecx,
                   double vecy,
                   double anchorx,
                   double anchory)

Concatenates this transform with a transform that rotates coordinates around an anchor point according to a rotation vector. All coordinates rotate about the specified anchor coordinates by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both vecx and vecy are 0.0, the transform is not modified in any way. This method is equivalent to calling:

     rotate(Math.atan2(vecy, vecx), anchorx, anchory);
 

Parameters:

vecx vecx, vecy - the X coordinate coordinates of the rotation vector

vecy - the Y coordinate of the rotation vector

anchorx - the X coordinate of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point anchorx, anchory - the coordinates of the anchor point of the rotation

Since:

1.6

quadrantRotate

public void quadrantRotate(int numquadrants)

Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants. This is equivalent to calling:

     rotate(numquadrants * Math.PI / 2.0);
 

Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.

Parameters:

numquadrants - the number of 90 degree arcs to rotate by

Since:

1.6

quadrantRotate

public void quadrantRotate(int numquadrants,
                           double anchorx,
                           double anchory)

Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants around the specified anchor point. This method is equivalent to calling:

     rotate(numquadrants * Math.PI / 2.0, anchorx, anchory);
 

Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.

Parameters:

numquadrants - the number of 90 degree arcs to rotate by

anchorx anchorx, anchory - the X coordinate coordinates of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point

Since:

1.6

scale

public void scale(double sx,
                  double sy)

Concatenates this transform with a scaling transformation. This is equivalent to calling concatenate(S), where S is an AffineTransform represented by the following matrix:

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

Parameters:

sx - the factor by which coordinates are scaled along the X axis direction

sy - the factor by which coordinates are scaled along the Y axis direction

Since:

1.2

shear

public void shear(double shx,
                  double shy)

Concatenates this transform with a shearing transformation. This is equivalent to calling concatenate(SH), where SH is an AffineTransform represented by the following matrix:

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

Parameters:

shx - the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate

shy - the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate

Since:

1.2

setToIdentity

public void setToIdentity()

Resets this transform to the Identity transform.

Since:

1.2

setToTranslation

public void setToTranslation(double tx,
                             double ty)

Sets this transform to a translation transformation. The matrix representing this transform becomes:

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

Parameters:

tx - the distance by which coordinates are translated in the X axis direction

ty - the distance by which coordinates are translated in the Y axis direction

Since:

1.2

setToRotation

public void setToRotation(double theta)

Sets this transform to a rotation transformation. The matrix representing this transform becomes:

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

Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.

Parameters:

theta - the angle of rotation measured in radians

Since:

1.2

setToRotation

public void setToRotation(double theta,
                          double anchorx,
                          double anchory)

Sets this transform to a translated rotation transformation. This operation is equivalent to translating the coordinates so that the anchor point is at the origin (S1), then rotating them about the new origin (S2), and finally translating so that the intermediate origin is restored to the coordinates of the original anchor point (S3).

This operation is equivalent to the following sequence of calls:

     setToTranslation(anchorx, anchory); // S3: final translation
     rotate(theta);                      // S2: rotate around anchor
     translate(-anchorx, -anchory);      // S1: translate anchor to origin
 

The matrix representing this transform becomes:

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

Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.

Parameters:

theta - the angle of rotation measured in radians

anchorx - the X coordinate of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point

Since:

1.2

anchorx, anchory - the coordinates of the anchor point of the rotation

setToRotation

public void setToRotation(double vecx,
                          double vecy)

Sets this transform to a rotation transformation that rotates coordinates according to a rotation vector. All coordinates rotate about the origin by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both vecx and vecy are 0.0, the transform is set to an identity transform. This operation is equivalent to calling:

     setToRotation(Math.atan2(vecy, vecx));
 

Parameters:

vecx - the X coordinate of the rotation vector

vecy - the Y coordinate of the rotation vector vecx, vecy - the coordinates of the rotation vector

Since:

1.6

setToRotation

public void setToRotation(double vecx,
                          double vecy,
                          double anchorx,
                          double anchory)

Sets this transform to a rotation transformation that rotates coordinates around an anchor point according to a rotation vector. All coordinates rotate about the specified anchor coordinates by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both vecx and vecy are 0.0, the transform is set to an identity transform. This operation is equivalent to calling:

     setToTranslation(Math.atan2(vecy, vecx), anchorx, anchory);
 

Parameters:

vecx vecx, vecy - the X coordinate coordinates of the rotation vector

vecy - the Y coordinate of the rotation vector

anchorx - the X coordinate of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point anchorx, anchory - the coordinates of the anchor point of the rotation

Since:

1.6

setToQuadrantRotation

public void setToQuadrantRotation(int numquadrants)

Sets this transform to a rotation transformation that rotates coordinates by the specified number of quadrants. This operation is equivalent to calling:

     setToRotation(numquadrants * Math.PI / 2.0);
 

Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.

