/* AffineTransform.java -- transform coordinates between two 2-D spaces
Copyright (C) 2000, 2001, 2002, 2004 Free Software Foundation
This file is part of GNU Classpath.
GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
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Linking this library statically or dynamically with other modules is
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permission to link this library with independent modules to produce an
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package java.awt.geom;
import java.awt.Shape;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.io.Serializable;
/**
* This class represents an affine transformation between two coordinate
* spaces in 2 dimensions. Such a transform preserves the "straightness"
* and "parallelness" of lines. The transform is built from a sequence of
* translations, scales, flips, rotations, and shears.
*
* <p>The transformation can be represented using matrix math on a 3x3 array.
* Given (x,y), the transformation (x',y') can be found by:
* <pre>
* [ x'] [ m00 m01 m02 ] [ x ] [ m00*x + m01*y + m02 ]
* [ y'] = [ m10 m11 m12 ] [ y ] = [ m10*x + m11*y + m12 ]
* [ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ]
* </pre>
* The bottom row of the matrix is constant, so a transform can be uniquely
* represented (as in {@link #toString()}) by
* "[[m00, m01, m02], [m10, m11, m12]]".
*
* @author Tom Tromey (tromey@cygnus.com)
* @author Eric Blake (ebb9@email.byu.edu)
* @since 1.2
* @status partially updated to 1.4, still has some problems
*/
public class AffineTransform implements Cloneable, Serializable
{
/**
* Compatible with JDK 1.2+.
*/
private static final long serialVersionUID = 1330973210523860834L;
/**
* The transformation is the identity (x' = x, y' = y). All other transforms
* have either a combination of the appropriate transform flag bits for
* their type, or the type GENERAL_TRANSFORM.
*
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_FLIP
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #getType()
*/
public static final int TYPE_IDENTITY = 0;
/**
* The transformation includes a translation - shifting in the x or y
* direction without changing length or angles.
*
* @see #TYPE_IDENTITY
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_FLIP
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #getType()
*/
public static final int TYPE_TRANSLATION = 1;
/**
* The transformation includes a uniform scale - length is scaled in both
* the x and y directions by the same amount, without affecting angles.
* This is mutually exclusive with TYPE_GENERAL_SCALE.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_FLIP
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #TYPE_MASK_SCALE
* @see #getType()
*/
public static final int TYPE_UNIFORM_SCALE = 2;
/**
* The transformation includes a general scale - length is scaled in either
* or both the x and y directions, but by different amounts; without
* affecting angles. This is mutually exclusive with TYPE_UNIFORM_SCALE.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_FLIP
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #TYPE_MASK_SCALE
* @see #getType()
*/
public static final int TYPE_GENERAL_SCALE = 4;
/**
* This constant checks if either variety of scale transform is performed.
*
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
*/
public static final int TYPE_MASK_SCALE = 6;
/**
* The transformation includes a flip about an axis, swapping between
* right-handed and left-handed coordinate systems. In a right-handed
* system, the positive x-axis rotates counter-clockwise to the positive
* y-axis; in a left-handed system it rotates clockwise.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #getType()
*/
public static final int TYPE_FLIP = 64;
/**
* The transformation includes a rotation of a multiple of 90 degrees (PI/2
* radians). Angles are rotated, but length is preserved. This is mutually
* exclusive with TYPE_GENERAL_ROTATION.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_FLIP
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #TYPE_MASK_ROTATION
* @see #getType()
*/
public static final int TYPE_QUADRANT_ROTATION = 8;
/**
* The transformation includes a rotation by an arbitrary angle. Angles are
* rotated, but length is preserved. This is mutually exclusive with
* TYPE_QUADRANT_ROTATION.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_FLIP
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
* @see #TYPE_MASK_ROTATION
* @see #getType()
*/
public static final int TYPE_GENERAL_ROTATION = 16;
/**
* This constant checks if either variety of rotation is performed.
*
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
*/
public static final int TYPE_MASK_ROTATION = 24;
/**
* The transformation is an arbitrary conversion of coordinates which
* could not be decomposed into the other TYPEs.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_FLIP
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #getType()
*/
public static final int TYPE_GENERAL_TRANSFORM = 32;
/**
* The X coordinate scaling element of the transform matrix.
*
* @serial matrix[0,0]
*/
private double m00;
/**
* The Y coordinate shearing element of the transform matrix.
*
* @serial matrix[1,0]
*/
private double m10;
/**
* The X coordinate shearing element of the transform matrix.
*
* @serial matrix[0,1]
*/
private double m01;
/**
* The Y coordinate scaling element of the transform matrix.
*
* @serial matrix[1,1]
*/
private double m11;
/**
* The X coordinate translation element of the transform matrix.
*
* @serial matrix[0,2]
*/
private double m02;
/**
* The Y coordinate translation element of the transform matrix.
