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) into destination coordinates (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

Field Summary
static 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.
static 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.
static 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.
static int	TYPE_GENERAL_TRANSFORM           This constant indicates that the transform defined by this object performs an arbitrary conversion of the input coordinates.
static int	TYPE_IDENTITY           This constant indicates that the transform defined by this object is an identity transform.
static int	TYPE_MASK_ROTATION           This constant is a bit mask for any of the rotation flag bits.
static int	TYPE_MASK_SCALE           This constant is a bit mask for any of the scale flag bits.
static 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.
static 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.
static 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.

 

Constructor Summary
AffineTransform()           Constructs a new AffineTransform representing the Identity transformation.
AffineTransform(AffineTransform Tx)           Constructs a new AffineTransform that is a copy of the specified AffineTransform object.
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.
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.
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.
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.

 

Method Summary
Object	clone()           Returns a copy of this AffineTransform object.
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.
AffineTransform	createInverse()           Returns an AffineTransform object representing the inverse transformation.
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.
void	deltaTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)           Transforms an array of relative distance vectors by this transform.
Point2D	deltaTransform(Point2D ptSrc, Point2D ptDst)           Transforms the relative distance vector specified by ptSrc and stores the result in ptDst.
boolean	equals(Object obj)           Returns true if this AffineTransform represents the same affine coordinate transform as the specified argument.
double	getDeterminant()           Returns the determinant of the matrix representation of the transform.
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.
static AffineTransform	getQuadrantRotateInstance(int numquadrants)           Returns a transform that rotates coordinates by the specified number of quadrants.
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.
static AffineTransform	getRotateInstance(double theta)           Returns a transform representing a rotation transformation.
static AffineTransform	getRotateInstance(double vecx, double vecy)           Returns a transform that rotates coordinates according to a rotation vector.
static AffineTransform	getRotateInstance(double theta, double anchorx, double anchory)           Returns a transform that rotates coordinates around an anchor point.
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.
static AffineTransform	getScaleInstance(double sx, double sy)           Returns a transform representing a scaling transformation.
double	getScaleX()           Returns the X coordinate scaling element (m00) of the 3x3 affine transformation matrix.
double	getScaleY()           Returns the Y coordinate scaling element (m11) of the 3x3 affine transformation matrix.
static AffineTransform	getShearInstance(double shx, double shy)           Returns a transform representing a shearing transformation.
double	getShearX()           Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.
double	getShearY()           Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.
static AffineTransform	getTranslateInstance(double tx, double ty)           Returns a transform representing a translation transformation.
double	getTranslateX()           Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.
double	getTranslateY()           Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.
int	getType()           Retrieves the flag bits describing the conversion properties of this transform.
int	hashCode()           Returns the hashcode for this transform.
void	inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)           Inverse transforms an array of double precision coordinates by this transform.
Point2D	inverseTransform(Point2D ptSrc, Point2D ptDst)           Inverse transforms the specified ptSrc and stores the result in ptDst.
void	invert()           Sets this transform to the inverse of itself.
boolean	isIdentity()           Returns true if this AffineTransform is an identity transform.
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.
void	quadrantRotate(int numquadrants)           Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants.
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.
void	rotate(double theta)           Concatenates this transform with a rotation transformation.
void	rotate(double vecx, double vecy)           Concatenates this transform with a transform that rotates coordinates according to a rotation vector.
void	rotate(double theta, double anchorx, double anchory)           Concatenates this transform with a transform that rotates coordinates around an anchor point.
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.
void	scale(double sx, double sy)           Concatenates this transform with a scaling transformation.
void	setToIdentity()           Resets this transform to the Identity transform.
void	setToQuadrantRotation(int numquadrants)           Sets this transform to a rotation transformation that rotates coordinates by the specified number of quadrants.
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.
void	setToRotation(double theta)           Sets this transform to a rotation transformation.
void	setToRotation(double vecx, double vecy)           Sets this transform to a rotation transformation that rotates coordinates according to a rotation vector.
void	setToRotation(double theta, double anchorx, double anchory)           Sets this transform to a translated rotation transformation.
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.
void	setToScale(double sx, double sy)           Sets this transform to a scaling transformation.
void	setToShear(double shx, double shy)           Sets this transform to a shearing transformation.
void	setToTranslation(double tx, double ty)           Sets this transform to a translation transformation.
void	setTransform(AffineTransform Tx)           Sets this transform to a copy of the transform in the specified AffineTransform object.
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.
void	shear(double shx, double shy)           Concatenates this transform with a shearing transformation.
String	toString()           Returns a String that represents the value of this Object.
void	transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)           Transforms an array of double precision coordinates by this transform.
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.
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.
void	transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)           Transforms an array of floating point coordinates by this transform.
void	transform(Point2D[] ptSrc, int srcOff, Point2D[] ptDst, int dstOff, int numPts)           Transforms an array of point objects by this transform.
Point2D	transform(Point2D ptSrc, Point2D ptDst)           Transforms the specified ptSrc and stores the result in ptDst.
void	translate(double tx, double ty)           Concatenates this transform with a translation transformation.

 

Methods inherited from class java.lang.Object
finalize, getClass, notify, notifyAll, wait, wait, wait

 

Field Detail

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

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

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 - the X coordinate 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

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 - the X coordinate 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

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 - the X coordinate 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

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

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 - the X coordinate 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

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 - the X coordinate 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

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

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 - the X coordinate 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

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