Parameters:

numquadrants - the number of 90 degree arcs to rotate by

Since:

1.6

setToQuadrantRotation

public void setToQuadrantRotation(int numquadrants,
                                  double anchorx,
                                  double anchory)

Sets this transform to a translated rotation transformation that rotates coordinates by the specified number of quadrants around the specified anchor point. This operation is equivalent to calling:

     setToRotation(numquadrants * Math.PI / 2.0, anchorx, anchory);
 

Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.

Parameters:

numquadrants - the number of 90 degree arcs to rotate by

anchorx anchorx, anchory - the X coordinate coordinates of the rotation anchor point

anchory - the Y coordinate of the rotation anchor point

Since:

1.6

setToScale

public void setToScale(double sx,
                       double sy)

Sets this transform to a scaling transformation. The matrix representing this transform becomes:

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

Parameters:

sx - the factor by which coordinates are scaled along the X axis direction

sy - the factor by which coordinates are scaled along the Y axis direction

Since:

1.2

setToShear

public void setToShear(double shx,
                       double shy)

Sets this transform to a shearing transformation. The matrix representing this transform becomes:

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

Parameters:

shx - the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate

shy - the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate

Since:

1.2

setTransform

public void setTransform(AffineTransform Tx)

Sets this transform to a copy of the transform in the specified AffineTransform object.

Parameters:

Tx - the AffineTransform object from which to copy the transform

Since:

1.2

setTransform

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

Sets this transform to the matrix specified by the 6 double precision values.

Parameters:

m00 - the X coordinate scaling element of the 3x3 matrix

m10 - the Y coordinate shearing element of the 3x3 matrix

m01 - the X coordinate shearing element of the 3x3 matrix

m11 - the Y coordinate scaling element of the 3x3 matrix

m02 - the X coordinate translation element of the 3x3 matrix

m12 - the Y coordinate translation element of the 3x3 matrix

Since:

1.2

m00, m01, m02, m10, m11, m12 - the 6 floating point values that compose the 3x3 transformation matrix

concatenate

public void concatenate(AffineTransform Tx)

Concatenates an AffineTransform Tx to this AffineTransform Cx in the most commonly useful way to provide a new user space that is mapped to the former user space by Tx. Cx is updated to perform the combined transformation. Transforming a point p by the updated transform Cx' is equivalent to first transforming p by Tx and then transforming the result by the original transform Cx like this: Cx'(p) = Cx(Tx(p)) In matrix notation, if this transform Cx is represented by the matrix [this] and Tx is represented by the matrix [Tx] then this method does the following:

                [this] = [this] x [Tx]
 

Parameters:

Tx - the AffineTransform object to be concatenated with this AffineTransform object.

Since:

1.2

See Also:

preConcatenate(java.awt.geom.AffineTransform)

preConcatenate

public void preConcatenate(AffineTransform Tx)

Concatenates an AffineTransform Tx to this AffineTransform Cx in a less commonly used way such that Tx modifies the coordinate transformation relative to the absolute pixel space rather than relative to the existing user space. Cx is updated to perform the combined transformation. Transforming a point p by the updated transform Cx' is equivalent to first transforming p by the original transform Cx and then transforming the result by Tx like this: Cx'(p) = Tx(Cx(p)) In matrix notation, if this transform Cx is represented by the matrix [this] and Tx is represented by the matrix [Tx] then this method does the following:

                [this] = [Tx] x [this]
 

Parameters:

Tx - the AffineTransform object to be concatenated with this AffineTransform object.

Since:

1.2

See Also:

concatenate(java.awt.geom.AffineTransform)

createInverse

public AffineTransform createInverse()
                              throws NoninvertibleTransformException

Returns an AffineTransform object representing the inverse transformation. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The getDeterminant method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the createInverse method is called.

