public class AffineTransform extends Object implements Cloneable, Serializable
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 ]
In some variations of the rotate
methods in the
AffineTransform
class, a doubleprecision 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
nonzero 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 radianbased 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 non0.0 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
.
Modifier and Type  Field and Description 

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 and Description 

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 nontranslation
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 nontranslation
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. 
Modifier and Type  Method and Description 

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.

public static final int TYPE_IDENTITY
public static final int TYPE_TRANSLATION
public static final int TYPE_UNIFORM_SCALE
public static final int TYPE_GENERAL_SCALE
public static final int TYPE_MASK_SCALE
TYPE_UNIFORM_SCALE
,
TYPE_GENERAL_SCALE
,
Constant Field Valuespublic static final int TYPE_FLIP
public static final int TYPE_QUADRANT_ROTATION
public static final int TYPE_GENERAL_ROTATION
public static final int TYPE_MASK_ROTATION
TYPE_QUADRANT_ROTATION
,
TYPE_GENERAL_ROTATION
,
Constant Field Valuespublic static final int TYPE_GENERAL_TRANSFORM
public AffineTransform()
AffineTransform
representing the
Identity transformation.public AffineTransform(AffineTransform Tx)
AffineTransform
that is a copy of
the specified AffineTransform
object.Tx
 the AffineTransform
object to copy@ConstructorProperties(value={"scaleX","shearY","shearX","scaleY","translateX","translateY"}) public AffineTransform(float m00, float m10, float m01, float m11, float m02, float m12)
AffineTransform
from 6 floating point
values representing the 6 specifiable entries of the 3x3
transformation matrix.m00
 the X coordinate scaling element of the 3x3 matrixm10
 the Y coordinate shearing element of the 3x3 matrixm01
 the X coordinate shearing element of the 3x3 matrixm11
 the Y coordinate scaling element of the 3x3 matrixm02
 the X coordinate translation element of the 3x3 matrixm12
 the Y coordinate translation element of the 3x3 matrixpublic AffineTransform(float[] flatmatrix)
AffineTransform
from an array of
floating point values representing either the 4 nontranslation
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]}.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.public AffineTransform(double m00, double m10, double m01, double m11, double m02, double m12)
AffineTransform
from 6 double
precision values representing the 6 specifiable entries of the 3x3
transformation matrix.m00
 the X coordinate scaling element of the 3x3 matrixm10
 the Y coordinate shearing element of the 3x3 matrixm01
 the X coordinate shearing element of the 3x3 matrixm11
 the Y coordinate scaling element of the 3x3 matrixm02
 the X coordinate translation element of the 3x3 matrixm12
 the Y coordinate translation element of the 3x3 matrixpublic AffineTransform(double[] flatmatrix)
AffineTransform
from an array of
double precision values representing either the 4 nontranslation
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]}.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.public static AffineTransform getTranslateInstance(double tx, double ty)
[ 1 0 tx ] [ 0 1 ty ] [ 0 0 1 ]
tx
 the distance by which coordinates are translated in the
X axis directionty
 the distance by which coordinates are translated in the
Y axis directionAffineTransform
object that represents a
translation transformation, created with the specified vector.public static AffineTransform getRotateInstance(double theta)
[ 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 90Degree Rotations above.
theta
 the angle of rotation measured in radiansAffineTransform
object that is a rotation
transformation, created with the specified angle of rotation.public static AffineTransform getRotateInstance(double theta, double anchorx, double anchory)
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 originThe matrix representing the returned transform is:
[ cos(theta) sin(theta) xx*cos+y*sin ] [ sin(theta) cos(theta) yx*siny*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 90Degree Rotations above.
theta
 the angle of rotation measured in radiansanchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointAffineTransform
object that rotates
coordinates around the specified point by the specified angle of
rotation.public static AffineTransform getRotateInstance(double vecx, double vecy)
vecx
and vecy
are 0.0,
an identity transform is returned.