*
* @serial matrix[1,2]
*/
private double m12;
/** The type of this transform. */
private transient int type;
/**
* Construct a new identity transform:
* <pre>
* [ 1 0 0 ]
* [ 0 1 0 ]
* [ 0 0 1 ]
* </pre>
*/
public AffineTransform()
{
m00 = m11 = 1;
}
/**
* Create a new transform which copies the given one.
*
* @param tx the transform to copy
* @throws NullPointerException if tx is null
*/
public AffineTransform(AffineTransform tx)
{
setTransform(tx);
}
/**
* Construct a transform with the given matrix entries:
* <pre>
* [ m00 m01 m02 ]
* [ m10 m11 m12 ]
* [ 0 0 1 ]
* </pre>
*
* @param m00 the x scaling component
* @param m10 the y shearing component
* @param m01 the x shearing component
* @param m11 the y scaling component
* @param m02 the x translation component
* @param m12 the y translation component
*/
public AffineTransform(float m00, float m10,
float m01, float m11,
float m02, float m12)
{
this.m00 = m00;
this.m10 = m10;
this.m01 = m01;
this.m11 = m11;
this.m02 = m02;
this.m12 = m12;
updateType();
}
/**
* Construct a transform from a sequence of float entries. The array must
* have at least 4 entries, which has a translation factor of 0; or 6
* entries, for specifying all parameters:
* <pre>
* [ f[0] f[2] (f[4]) ]
* [ f[1] f[3] (f[5]) ]
* [ 0 0 1 ]
* </pre>
*
* @param f the matrix to copy from, with at least 4 (6) entries
* @throws NullPointerException if f is null
* @throws ArrayIndexOutOfBoundsException if f is too small
*/
public AffineTransform(float[] f)
{
m00 = f[0];
m10 = f[1];
m01 = f[2];
m11 = f[3];
if (f.length >= 6)
{
m02 = f[4];
m12 = f[5];
}
updateType();
}
/**
* Construct a transform with the given matrix entries:
* <pre>
* [ m00 m01 m02 ]
* [ m10 m11 m12 ]
* [ 0 0 1 ]
* </pre>
*
* @param m00 the x scaling component
* @param m10 the y shearing component
* @param m01 the x shearing component
* @param m11 the y scaling component
* @param m02 the x translation component
* @param m12 the y translation component
*/
public AffineTransform(double m00, double m10, double m01,
double m11, double m02, double m12)
{
this.m00 = m00;
this.m10 = m10;
this.m01 = m01;
this.m11 = m11;
this.m02 = m02;
this.m12 = m12;
updateType();
}
/**
* Construct a transform from a sequence of double entries. The array must
* have at least 4 entries, which has a translation factor of 0; or 6
* entries, for specifying all parameters:
* <pre>
* [ d[0] d[2] (d[4]) ]
* [ d[1] d[3] (d[5]) ]
* [ 0 0 1 ]
* </pre>
*
* @param d the matrix to copy from, with at least 4 (6) entries
* @throws NullPointerException if d is null
* @throws ArrayIndexOutOfBoundsException if d is too small
*/
public AffineTransform(double[] d)
{
m00 = d[0];
m10 = d[1];
m01 = d[2];
m11 = d[3];
if (d.length >= 6)
{
m02 = d[4];
m12 = d[5];
}
updateType();
}
/**
* Returns a translation transform:
* <pre>
* [ 1 0 tx ]
* [ 0 1 ty ]
* [ 0 0 1 ]
* </pre>
*
* @param tx the x translation distance
* @param ty the y translation distance
* @return the translating transform
*/
public static AffineTransform getTranslateInstance(double tx, double ty)
{
AffineTransform t = new AffineTransform();
t.setToTranslation(tx, ty);
return t;
}
/**
* Returns a rotation transform. A positive angle (in radians) rotates
* the positive x-axis to the positive y-axis:
* <pre>
* [ cos(theta) -sin(theta) 0 ]
* [ sin(theta) cos(theta) 0 ]
* [ 0 0 1 ]
* </pre>
*
* @param theta the rotation angle
* @return the rotating transform
*/
public static AffineTransform getRotateInstance(double theta)
{
AffineTransform t = new AffineTransform();
t.setToRotation(theta);
return t;
}
/**
* Returns a rotation transform about a point. A positive angle (in radians)
* rotates the positive x-axis to the positive y-axis. This is the same
* as calling:
* <pre>
* AffineTransform tx = new AffineTransform();
* tx.setToTranslation(x, y);
* tx.rotate(theta);
* tx.translate(-x, -y);
* </pre>
*
* <p>The resulting matrix is:
* <pre>
* [ cos(theta) -sin(theta) x-x*cos+y*sin ]
* [ sin(theta) cos(theta) y-x*sin-y*cos ]
* [ 0 0 1 ]
* </pre>
*
* @param theta the rotation angle
* @param x the x coordinate of the pivot point
* @param y the y coordinate of the pivot point
* @return the rotating transform
*/