Returns:

a new AffineTransform object representing the inverse transformation.

Throws:

NoninvertibleTransformException - if the matrix cannot be inverted.

Since:

1.2

See Also:

getDeterminant()

invert

public void invert()
            throws NoninvertibleTransformException

Sets this transform to the inverse of itself. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The getDeterminant method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the invert method is called.

Throws:

NoninvertibleTransformException - if the matrix cannot be inverted.

Since:

1.6

See Also:

getDeterminant()

transform

public Point2D transform(Point2D ptSrc,
                         Point2D ptDst)

Transforms the specified ptSrc and stores the result in ptDst. If ptDst is null, a new Point2D object is allocated and then the result of the transformation is stored in this object. In either case, ptDst, which contains the transformed point, is returned for convenience. If ptSrc and ptDst are the same object, the input point is correctly overwritten with the transformed point.

Parameters:

ptSrc - the specified Point2D to be transformed

ptDst - the specified Point2D that stores the result of transforming ptSrc

Returns:

the ptDst after transforming ptSrc and stroring the result in ptDst.

Since:

1.2

transform

public void transform(Point2D[] ptSrc,
                      int srcOff,
                      Point2D[] ptDst,
                      int dstOff,
                      int numPts)

Transforms an array of point objects by this transform. If any element of the ptDst array is null, a new Point2D object is allocated and stored into that element before storing the results of the transformation.

Note that this method does not take any precautions to avoid problems caused by storing results into Point2D objects that will be used as the source for calculations further down the source array. This method does guarantee that if a specified Point2D object is both the source and destination for the same single point transform operation then the results will not be stored until the calculations are complete to avoid storing the results on top of the operands. If, however, the destination Point2D object for one operation is the same object as the source Point2D object for another operation further down the source array then the original coordinates in that point are overwritten before they can be converted.

Parameters:

ptSrc - the array containing the source point objects

ptDst - the array into which the transform point objects are returned

srcOff - the offset to the first point object to be transformed in the source array

dstOff - the offset to the location of the first transformed point object that is stored in the destination array

numPts - the number of point objects to be transformed

Since:

1.2

transform

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

Transforms an array of floating point coordinates by this transform. The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the specified offset in the order [x0, y0, x1, y1, ..., xn, yn].

Parameters:

srcPts - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.

dstPts - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.

srcOff - the offset to the first point to be transformed in the source array

dstOff - the offset to the location of the first transformed point that is stored in the destination array

numPts - the number of points to be transformed

Since:

1.2

transform

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

Transforms an array of double precision coordinates by this transform. The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the indicated offset in the order [x0, y0, x1, y1, ..., xn, yn].

Parameters:

srcPts - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.

dstPts - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.

srcOff - the offset to the first point to be transformed in the source array

dstOff - the offset to the location of the first transformed point that is stored in the destination array

numPts - the number of point objects to be transformed

Since:

1.2

transform

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

Transforms an array of floating point coordinates by this transform and stores the results into an array of doubles. The coordinates are stored in the arrays starting at the specified offset in the order [x0, y0, x1, y1, ..., xn, yn].

Parameters:

srcPts - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.

dstPts - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.

srcOff - the offset to the first point to be transformed in the source array

dstOff - the offset to the location of the first transformed point that is stored in the destination array

numPts - the number of points to be transformed

Since:

1.2

transform

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

Transforms an array of double precision coordinates by this transform and stores the results into an array of floats. The coordinates are stored in the arrays starting at the specified offset in the order [x0, y0, x1, y1, ..., xn, yn].

Parameters:

srcPts - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.

dstPts - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.

srcOff - the offset to the first point to be transformed in the source array

dstOff - the offset to the location of the first transformed point that is stored in the destination array

numPts - the number of point objects to be transformed

Since:

1.2

inverseTransform

public Point2D inverseTransform(Point2D ptSrc,
                                Point2D ptDst)
                         throws NoninvertibleTransformException

Inverse transforms the specified ptSrc and stores the result in ptDst. If ptDst is null, a new Point2D object is allocated and then the result of the transform is stored in this object. In either case, ptDst, which contains the transformed point, is returned for convenience. If ptSrc and ptDst are the same object, the input point is correctly overwritten with the transformed point.

