java.lang.Object | |
↳ | java.awt.geom.AffineTransform |
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 ]
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
.
Constants | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
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. | |||||||||
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. | |||||||||
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. | |||||||||
int | TYPE_GENERAL_TRANSFORM | This constant indicates that the transform defined by this object performs an arbitrary conversion of the input coordinates. | |||||||||
int | TYPE_IDENTITY | This constant indicates that the transform defined by this object is an identity transform. | |||||||||
int | TYPE_MASK_ROTATION | This constant is a bit mask for any of the rotation flag bits. | |||||||||
int | TYPE_MASK_SCALE | This constant is a bit mask for any of the scale flag bits. | |||||||||
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. | |||||||||
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. | |||||||||
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. |
Public Constructors | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Constructs a new
AffineTransform representing the
Identity transformation. | |||||||||||
Constructs a new
AffineTransform that is a copy of
the specified AffineTransform object. | |||||||||||
Constructs a new
AffineTransform from 6 floating point
values representing the 6 specifiable entries of the 3x3
transformation matrix. | |||||||||||
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. | |||||||||||
Constructs a new
AffineTransform from 6 double
precision values representing the 6 specifiable entries of the 3x3
transformation matrix. | |||||||||||
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. |
Public Methods | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Returns a copy of this
AffineTransform object. | |||||||||||
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 . | |||||||||||
Returns an
AffineTransform object representing the
inverse transformation. | |||||||||||
Returns a new
Shape object defined by the geometry of the
specified Shape after it has been transformed by
this transform. | |||||||||||
Transforms an array of relative distance vectors by this
transform.
| |||||||||||
Transforms the relative distance vector specified by
ptSrc and stores the result in ptDst . | |||||||||||
Returns
true if this AffineTransform
represents the same affine coordinate transform as the specified
argument. | |||||||||||
Returns the determinant of the matrix representation of the transform.
| |||||||||||
Retrieves the 6 specifiable values in the 3x3 affine transformation
matrix and places them into an array of double precisions values.
| |||||||||||
Returns a transform that rotates coordinates by the specified
number of quadrants.
| |||||||||||
Returns a transform that rotates coordinates by the specified
number of quadrants around the specified anchor point.
| |||||||||||
Returns a transform that rotates coordinates according to
a rotation vector.
| |||||||||||
Returns a transform that rotates coordinates around an anchor point.
| |||||||||||
Returns a transform that rotates coordinates around an anchor
point accordinate to a rotation vector.
| |||||||||||
Returns a transform representing a rotation transformation.
| |||||||||||
Returns a transform representing a scaling transformation.
| |||||||||||
Returns the X coordinate scaling element (m00) of the 3x3
affine transformation matrix.
| |||||||||||
Returns the Y coordinate scaling element (m11) of the 3x3
affine transformation matrix.
| |||||||||||
Returns a transform representing a shearing transformation.
| |||||||||||
Returns the X coordinate shearing element (m01) of the 3x3
affine transformation matrix.
| |||||||||||
Returns the Y coordinate shearing element (m10) of the 3x3
affine transformation matrix.
| |||||||||||
Returns a transform representing a translation transformation.
| |||||||||||
Returns the X coordinate of the translation element (m02) of the
3x3 affine transformation matrix.
| |||||||||||
Returns the Y coordinate of the translation element (m12) of the
3x3 affine transformation matrix.
| |||||||||||
Retrieves the flag bits describing the conversion properties of
this transform.
| |||||||||||
Returns the hashcode for this transform.
| |||||||||||
Inverse transforms an array of double precision coordinates by
this transform.
| |||||||||||
Inverse transforms the specified
ptSrc and stores the
result in ptDst . | |||||||||||
Sets this transform to the inverse of itself.
| |||||||||||
Returns
true if this AffineTransform is
an identity transform. | |||||||||||
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. | |||||||||||
Concatenates this transform with a transform that rotates
coordinates by the specified number of quadrants.
| |||||||||||
Concatenates this transform with a transform that rotates
coordinates by the specified number of quadrants around
the specified anchor point.
| |||||||||||
Concatenates this transform with a transform that rotates
coordinates according to a rotation vector.