public static AffineTransform getRotateInstance(double theta,
double x, double y)
{
AffineTransform t = new AffineTransform();
t.setToTranslation(x, y);
t.rotate(theta);
t.translate(-x, -y);
return t;
}
/**
* Returns a scaling transform:
* <pre>
* [ sx 0 0 ]
* [ 0 sy 0 ]
* [ 0 0 1 ]
* </pre>
*
* @param sx the x scaling factor
* @param sy the y scaling factor
* @return the scaling transform
*/
public static AffineTransform getScaleInstance(double sx, double sy)
{
AffineTransform t = new AffineTransform();
t.setToScale(sx, sy);
return t;
}
/**
* Returns a shearing transform (points are shifted in the x direction based
* on a factor of their y coordinate, and in the y direction as a factor of
* their x coordinate):
* <pre>
* [ 1 shx 0 ]
* [ shy 1 0 ]
* [ 0 0 1 ]
* </pre>
*
* @param shx the x shearing factor
* @param shy the y shearing factor
* @return the shearing transform
*/
public static AffineTransform getShearInstance(double shx, double shy)
{
AffineTransform t = new AffineTransform();
t.setToShear(shx, shy);
return t;
}
/**
* Returns the type of this transform. The result is always valid, although
* it may not be the simplest interpretation (in other words, there are
* sequences of transforms which reduce to something simpler, which this
* does not always detect). The result is either TYPE_GENERAL_TRANSFORM,
* or a bit-wise combination of TYPE_TRANSLATION, the mutually exclusive
* TYPE_*_ROTATIONs, and the mutually exclusive TYPE_*_SCALEs.
*
* @return The type.
*
* @see #TYPE_IDENTITY
* @see #TYPE_TRANSLATION
* @see #TYPE_UNIFORM_SCALE
* @see #TYPE_GENERAL_SCALE
* @see #TYPE_QUADRANT_ROTATION
* @see #TYPE_GENERAL_ROTATION
* @see #TYPE_GENERAL_TRANSFORM
*/
public int getType()
{
return type;
}
/**
* Return the determinant of this transform matrix. If the determinant is
* non-zero, the transform is invertible; otherwise operations which require
* an inverse throw a NoninvertibleTransformException. A result very near
* zero, due to rounding errors, may indicate that inversion results do not
* carry enough precision to be meaningful.
*
* <p>If this is a uniform scale transformation, the determinant also
* represents the squared value of the scale. Otherwise, it carries little
* additional meaning. The determinant is calculated as:
* <pre>
* | m00 m01 m02 |
* | m10 m11 m12 | = m00 * m11 - m01 * m10
* | 0 0 1 |
* </pre>
*
* @return the determinant
* @see #createInverse()
*/
public double getDeterminant()
{
return m00 * m11 - m01 * m10;
}
/**
* Return the matrix of values used in this transform. If the matrix has
* fewer than 6 entries, only the scale and shear factors are returned;
* otherwise the translation factors are copied as well. The resulting
* values are:
* <pre>
* [ d[0] d[2] (d[4]) ]
* [ d[1] d[3] (d[5]) ]
* [ 0 0 1 ]
* </pre>
*
* @param d the matrix to store the results into; with 4 (6) entries
* @throws NullPointerException if d is null
* @throws ArrayIndexOutOfBoundsException if d is too small
*/
public void getMatrix(double[] d)
{
d[0] = m00;
d[1] = m10;
d[2] = m01;
d[3] = m11;
if (d.length >= 6)
{
d[4] = m02;
d[5] = m12;
}
}
/**
* Returns the X coordinate scaling factor of the matrix.
*
* @return m00
* @see #getMatrix(double[])
*/
public double getScaleX()
{
return m00;
}
/**
* Returns the Y coordinate scaling factor of the matrix.
*
* @return m11
* @see #getMatrix(double[])
*/
public double getScaleY()
{
return m11;
}
/**
* Returns the X coordinate shearing factor of the matrix.
*
* @return m01
* @see #getMatrix(double[])
*/
public double getShearX()
{
return m01;
}
/**
* Returns the Y coordinate shearing factor of the matrix.
*
* @return m10
* @see #getMatrix(double[])
*/
public double getShearY()
{
return m10;
}
/**
* Returns the X coordinate translation factor of the matrix.
*
* @return m02
* @see #getMatrix(double[])
*/
public double getTranslateX()
{
return m02;
}
/**
* Returns the Y coordinate translation factor of the matrix.
*
* @return m12
* @see #getMatrix(double[])
*/
public double getTranslateY()
{
return m12;
}
/**
* Concatenate a translation onto this transform. This is equivalent, but
* more efficient than
* <code>concatenate(AffineTransform.getTranslateInstance(tx, ty))</code>.