Parameters:

ptSrc - the point to be inverse transformed

ptDst - the resulting transformed point

Returns:

ptDst, which contains the result of the inverse transform.

Throws:

NoninvertibleTransformException - if the matrix cannot be inverted.

Since:

1.2

inverseTransform

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

Inverse transforms an array of double precision coordinates by this transform. The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the specified offset in the order [x0, y0, x1, y1, ..., xn, yn].

Parameters:

srcPts - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.

dstPts - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.

srcOff - the offset to the first point to be transformed in the source array

dstOff - the offset to the location of the first transformed point that is stored in the destination array

numPts - the number of point objects to be transformed

Throws:

NoninvertibleTransformException - if the matrix cannot be inverted.

Since:

1.2

deltaTransform

public Point2D deltaTransform(Point2D ptSrc,
                              Point2D ptDst)

Transforms the relative distance vector specified by ptSrc and stores the result in ptDst. A relative distance vector is transformed without applying the translation components of the affine transformation matrix using the following equations:

        [  x' ]   [  m00  m01 (m02) ] [  x  ]   [ m00x + m01y ]
        [  y' ] = [  m10  m11 (m12) ] [  y  ] = [ m10x + m11y ]
        [ (1) ]   [  (0)  (0) ( 1 ) ] [ (1) ]   [     (1)     ]
 

If ptDst is null, a new Point2D object is allocated and then the result of the transform is stored in this object. In either case, ptDst, which contains the transformed point, is returned for convenience. If ptSrc and ptDst are the same object, the input point is correctly overwritten with the transformed point.

Parameters:

ptSrc - the distance vector to be delta transformed

ptDst - the resulting transformed distance vector

Returns:

ptDst, which contains the result of the transformation.

Since:

1.2

deltaTransform

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

Transforms an array of relative distance vectors by this transform. A relative distance vector is transformed without applying the translation components of the affine transformation matrix using the following equations:

        [  x' ]   [  m00  m01 (m02) ] [  x  ]   [ m00x + m01y ]
        [  y' ] = [  m10  m11 (m12) ] [  y  ] = [ m10x + m11y ]
        [ (1) ]   [  (0)  (0) ( 1 ) ] [ (1) ]   [     (1)     ]
 

The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the indicated offset in the order [x0, y0, x1, y1, ..., xn, yn].

Parameters:

srcPts - the array containing the source distance vectors. Each vector is stored as a pair of relative x, y coordinates.

dstPts - the array into which the transformed distance vectors are returned. Each vector is stored as a pair of relative x, y coordinates.

srcOff - the offset to the first vector to be transformed in the source array

dstOff - the offset to the location of the first transformed vector that is stored in the destination array

numPts - the number of vector coordinate pairs to be transformed

Since:

1.2

createTransformedShape

public Shape createTransformedShape(Shape pSrc)

Returns a new Shape object defined by the geometry of the specified Shape after it has been transformed by this transform.

Parameters:

pSrc - the specified Shape object to be transformed by this transform.

Returns:

a new Shape object that defines the geometry of the transformed Shape, or null if pSrc is null.

Since:

1.2

Shape.

toString

public String toString()

Returns a String that represents the value of this Object .

Overrides:

toString in class Object

Returns:

a String representing the value of this Object.

Since:

1.2

isIdentity

public boolean isIdentity()

Returns true if this AffineTransform is an identity transform.

Returns:

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

Since:

1.2

clone

public Object clone()

Returns a copy of this AffineTransform object.

Overrides:

clone in class Object

Returns:

an Object that is a copy of this AffineTransform object.

Since:

1.2

See Also:

Cloneable

hashCode

public int hashCode()

Returns the hashcode for this transform.

Overrides:

hashCode in class Object

Returns:

a hash code for this transform.

Since:

1.2

See Also:

Object.equals(java.lang.Object) , Hashtable

equals

public boolean equals(Object obj)

Returns true if this AffineTransform represents the same affine coordinate transform as the specified argument.

Overrides:

equals in class Object

Parameters:

obj - the Object to test for equality with this AffineTransform

Returns:

true if obj equals this AffineTransform object; false otherwise.

Since:

1.2

See Also:

Object.hashCode() , Hashtable