affinetransform.java

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	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
    }

    /**
     * Constructs a new <code>AffineTransform</code> 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 
     * {&nbsp;m00&nbsp;m10&nbsp;m01&nbsp;m11&nbsp;[m02&nbsp;m12]}.
     * @param flatmatrix the float array containing the values to be set
     * in the new <code>AffineTransform</code> 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(float[] flatmatrix) {
	m00 = flatmatrix[0];
	m10 = flatmatrix[1];
	m01 = flatmatrix[2];
	m11 = flatmatrix[3];
	if (flatmatrix.length > 5) {
	    m02 = flatmatrix[4];
	    m12 = flatmatrix[5];
	}
	updateState();
    }

    /**
     * Constructs a new <code>AffineTransform</code> from 6 double
     * precision values representing the 6 specifiable entries of the 3x3
     * transformation matrix.
     * @param m00,&nbsp;m01,&nbsp;m02,&nbsp;m10,&nbsp;m11,&nbsp;m12 the 
     * 6 floating point values that compose the 3x3 transformation matrix
     */
    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;
	updateState();
    }

    /**
     * Constructs a new <code>AffineTransform</code> 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 
     * {&nbsp;m00&nbsp;m10&nbsp;m01&nbsp;m11&nbsp;[m02&nbsp;m12]}.     
     * @param flatmatrix the double array containing the values to be set
     * in the new <code>AffineTransform</code> 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[] flatmatrix) {
	m00 = flatmatrix[0];
	m10 = flatmatrix[1];
	m01 = flatmatrix[2];
	m11 = flatmatrix[3];
	if (flatmatrix.length > 5) {
	    m02 = flatmatrix[4];
	    m12 = flatmatrix[5];
	}
	updateState();
    }

    /**
     * Returns a transform representing a translation transformation.
     * The matrix representing the returned transform is:
     * <pre>
     *		[   1    0    tx  ]
     *		[   0    1    ty  ]
     *		[   0    0    1   ]
     * </pre>
     * @param tx the distance by which coordinates are translated in the
     * X axis direction
     * @param ty the distance by which coordinates are translated in the
     * Y axis direction
     * @return an <code>AffineTransform</code> object that represents a
     * 	translation transformation, created with the specified vector.
     */
    public static AffineTransform getTranslateInstance(double tx, double ty) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToTranslation(tx, ty);
	return Tx;
    }

    /**
     * Returns a transform representing a rotation transformation.
     * The matrix representing the returned transform is:
     * <pre>
     *		[   cos(theta)    -sin(theta)    0   ]
     *		[   sin(theta)     cos(theta)    0   ]
     *		[       0              0         1   ]
     * </pre>
     * Rotating with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     * @return an <code>AffineTransform</code> object that is a rotation
     *	transformation, created with the specified angle of rotation.
     */
    public static AffineTransform getRotateInstance(double theta) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta);
	return Tx;
    }

    /**
     * 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).
     * <p>
     * This operation is equivalent to the following sequence of calls:
     * <pre>
     *	    AffineTransform Tx = new AffineTransform();
     *	    Tx.setToTranslation(x, y);	// S3: final translation
     *	    Tx.rotate(theta);		// S2: rotate around anchor
     *	    Tx.translate(-x, -y);	// S1: translate anchor to origin
     * </pre>
     * The matrix representing the returned transform is:
     * <pre>
     *		[   cos(theta)    -sin(theta)    x-x*cos+y*sin  ]
     *		[   sin(theta)     cos(theta)    y-x*sin-y*cos  ]
     *		[       0              0               1        ]
     * </pre>
     * Rotating with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     * @param x,&nbsp;y the coordinates of the anchor point of the
     * rotation
     * @return an <code>AffineTransform</code> object that rotates 
     *	coordinates around the specified point by the specified angle of
     *	rotation.
     */
    public static AffineTransform getRotateInstance(double theta,
						    double x, double y) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta, x, y);
	return Tx;
    }

    /**
     * Returns a transform representing a scaling transformation.
     * The matrix representing the returned transform is:
     * <pre>
     *		[   sx   0    0   ]
     *		[   0    sy   0   ]
     *		[   0    0    1   ]
     * </pre>
     * @param sx the factor by which coordinates are scaled along the
     * X axis direction
     * @param sy the factor by which coordinates are scaled along the
     * Y axis direction
     * @return an <code>AffineTransform</code> object that scales 
     *	coordinates by the specified factors.
     */
    public static AffineTransform getScaleInstance(double sx, double sy) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToScale(sx, sy);
	return Tx;
    }

    /**
     * Returns a transform representing a shearing transformation.
     * The matrix representing the returned transform is:
     * <pre>
     *		[   1   shx   0   ]
     *		[  shy   1    0   ]
     *		[   0    0    1   ]
     * </pre>
     * @param shx the multiplier by which coordinates are shifted in the
     * direction of the positive X axis as a factor of their Y coordinate
     * @param shy the multiplier by which coordinates are shifted in the
     * direction of the positive Y axis as a factor of their X coordinate
     * @return an <code>AffineTransform</code> object that shears 
     *	coordinates by the specified multipliers.
     */
    public static AffineTransform getShearInstance(double shx, double shy) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToShear(shx, shy);
	return Tx;
    }

    /**
     * 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.
     * @return the OR combination of any of the indicated flags that
     * apply to this transform
     * @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() {
	if (type == TYPE_UNKNOWN) {
	    calculateType();
	}
	return type;
    }