*
* @param tx the x translation distance
* @param ty the y translation distance
* @see #getTranslateInstance(double, double)
* @see #concatenate(AffineTransform)
*/
public void translate(double tx, double ty)
{
m02 += tx * m00 + ty * m01;
m12 += tx * m10 + ty * m11;
updateType();
}
/**
* Concatenate a rotation onto this transform. This is equivalent, but
* more efficient than
* <code>concatenate(AffineTransform.getRotateInstance(theta))</code>.
*
* @param theta the rotation angle
* @see #getRotateInstance(double)
* @see #concatenate(AffineTransform)
*/
public void rotate(double theta)
{
double c = Math.cos(theta);
double s = Math.sin(theta);
double n00 = m00 * c + m01 * s;
double n01 = m00 * -s + m01 * c;
double n10 = m10 * c + m11 * s;
double n11 = m10 * -s + m11 * c;
m00 = n00;
m01 = n01;
m10 = n10;
m11 = n11;
updateType();
}
/**
* Concatenate a rotation about a point onto this transform. This is
* equivalent, but more efficient than
* <code>concatenate(AffineTransform.getRotateInstance(theta, x, y))</code>.
*
* @param theta the rotation angle
* @param x the x coordinate of the pivot point
* @param y the y coordinate of the pivot point
* @see #getRotateInstance(double, double, double)
* @see #concatenate(AffineTransform)
*/
public void rotate(double theta, double x, double y)
{
translate(x, y);
rotate(theta);
translate(-x, -y);
}
/**
* Concatenate a scale onto this transform. This is equivalent, but more
* efficient than
* <code>concatenate(AffineTransform.getScaleInstance(sx, sy))</code>.
*
* @param sx the x scaling factor
* @param sy the y scaling factor
* @see #getScaleInstance(double, double)
* @see #concatenate(AffineTransform)
*/
public void scale(double sx, double sy)
{
m00 *= sx;
m01 *= sy;
m10 *= sx;
m11 *= sy;
updateType();
}
/**
* Concatenate a shearing onto this transform. This is equivalent, but more
* efficient than
* <code>concatenate(AffineTransform.getShearInstance(sx, sy))</code>.
*
* @param shx the x shearing factor
* @param shy the y shearing factor
* @see #getShearInstance(double, double)
* @see #concatenate(AffineTransform)
*/
public void shear(double shx, double shy)
{
double n00 = m00 + (shy * m01);
double n01 = m01 + (shx * m00);
double n10 = m10 + (shy * m11);
double n11 = m11 + (shx * m10);
m00 = n00;
m01 = n01;
m10 = n10;
m11 = n11;
updateType();
}
/**
* Reset this transform to the identity (no transformation):
* <pre>
* [ 1 0 0 ]
* [ 0 1 0 ]
* [ 0 0 1 ]
* </pre>
*/
public void setToIdentity()
{
m00 = m11 = 1;
m01 = m02 = m10 = m12 = 0;
type = TYPE_IDENTITY;
}
/**
* Set this transform to a translation:
* <pre>
* [ 1 0 tx ]
* [ 0 1 ty ]
* [ 0 0 1 ]
* </pre>
*
* @param tx the x translation distance
* @param ty the y translation distance
*/
public void setToTranslation(double tx, double ty)
{
m00 = m11 = 1;
m01 = m10 = 0;
m02 = tx;
m12 = ty;
type = (tx == 0 && ty == 0) ? TYPE_UNIFORM_SCALE : TYPE_TRANSLATION;
}
/**
* Set this transform to a rotation. A positive angle (in radians) rotates
* the positive x-axis to the positive y-axis:
* <pre>
* [ cos(theta) -sin(theta) 0 ]
* [ sin(theta) cos(theta) 0 ]
* [ 0 0 1 ]
* </pre>
*
* @param theta the rotation angle
*/
public void setToRotation(double theta)
{
double c = Math.cos(theta);
double s = Math.sin(theta);
m00 = c;
m01 = -s;
m02 = 0;
m10 = s;
m11 = c;
m12 = 0;
type = (c == 1 ? TYPE_IDENTITY
: c == 0 || c == -1 ? TYPE_QUADRANT_ROTATION
: TYPE_GENERAL_ROTATION);
}
/**
* Set this transform to a rotation about a point. A positive angle (in
* radians) rotates the positive x-axis to the positive y-axis. This is the
* same as calling:
* <pre>
* tx.setToTranslation(x, y);
* tx.rotate(theta);
* tx.translate(-x, -y);
* </pre>
*
* <p>The resulting matrix is:
* <pre>
* [ cos(theta) -sin(theta) x-x*cos+y*sin ]
* [ sin(theta) cos(theta) y-x*sin-y*cos ]
* [ 0 0 1 ]
* </pre>
*
* @param theta the rotation angle
* @param x the x coordinate of the pivot point
* @param y the y coordinate of the pivot point
*/
public void setToRotation(double theta, double x, double y)
{
double c = Math.cos(theta);
double s = Math.sin(theta);
m00 = c;
m01 = -s;
m02 = x - x * c + y * s;
m10 = s;
m11 = c;
m12 = y - x * s - y * c;
updateType();
}
/**
* Set this transform to a scale:
* <pre>
* [ sx 0 0 ]
* [ 0 sy 0 ]
* [ 0 0 1 ]
* </pre>
*
* @param sx the x scaling factor
* @param sy the y scaling factor
*/
public void setToScale(double sx, double sy)
{
m00 = sx;
m01 = m02 = m10 = m12 = 0;
m11 = sy;
type = (sx != sy ? TYPE_GENERAL_SCALE
: sx == 1 ? TYPE_IDENTITY : TYPE_UNIFORM_SCALE);
}
/**
* Set this transform to a shear (points are shifted in the x direction based
* on a factor of their y coordinate, and in the y direction as a factor of
* their x coordinate):
* <pre>
* [ 1 shx 0 ]
* [ shy 1 0 ]
* [ 0 0 1 ]
* </pre>
*
* @param shx the x shearing factor
* @param shy the y shearing factor
*/
public void setToShear(double shx, double shy)
{
m00 = m11 = 1;
m01 = shx;
m10 = shy;
m02 = m12 = 0;
updateType();
}
/**
* Set this transform to a copy of the given one.