| |||||||||||
Concatenates this transform with a transform that rotates
coordinates around an anchor point according to a rotation
vector.
| |||||||||||
Concatenates this transform with a transform that rotates
coordinates around an anchor point.
| |||||||||||
Concatenates this transform with a rotation transformation.
| |||||||||||
Concatenates this transform with a scaling transformation.
| |||||||||||
Resets this transform to the Identity transform.
| |||||||||||
Sets this transform to a translated rotation transformation
that rotates coordinates by the specified number of quadrants
around the specified anchor point.
| |||||||||||
Sets this transform to a rotation transformation that rotates
coordinates by the specified number of quadrants.
| |||||||||||
Sets this transform to a rotation transformation that rotates
coordinates around an anchor point according to a rotation
vector.
| |||||||||||
Sets this transform to a rotation transformation that rotates
coordinates according to a rotation vector.
| |||||||||||
Sets this transform to a translated rotation transformation.
| |||||||||||
Sets this transform to a rotation transformation.
| |||||||||||
Sets this transform to a scaling transformation.
| |||||||||||
Sets this transform to a shearing transformation.
| |||||||||||
Sets this transform to a translation transformation.
| |||||||||||
Sets this transform to the matrix specified by the 6
double precision values.
| |||||||||||
Sets this transform to a copy of the transform in the specified
AffineTransform object. | |||||||||||
Concatenates this transform with a shearing transformation.
| |||||||||||
Returns a
String that represents the value of this
Object . | |||||||||||
Transforms an array of double precision coordinates by this transform
and stores the results into an array of floats.
| |||||||||||
Transforms an array of double precision coordinates by this transform.
| |||||||||||
Transforms an array of floating point coordinates by this transform.
| |||||||||||
Transforms the specified
ptSrc and stores the result
in ptDst . | |||||||||||
Transforms an array of floating point coordinates by this transform
and stores the results into an array of doubles.
| |||||||||||
Transforms an array of point objects by this transform.
| |||||||||||
Concatenates this transform with a translation transformation.
|
[Expand]
Inherited Methods | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
From class
java.lang.Object
|
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.
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.
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.
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.
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.
This constant is a bit mask for any of the rotation flag bits.
This constant is a bit mask for any of the scale flag bits.
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.
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.
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.
Constructs a new AffineTransform
representing the
Identity transformation.
Constructs a new AffineTransform
that is a copy of
the specified AffineTransform
object.
Tx | the AffineTransform object to copy |
---|
Constructs a new 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 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 |
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]}.
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. |
---|
Constructs a new 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 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 |
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]}.
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. |
---|
Returns a copy of this AffineTransform
object.
Object
that is a copy of this
AffineTransform
object.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]
Tx | the AffineTransform object to be
concatenated with this AffineTransform object. |
---|
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.
AffineTransform
object representing the
inverse transformation.NoninvertibleTransformException | if the matrix cannot be inverted. |
---|
Returns a new 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.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]
.srcPts | the array containing the source distance vectors. 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 |
dstPts | the array into which the transformed distance vectors are returned. Each vector is stored as a pair of relative x, y coordinates. |
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 |
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.ptSrc | the distance vector to be delta transformed |
---|---|
ptDst | the resulting transformed distance vector |
ptDst
, which contains the result of the
transformation.Returns true
if this AffineTransform
represents the same affine coordinate transform as the specified
argument.
obj | the Object to test for equality with this
AffineTransform |
---|
true
if obj
equals this
AffineTransform
object; false
otherwise.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 |
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 }
flatmatrix | the double array used to store the returned values. |
---|
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.
numquadrants | the number of 90 degree arcs to rotate by |
---|
AffineTransform
object that rotates
coordinates by the specified number of quadrants.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.
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 |
AffineTransform
object that rotates
coordinates by the specified number of quadrants around the
specified anchor point.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));
vecx | the X coordinate of the rotation vector |
---|---|
vecy | the Y coordinate of the rotation vector |
AffineTransform
object that rotates
coordinates according to the specified rotation vector.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 originThe 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.