This operation is equivalent to calling:
AffineTransform.getRotateInstance(Math.atan2(vecy, vecx));
vecx
 the X coordinate of the rotation vectorvecy
 the Y coordinate of the rotation vectorAffineTransform
object that rotates
coordinates according to the specified rotation vector.public static AffineTransform getRotateInstance(double vecx, double vecy, double anchorx, double anchory)
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);
vecx
 the X coordinate of the rotation vectorvecy
 the Y coordinate of the rotation vectoranchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointAffineTransform
object that rotates
coordinates around the specified point according to the
specified rotation vector.public static AffineTransform getQuadrantRotateInstance(int numquadrants)
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.
numquadrants
 the number of 90 degree arcs to rotate byAffineTransform
object that rotates
coordinates by the specified number of quadrants.public static AffineTransform getQuadrantRotateInstance(int numquadrants, double anchorx, double anchory)
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.
numquadrants
 the number of 90 degree arcs to rotate byanchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointAffineTransform
object that rotates
coordinates by the specified number of quadrants around the
specified anchor point.public static AffineTransform getScaleInstance(double sx, double sy)
[ sx 0 0 ] [ 0 sy 0 ] [ 0 0 1 ]
sx
 the factor by which coordinates are scaled along the
X axis directionsy
 the factor by which coordinates are scaled along the
Y axis directionAffineTransform
object that scales
coordinates by the specified factors.public static AffineTransform getShearInstance(double shx, double shy)
[ 1 shx 0 ] [ shy 1 0 ] [ 0 0 1 ]
shx
 the multiplier by which coordinates are shifted in the
direction of the positive X axis as a factor of their Y coordinateshy
 the multiplier by which coordinates are shifted in the
direction of the positive Y axis as a factor of their X coordinateAffineTransform
object that shears
coordinates by the specified multipliers.public int getType()
TYPE_IDENTITY
,
TYPE_TRANSLATION
,
TYPE_UNIFORM_SCALE
,
TYPE_GENERAL_SCALE
,
TYPE_QUADRANT_ROTATION
,
TYPE_GENERAL_ROTATION
,
TYPE_GENERAL_TRANSFORM
public double getDeterminant()
If the determinant is nonzero, 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 nonuniform 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 
getType()
,
createInverse()
,
inverseTransform(java.awt.geom.Point2D, java.awt.geom.Point2D)
,
TYPE_UNIFORM_SCALE
public void getMatrix(double[] flatmatrix)
flatmatrix
 the double array used to store the returned
values.getScaleX()
,
getScaleY()
,
getShearX()
,
getShearY()
,
getTranslateX()
,
getTranslateY()
public double getScaleX()
getMatrix(double[])
public double getScaleY()
getMatrix(double[])
public double getShearX()
getMatrix(double[])
public double getShearY()
getMatrix(double[])
public double getTranslateX()
getMatrix(double[])
public double getTranslateY()
getMatrix(double[])
public void translate(double tx, double ty)
AffineTransform
represented by the following matrix:
[ 1 0 tx ] [ 0 1 ty ] [ 0 0 1 ]
tx
 the distance by which coordinates are translated in the
X axis directionty
 the distance by which coordinates are translated in the
Y axis directionpublic void rotate(double theta)
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 90Degree Rotations above.
theta
 the angle of rotation measured in radianspublic void rotate(double theta, double anchorx, double anchory)
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 originRotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90Degree Rotations above.
theta
 the angle of rotation measured in radiansanchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointpublic void rotate(double vecx, double vecy)
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));
vecx
 the X coordinate of the rotation vectorvecy
 the Y coordinate of the rotation vectorpublic void rotate(double vecx, double vecy, double anchorx, double anchory)
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);
vecx
 the X coordinate of the rotation vectorvecy
 the Y coordinate of the rotation vectoranchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointpublic void quadrantRotate(int numquadrants)
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.