*
* @param tx the transform to copy
* @throws NullPointerException if tx is null
*/
public void setTransform(AffineTransform tx)
{
m00 = tx.m00;
m01 = tx.m01;
m02 = tx.m02;
m10 = tx.m10;
m11 = tx.m11;
m12 = tx.m12;
type = tx.type;
}
/**
* Set this transform to the given values:
* <pre>
* [ m00 m01 m02 ]
* [ m10 m11 m12 ]
* [ 0 0 1 ]
* </pre>
*
* @param m00 the x scaling component
* @param m10 the y shearing component
* @param m01 the x shearing component
* @param m11 the y scaling component
* @param m02 the x translation component
* @param m12 the y translation component
*/
public void setTransform(double m00, double m10, double m01,
double m11, double m02, double m12)
{
this.m00 = m00;
this.m10 = m10;
this.m01 = m01;
this.m11 = m11;
this.m02 = m02;
this.m12 = m12;
updateType();
}
/**
* Set this transform to the result of performing the original version of
* this followed by tx. This is commonly used when chaining transformations
* from one space to another. In matrix form:
* <pre>
* [ this ] = [ this ] x [ tx ]
* </pre>
*
* @param tx the transform to concatenate
* @throws NullPointerException if tx is null
* @see #preConcatenate(AffineTransform)
*/
public void concatenate(AffineTransform tx)
{
double n00 = m00 * tx.m00 + m01 * tx.m10;
double n01 = m00 * tx.m01 + m01 * tx.m11;
double n02 = m00 * tx.m02 + m01 * tx.m12 + m02;
double n10 = m10 * tx.m00 + m11 * tx.m10;
double n11 = m10 * tx.m01 + m11 * tx.m11;
double n12 = m10 * tx.m02 + m11 * tx.m12 + m12;
m00 = n00;
m01 = n01;
m02 = n02;
m10 = n10;
m11 = n11;
m12 = n12;
updateType();
}
/**
* Set this transform to the result of performing tx followed by the
* original version of this. This is less common than normal concatenation,
* but can still be used to chain transformations from one space to another.
* In matrix form:
* <pre>
* [ this ] = [ tx ] x [ this ]
* </pre>
*
* @param tx the transform to concatenate
* @throws NullPointerException if tx is null
* @see #concatenate(AffineTransform)
*/
public void preConcatenate(AffineTransform tx)
{
double n00 = tx.m00 * m00 + tx.m01 * m10;
double n01 = tx.m00 * m01 + tx.m01 * m11;
double n02 = tx.m00 * m02 + tx.m01 * m12 + tx.m02;
double n10 = tx.m10 * m00 + tx.m11 * m10;
double n11 = tx.m10 * m01 + tx.m11 * m11;
double n12 = tx.m10 * m02 + tx.m11 * m12 + tx.m12;
m00 = n00;
m01 = n01;
m02 = n02;
m10 = n10;
m11 = n11;
m12 = n12;
updateType();
}
/**
* Returns a transform, which if concatenated to this one, will result in
* the identity transform. This is useful for undoing transformations, but
* is only possible if the original transform has an inverse (ie. does not
* map multiple points to the same line or point). A transform exists only
* if getDeterminant() has a non-zero value.