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 |
AffineTransform
object that rotates
coordinates around the specified point by the specified angle of
rotation.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);
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 |
AffineTransform
object that rotates
coordinates around the specified point according to the
specified rotation vector.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.
theta | the angle of rotation measured in radians |
---|
AffineTransform
object that is a rotation
transformation, created with the specified angle of rotation.Returns a transform representing a scaling transformation. The matrix representing the returned transform is:
[ sx 0 0 ] [ 0 sy 0 ] [ 0 0 1 ]
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 |
AffineTransform
object that scales
coordinates by the specified factors.Returns the X coordinate scaling element (m00) of the 3x3 affine transformation matrix.
Returns the Y coordinate scaling element (m11) of the 3x3 affine transformation matrix.
Returns a transform representing a shearing transformation. The matrix representing the returned transform is:
[ 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 coordinate |
---|---|
shy | the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate |
AffineTransform
object that shears
coordinates by the specified multipliers.Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.
Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.
Returns a transform representing a translation transformation. The matrix representing the returned transform is:
[ 1 0 tx ] [ 0 1 ty ] [ 0 0 1 ]
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 |
AffineTransform
object that represents a
translation transformation, created with the specified vector.Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.
Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.
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 hashcode for this transform.
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]
.
srcPts | the array containing the source point coordinates. 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 |
dstPts | the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates. |
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 |
NoninvertibleTransformException | if the matrix cannot be inverted. |
---|
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.
ptSrc | the point to be inverse transformed |
---|---|
ptDst | the resulting transformed point |
ptDst
, which contains the result of the
inverse transform.NoninvertibleTransformException | if the matrix cannot be inverted. |
---|
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.
NoninvertibleTransformException | if the matrix cannot be inverted. |
---|
Returns true
if this AffineTransform
is
an identity transform.
true
if this AffineTransform
is
an identity transform; false
otherwise.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]
Tx | the AffineTransform object to be
concatenated with this AffineTransform object. |
---|
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.
numquadrants | the number of 90 degree arcs to rotate by |
---|
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.
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 |
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));
vecx | the X coordinate of the rotation vector |
---|---|
vecy | the Y coordinate of the rotation vector |
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);
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 |
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 originRotating 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.
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 |
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.
theta | the angle of rotation measured in radians |
---|
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 ]
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 |
Resets this transform to the Identity transform.
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.
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 |
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.
numquadrants | the number of 90 degree arcs to rotate by |
---|
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);
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 |
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));
vecx | the X coordinate of the rotation vector |
---|---|
vecy | the Y coordinate of the rotation vector |
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 originThe 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.
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 |
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.
theta | the angle of rotation measured in radians |
---|
Sets this transform to a scaling transformation. The matrix representing this transform becomes:
[ sx 0 0 ] [ 0 sy 0 ] [ 0 0 1 ]
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 |
Sets this transform to a shearing transformation. The matrix representing this transform becomes:
[ 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 coordinate |
---|---|
shy | the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate |
Sets this transform to a translation transformation. The matrix representing this transform becomes:
[ 1 0 tx ] [ 0 1 ty ] [ 0 0 1 ]
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 |
Sets this transform to the matrix specified by the 6 double precision values.
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 |
Sets this transform to a copy of the transform in the specified
AffineTransform
object.
Tx | the AffineTransform object from which to
copy the transform |
---|
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 ]
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 a String
that represents the value of this
Object
.
String
representing the value of this
Object
.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]
.
srcPts | the array containing the source point coordinates. 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 |
dstPts | the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates. |
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 |
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]
.
srcPts | the array containing the source point coordinates. 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 |
dstPts | the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates. |
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 |
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]
.
srcPts | the array containing the source point coordinates. 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 |
dstPts | the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates. |
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 |
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.
ptSrc | the specified Point2D to be transformed |
---|---|
ptDst | the specified Point2D that stores the
result of transforming ptSrc |
ptDst
after transforming
ptSrc
and stroring the result in ptDst
.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]
.
srcPts | the array containing the source point coordinates. 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 |
dstPts | the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates. |
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 |
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.
ptSrc | the array containing the source point objects |
---|---|
srcOff | the offset to the first point object to be transformed in the source array |
ptDst | the array into which the transform point objects are returned |
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 |
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 ]
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 |