numquadrants
 the number of 90 degree arcs to rotate bypublic void quadrantRotate(int numquadrants, double anchorx, double anchory)
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.
numquadrants
 the number of 90 degree arcs to rotate byanchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointpublic void scale(double sx, double sy)
AffineTransform
represented by the following matrix:
[ sx 0 0 ] [ 0 sy 0 ] [ 0 0 1 ]
sx
 the factor by which coordinates are scaled along the
X axis directionsy
 the factor by which coordinates are scaled along the
Y axis directionpublic void shear(double shx, double shy)
AffineTransform
represented by the following matrix:
[ 1 shx 0 ] [ shy 1 0 ] [ 0 0 1 ]
shx
 the multiplier by which coordinates are shifted in the
direction of the positive X axis as a factor of their Y coordinateshy
 the multiplier by which coordinates are shifted in the
direction of the positive Y axis as a factor of their X coordinatepublic void setToIdentity()
public void setToTranslation(double tx, double ty)
[ 1 0 tx ] [ 0 1 ty ] [ 0 0 1 ]
tx
 the distance by which coordinates are translated in the
X axis directionty
 the distance by which coordinates are translated in the
Y axis directionpublic void setToRotation(double theta)
[ 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 90Degree Rotations above.
theta
 the angle of rotation measured in radianspublic void setToRotation(double theta, double anchorx, double anchory)
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 originThe matrix representing this transform becomes:
[ cos(theta) sin(theta) xx*cos+y*sin ] [ sin(theta) cos(theta) yx*siny*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 90Degree Rotations above.
theta
 the angle of rotation measured in radiansanchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointpublic void setToRotation(double vecx, double vecy)
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));
vecx
 the X coordinate of the rotation vectorvecy
 the Y coordinate of the rotation vectorpublic void setToRotation(double vecx, double vecy, double anchorx, double anchory)
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);
vecx
 the X coordinate of the rotation vectorvecy
 the Y coordinate of the rotation vectoranchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointpublic void setToQuadrantRotation(int numquadrants)
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.
numquadrants
 the number of 90 degree arcs to rotate bypublic void setToQuadrantRotation(int numquadrants, double anchorx, double anchory)
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.
numquadrants
 the number of 90 degree arcs to rotate byanchorx
 the X coordinate of the rotation anchor pointanchory
 the Y coordinate of the rotation anchor pointpublic void setToScale(double sx, double sy)
[ sx 0 0 ] [ 0 sy 0 ] [ 0 0 1 ]
sx
 the factor by which coordinates are scaled along the
X axis directionsy
 the factor by which coordinates are scaled along the
Y axis directionpublic void setToShear(double shx, double shy)
[ 1 shx 0 ] [ shy 1 0 ] [ 0 0 1 ]
shx
 the multiplier by which coordinates are shifted in the
direction of the positive X axis as a factor of their Y coordinateshy
 the multiplier by which coordinates are shifted in the
direction of the positive Y axis as a factor of their X coordinatepublic void setTransform(AffineTransform Tx)
AffineTransform
object.Tx
 the AffineTransform
object from which to
copy the transformpublic void setTransform(double m00, double m10, double m01, double m11, double m02, double m12)
m00
 the X coordinate scaling element of the 3x3 matrixm10
 the Y coordinate shearing element of the 3x3 matrixm01
 the X coordinate shearing element of the 3x3 matrixm11
 the Y coordinate scaling element of the 3x3 matrixm02
 the X coordinate translation element of the 3x3 matrixm12
 the Y coordinate translation element of the 3x3 matrixpublic void concatenate(AffineTransform Tx)
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]
Tx
 the AffineTransform
object to be
concatenated with this AffineTransform
object.preConcatenate(java.awt.geom.AffineTransform)
public void preConcatenate(AffineTransform Tx)
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]
Tx
 the AffineTransform
object to be
concatenated with this AffineTransform
object.concatenate(java.awt.geom.AffineTransform)
public AffineTransform createInverse() throws NoninvertibleTransformException
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.