*
* The inverse is calculated as:
*
* <pre>
*
* Let A be the matrix for which we want to find the inverse:
*
* A = [ m00 m01 m02 ]
* [ m10 m11 m12 ]
* [ 0 0 1 ]
*
*
* 1
* inverse (A) = --- x adjoint(A)
* det
*
*
*
* = 1 [ m11 -m01 m01*m12-m02*m11 ]
* --- x [ -m10 m00 -m00*m12+m10*m02 ]
* det [ 0 0 m00*m11-m10*m01 ]
*
*
*
* = [ m11/det -m01/det m01*m12-m02*m11/det ]
* [ -m10/det m00/det -m00*m12+m10*m02/det ]
* [ 0 0 1 ]
*
*
* </pre>
*
*
*
* @return a new inverse transform
* @throws NoninvertibleTransformException if inversion is not possible
* @see #getDeterminant()
*/
public AffineTransform createInverse()
throws NoninvertibleTransformException
{
double det = getDeterminant();
if (det == 0)
throw new NoninvertibleTransformException("can't invert transform");
double im00 = m11 / det;
double im10 = -m10 / det;
double im01 = -m01 / det;
double im11 = m00 / det;
double im02 = (m01 * m12 - m02 * m11) / det;
double im12 = (-m00 * m12 + m10 * m02) / det;
return new AffineTransform (im00, im10, im01, im11, im02, im12);
}
/**
* Perform this transformation on the given source point, and store the
* result in the destination (creating it if necessary). It is safe for
* src and dst to be the same.
*
* @param src the source point
* @param dst the destination, or null
* @return the transformation of src, in dst if it was non-null
* @throws NullPointerException if src is null
*/
public Point2D transform(Point2D src, Point2D dst)
{
if (dst == null)
dst = new Point2D.Double();
double x = src.getX();
double y = src.getY();
double nx = m00 * x + m01 * y + m02;
double ny = m10 * x + m11 * y + m12;
dst.setLocation(nx, ny);
return dst;
}
/**
* Perform this transformation on an array of points, storing the results
* in another (possibly same) array. This will not create a destination
* array, but will create points for the null entries of the destination.
* The transformation is done sequentially. While having a single source
* and destination point be the same is safe, you should be aware that
* duplicate references to the same point in the source, and having the
* source overlap the destination, may result in your source points changing
* from a previous transform before it is their turn to be evaluated.
*
* @param src the array of source points
* @param srcOff the starting offset into src
* @param dst the array of destination points (may have null entries)
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null, or src has null
* entries
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
* @throws ArrayStoreException if new points are incompatible with dst
*/
public void transform(Point2D[] src, int srcOff,
Point2D[] dst, int dstOff, int num)
{
while (--num >= 0)
dst[dstOff] = transform(src[srcOff++], dst[dstOff++]);
}
/**
* Perform this transformation on an array of points, in (x,y) pairs,
* storing the results in another (possibly same) array. This will not
* create a destination array. All sources are copied before the
* transformation, so that no result will overwrite a point that has not yet
* been evaluated.
*
* @param srcPts the array of source points
* @param srcOff the starting offset into src
* @param dstPts the array of destination points
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
*/
public void transform(float[] srcPts, int srcOff,
float[] dstPts, int dstOff, int num)
{
if (srcPts == dstPts && dstOff > srcOff
&& num > 1 && srcOff + 2 * num > dstOff)
{
float[] f = new float[2 * num];
System.arraycopy(srcPts, srcOff, f, 0, 2 * num);
srcPts = f;
}
while (--num >= 0)
{
float x = srcPts[srcOff++];
float y = srcPts[srcOff++];
dstPts[dstOff++] = (float) (m00 * x + m01 * y + m02);
dstPts[dstOff++] = (float) (m10 * x + m11 * y + m12);
}
}
/**
* Perform this transformation on an array of points, in (x,y) pairs,
* storing the results in another (possibly same) array. This will not
* create a destination array. All sources are copied before the
* transformation, so that no result will overwrite a point that has not yet
* been evaluated.
*
* @param srcPts the array of source points
* @param srcOff the starting offset into src
* @param dstPts the array of destination points
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
*/
public void transform(double[] srcPts, int srcOff,
double[] dstPts, int dstOff, int num)
{
if (srcPts == dstPts && dstOff > srcOff
&& num > 1 && srcOff + 2 * num > dstOff)
{
double[] d = new double[2 * num];
System.arraycopy(srcPts, srcOff, d, 0, 2 * num);
srcPts = d;
}
while (--num >= 0)
{
double x = srcPts[srcOff++];
double y = srcPts[srcOff++];
dstPts[dstOff++] = m00 * x + m01 * y + m02;
dstPts[dstOff++] = m10 * x + m11 * y + m12;
}
}
/**
* Perform this transformation on an array of points, in (x,y) pairs,
* storing the results in another array. This will not create a destination
* array.
*
* @param srcPts the array of source points
* @param srcOff the starting offset into src
* @param dstPts the array of destination points
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
*/
public void transform(float[] srcPts, int srcOff,
double[] dstPts, int dstOff, int num)
{
while (--num >= 0)
{
float x = srcPts[srcOff++];
float y = srcPts[srcOff++];
dstPts[dstOff++] = m00 * x + m01 * y + m02;
dstPts[dstOff++] = m10 * x + m11 * y + m12;
}
}
/**
* Perform this transformation on an array of points, in (x,y) pairs,
* storing the results in another array. This will not create a destination
* array.
*
* @param srcPts the array of source points
* @param srcOff the starting offset into src
* @param dstPts the array of destination points
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
*/
public void transform(double[] srcPts, int srcOff,
float[] dstPts, int dstOff, int num)
{
while (--num >= 0)
{
double x = srcPts[srcOff++];
double y = srcPts[srcOff++];
dstPts[dstOff++] = (float) (m00 * x + m01 * y + m02);
dstPts[dstOff++] = (float) (m10 * x + m11 * y + m12);
}
}
/**
* Perform the inverse of this transformation on the given source point,
* and store the result in the destination (creating it if necessary). It
* is safe for src and dst to be the same.
*
* @param src the source point
* @param dst the destination, or null
* @return the inverse transformation of src, in dst if it was non-null
* @throws NullPointerException if src is null
* @throws NoninvertibleTransformException if the inverse does not exist
* @see #getDeterminant()
*/
public Point2D inverseTransform(Point2D src, Point2D dst)
throws NoninvertibleTransformException
{
double det = getDeterminant();
if (det == 0)
throw new NoninvertibleTransformException("couldn't invert transform");
if (dst == null)
dst = new Point2D.Double();
double x = src.getX();
double y = src.getY();
double nx = (m11 * x + -m10 * y) / det - m02;
double ny = (m01 * x + -m00 * y) / det - m12;
dst.setLocation(nx, ny);
return dst;
}
/**
* Perform the inverse of this transformation on an array of points, in
* (x,y) pairs, storing the results in another (possibly same) array. This
* will not create a destination array. All sources are copied before the
* transformation, so that no result will overwrite a point that has not yet
* been evaluated.
*
* @param srcPts the array of source points
* @param srcOff the starting offset into src
* @param dstPts the array of destination points
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
* @throws NoninvertibleTransformException if the inverse does not exist
* @see #getDeterminant()
*/
public void inverseTransform(double[] srcPts, int srcOff,
double[] dstPts, int dstOff, int num)
throws NoninvertibleTransformException
{
double det = getDeterminant();
if (det == 0)
throw new NoninvertibleTransformException("couldn't invert transform");
if (srcPts == dstPts && dstOff > srcOff
&& num > 1 && srcOff + 2 * num > dstOff)
{
double[] d = new double[2 * num];
System.arraycopy(srcPts, srcOff, d, 0, 2 * num);
srcPts = d;
}
while (--num >= 0)
{
double x = srcPts[srcOff++];
double y = srcPts[srcOff++];
dstPts[dstOff++] = (m11 * x + -m10 * y) / det - m02;
dstPts[dstOff++] = (m01 * x + -m00 * y) / det - m12;
}
}
/**
* Perform this transformation, less any translation, on the given source
* point, and store the result in the destination (creating it if
* necessary). It is safe for src and dst to be the same. The reduced
* transform is equivalent to:
* <pre>
* [ x' ] = [ m00 m01 ] [ x ] = [ m00 * x + m01 * y ]
* [ y' ] [ m10 m11 ] [ y ] = [ m10 * x + m11 * y ]
* </pre>
*
* @param src the source point
* @param dst the destination, or null
* @return the delta transformation of src, in dst if it was non-null
* @throws NullPointerException if src is null
*/
public Point2D deltaTransform(Point2D src, Point2D dst)
{
if (dst == null)
dst = new Point2D.Double();
double x = src.getX();
double y = src.getY();
double nx = m00 * x + m01 * y;
double ny = m10 * x + m11 * y;
dst.setLocation(nx, ny);
return dst;
}
/**
* Perform this transformation, less any translation, on an array of points,
* in (x,y) pairs, storing the results in another (possibly same) array.
* This will not create a destination array. All sources are copied before
* the transformation, so that no result will overwrite a point that has
* not yet been evaluated. The reduced transform is equivalent to:
* <pre>
* [ x' ] = [ m00 m01 ] [ x ] = [ m00 * x + m01 * y ]
* [ y' ] [ m10 m11 ] [ y ] = [ m10 * x + m11 * y ]
* </pre>
*
* @param srcPts the array of source points
* @param srcOff the starting offset into src
* @param dstPts the array of destination points
* @param dstOff the starting offset into dst
* @param num the number of points to transform
* @throws NullPointerException if src or dst is null
* @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
*/
public void deltaTransform(double[] srcPts, int srcOff,
double[] dstPts, int dstOff,
int num)
{
if (srcPts == dstPts && dstOff > srcOff
&& num > 1 && srcOff + 2 * num > dstOff)
{
double[] d = new double[2 * num];
System.arraycopy(srcPts, srcOff, d, 0, 2 * num);
srcPts = d;
}
while (--num >= 0)
{
double x = srcPts[srcOff++];
double y = srcPts[srcOff++];
dstPts[dstOff++] = m00 * x + m01 * y;
dstPts[dstOff++] = m10 * x + m11 * y;
}
}
/**
* Return a new Shape, based on the given one, where the path of the shape
* has been transformed by this transform. Notice that this uses GeneralPath,
* which only stores points in float precision.