AffineTransform
object representing the
inverse transformation.NoninvertibleTransformException
 if the matrix cannot be inverted.getDeterminant()
public void invert() throws NoninvertibleTransformException
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.
NoninvertibleTransformException
 if the matrix cannot be inverted.getDeterminant()
public Point2D transform(Point2D ptSrc, Point2D ptDst)
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.ptSrc
 the specified Point2D
to be transformedptDst
 the specified Point2D
that stores the
result of transforming ptSrc
ptDst
after transforming
ptSrc
and stroring the result in ptDst
.public void transform(Point2D[] ptSrc, int srcOff, Point2D[] ptDst, int dstOff, int numPts)
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.
ptSrc
 the array containing the source point objectsptDst
 the array into which the transform point objects are
returnedsrcOff
 the offset to the first point object to be
transformed in the source arraydstOff
 the offset to the location of the first
transformed point object that is stored in the destination arraynumPts
 the number of point objects to be transformedpublic void transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)
[x0, y0, x1, y1, ..., xn, yn]
.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 arraydstOff
 the offset to the location of the first
transformed point that is stored in the destination arraynumPts
 the number of points to be transformedpublic void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
[x0, y0, x1, y1, ..., xn, yn]
.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 arraydstOff
 the offset to the location of the first
transformed point that is stored in the destination arraynumPts
 the number of point objects to be transformedpublic void transform(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
[x0, y0, x1, y1, ..., xn, yn]
.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 arraydstOff
 the offset to the location of the first
transformed point that is stored in the destination arraynumPts
 the number of points to be transformedpublic void transform(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)
[x0, y0, x1, y1, ..., xn, yn]
.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 arraydstOff
 the offset to the location of the first
transformed point that is stored in the destination arraynumPts
 the number of point objects to be transformedpublic Point2D inverseTransform(Point2D ptSrc, Point2D ptDst) throws NoninvertibleTransformException
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.ptSrc
 the point to be inverse transformedptDst
 the resulting transformed pointptDst
, which contains the result of the
inverse transform.NoninvertibleTransformException
 if the matrix cannot be
inverted.public void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws NoninvertibleTransformException
[x0, y0, x1, y1, ..., xn, yn]
.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 arraydstOff
 the offset to the location of the first
transformed point that is stored in the destination arraynumPts
 the number of point objects to be transformedNoninvertibleTransformException
 if the matrix cannot be
inverted.public Point2D deltaTransform(Point2D ptSrc, Point2D ptDst)
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.ptSrc
 the distance vector to be delta transformedptDst
 the resulting transformed distance vectorptDst
, which contains the result of the
transformation.public void deltaTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
[ 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]
.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 arraydstOff
 the offset to the location of the first
transformed vector that is stored in the destination arraynumPts
 the number of vector coordinate pairs to be
transformedpublic Shape createTransformedShape(Shape pSrc)
Shape
object defined by the geometry of the
specified Shape
after it has been transformed by
this transform.pSrc
 the specified Shape
object to be
transformed by this transform.Shape
object that defines the geometry
of the transformed Shape
, or null if pSrc
is null.public boolean isIdentity()
true
if this AffineTransform
is
an identity transform.true
if this AffineTransform
is
an identity transform; false
otherwise.public Object clone()
AffineTransform
object.public int hashCode()
hashCode
in class Object
Object.equals(java.lang.Object)
,
System.identityHashCode(java.lang.Object)
public boolean equals(Object obj)
true
if this AffineTransform
represents the same affine coordinate transform as the specified
argument.equals
in class Object
obj
 the Object
to test for equality with this
AffineTransform
true
if obj
equals this
AffineTransform
object; false
otherwise.Object.hashCode()
,
HashMap
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