*
* @param src the shape source to transform
* @return the shape, transformed by this
* @throws NullPointerException if src is null
* @see GeneralPath#transform(AffineTransform)
*/
public Shape createTransformedShape(Shape src)
{
GeneralPath p = new GeneralPath(src);
p.transform(this);
return p;
}
/**
* Returns a string representation of the transform, in the format:
* <code>"AffineTransform[[" + m00 + ", " + m01 + ", " + m02 + "], ["
* + m10 + ", " + m11 + ", " + m12 + "]]"</code>.
*
* @return the string representation
*/
public String toString()
{
return "AffineTransform[[" + m00 + ", " + m01 + ", " + m02 + "], ["
+ m10 + ", " + m11 + ", " + m12 + "]]";
}
/**
* Tests if this transformation is the identity:
* <pre>
* [ 1 0 0 ]
* [ 0 1 0 ]
* [ 0 0 1 ]
* </pre>
*
* @return true if this is the identity transform
*/
public boolean isIdentity()
{
// Rather than rely on type, check explicitly.
return (m00 == 1 && m01 == 0 && m02 == 0
&& m10 == 0 && m11 == 1 && m12 == 0);
}
/**
* Create a new transform of the same run-time type, with the same
* transforming properties as this one.
*
* @return the clone
*/
public Object clone()
{
try
{
return super.clone();
}
catch (CloneNotSupportedException e)
{
throw (Error) new InternalError().initCause(e); // Impossible
}
}
/**
* Return the hashcode for this transformation. The formula is not
* documented, but appears to be the same as:
* <pre>
* long l = Double.doubleToLongBits(getScaleX());
* l = l * 31 + Double.doubleToLongBits(getShearY());
* l = l * 31 + Double.doubleToLongBits(getShearX());
* l = l * 31 + Double.doubleToLongBits(getScaleY());
* l = l * 31 + Double.doubleToLongBits(getTranslateX());
* l = l * 31 + Double.doubleToLongBits(getTranslateY());
* return (int) ((l >> 32) ^ l);
* </pre>
*
* @return the hashcode
*/
public int hashCode()
{
long l = Double.doubleToLongBits(m00);
l = l * 31 + Double.doubleToLongBits(m10);
l = l * 31 + Double.doubleToLongBits(m01);
l = l * 31 + Double.doubleToLongBits(m11);
l = l * 31 + Double.doubleToLongBits(m02);
l = l * 31 + Double.doubleToLongBits(m12);
return (int) ((l >> 32) ^ l);
}
/**
* Compares two transforms for equality. This returns true if they have the
* same matrix values.
*
* @param obj the transform to compare
* @return true if it is equal
*/
public boolean equals(Object obj)
{
if (! (obj instanceof AffineTransform))
return false;
AffineTransform t = (AffineTransform) obj;
return (m00 == t.m00 && m01 == t.m01 && m02 == t.m02
&& m10 == t.m10 && m11 == t.m11 && m12 == t.m12);
}
/**
* Helper to decode the type from the matrix. This is not guaranteed
* to find the optimal type, but at least it will be valid.
*/
private void updateType()
{
double det = getDeterminant();
if (det == 0)
{
type = TYPE_GENERAL_TRANSFORM;
return;
}
// Scale (includes rotation by PI) or translation.
if (m01 == 0 && m10 == 0)
{
if (m00 == m11)
type = m00 == 1 ? TYPE_IDENTITY : TYPE_UNIFORM_SCALE;
else
type = TYPE_GENERAL_SCALE;
if (m02 != 0 || m12 != 0)
type |= TYPE_TRANSLATION;
}
// Rotation.
else if (m00 == m11 && m01 == -m10)
{
type = m00 == 0 ? TYPE_QUADRANT_ROTATION : TYPE_GENERAL_ROTATION;
if (det != 1)
type |= TYPE_UNIFORM_SCALE;
if (m02 != 0 || m12 != 0)
type |= TYPE_TRANSLATION;
}
else
type = TYPE_GENERAL_TRANSFORM;
}
/**
* Reads a transform from an object stream.
*
* @param s the stream to read from
* @throws ClassNotFoundException if there is a problem deserializing
* @throws IOException if there is a problem deserializing
*/
private void readObject(ObjectInputStream s)
throws ClassNotFoundException, IOException
{
s.defaultReadObject();
updateType();
}
} // class AffineTransform