    /**
     * This is the utility function to calculate the flag bits when
     * they have not been cached.
     * @see #getType
     */
    private void calculateType() {
	int ret = TYPE_IDENTITY;
	boolean sgn0, sgn1;
	double M0, M1, M2, M3;
	updateState();
	switch (state) {
	  default:
	    stateError();
	    break;
	    /* NOTREACHED */
	  case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    /* NOBREAK */
	  case (APPLY_SHEAR | APPLY_SCALE):
	    if ((M0 = m00) * (M2 = m01) + (M3 = m10) * (M1 = m11) != 0) {
		// Transformed unit vectors are not perpendicular...
		this.type = TYPE_GENERAL_TRANSFORM;
		return;
	    }
	    sgn0 = (M0 >= 0.0);
	    sgn1 = (M1 >= 0.0);
	    if (sgn0 == sgn1) {
		// sgn(M0) == sgn(M1) therefore sgn(M2) == -sgn(M3)
		// This is the "unflipped" (right-handed) state
		if (M0 != M1 || M2 != -M3) {
		    ret |= (TYPE_GENERAL_ROTATION | TYPE_GENERAL_SCALE);
		} else if (M0 * M1 - M2 * M3 != 1.0) {
		    ret |= (TYPE_GENERAL_ROTATION | TYPE_UNIFORM_SCALE);
		} else {
		    ret |= TYPE_GENERAL_ROTATION;
		}
	    } else {
		// sgn(M0) == -sgn(M1) therefore sgn(M2) == sgn(M3)
		// This is the "flipped" (left-handed) state
		if (M0 != -M1 || M2 != M3) {
		    ret |= (TYPE_GENERAL_ROTATION |
			    TYPE_FLIP |
			    TYPE_GENERAL_SCALE);
		} else if (M0 * M1 - M2 * M3 != 1.0) {
		    ret |= (TYPE_GENERAL_ROTATION |
			    TYPE_FLIP |
			    TYPE_UNIFORM_SCALE);
		} else {
		    ret |= (TYPE_GENERAL_ROTATION | TYPE_FLIP);
		}
	    }
	    break;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    /* NOBREAK */
	case (APPLY_SHEAR):
	    sgn0 = ((M0 = m01) >= 0.0);
	    sgn1 = ((M1 = m10) >= 0.0);
	    if (sgn0 != sgn1) {
		// Different signs - simple 90 degree rotation
		if (M0 != -M1) {
		    ret |= (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_SCALE);
		} else if (M0 != 1.0 && M0 != -1.0) {
		    ret |= (TYPE_QUADRANT_ROTATION | TYPE_UNIFORM_SCALE);
		} else {
		    ret |= TYPE_QUADRANT_ROTATION;
		}
	    } else {
		// Same signs - 90 degree rotation plus an axis flip too
		if (M0 == M1) {
		    ret |= (TYPE_QUADRANT_ROTATION |
			    TYPE_FLIP |
			    TYPE_UNIFORM_SCALE);
		} else {
		    ret |= (TYPE_QUADRANT_ROTATION |
			    TYPE_FLIP |
			    TYPE_GENERAL_SCALE);
		}
	    }
	    break;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    /* NOBREAK */
	case (APPLY_SCALE):
	    sgn0 = ((M0 = m00) >= 0.0);
	    sgn1 = ((M1 = m11) >= 0.0);
	    if (sgn0 == sgn1) {
		if (sgn0) {
		    // Both scaling factors non-negative - simple scale
		    // Note: APPLY_SCALE implies M0, M1 are not both 1
		    if (M0 == M1) {
			ret |= TYPE_UNIFORM_SCALE;
		    } else {
			ret |= TYPE_GENERAL_SCALE;
		    }
		} else {
		    // Both scaling factors negative - 180 degree rotation
		    if (M0 != M1) {
			ret |= (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_SCALE);
		    } else if (M0 != -1.0) {
			ret |= (TYPE_QUADRANT_ROTATION | TYPE_UNIFORM_SCALE);
		    } else {
			ret |= TYPE_QUADRANT_ROTATION;
		    }
		}
	    } else {
		// Scaling factor signs different - flip about some axis
		if (M0 == -M1) {
		    if (M0 == 1.0 || M0 == -1.0) {
			ret |= TYPE_FLIP;
		    } else {
			ret |= (TYPE_FLIP | TYPE_UNIFORM_SCALE);
		    }
		} else {
		    ret |= (TYPE_FLIP | TYPE_GENERAL_SCALE);
		}
	    }
	    break;
	case (APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    break;
	case (APPLY_IDENTITY):
	    break;
	}
	this.type = ret;
    }

    /**
     * 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.
     * <p>
     * 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
     * {@link 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.
     * <p>
     * If this transform represents a uniform scale, as indicated by
     * the <code>getType</code> 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.
     * <p>
     * Mathematically, the determinant is calculated using the formula:
     * <pre>
     *		|  m00  m01  m02  |
     *		|  m10  m11  m12  |  =  m00 * m11 - m01 * m10
     *		|   0    0    1   |
     * </pre>
     *
     * @return the determinant of the matrix used to transform the
     * coordinates.
     * @see #getType
     * @see #createInverse
     * @see #inverseTransform
     * @see #TYPE_UNIFORM_SCALE
     */
    public double getDeterminant() {
	switch (state) {
	default:
	    stateError();
	    return 0;
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    return m00 * m11 - m01 * m10;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    return -(m01 * m10);
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    return m00 * m11;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    return 1.0;
	}
    }

    /**
     * Manually recalculates the state of the transform when the matrix
     * changes too much to predict the effects on the state.
     * The following table specifies what the various settings of the
     * state field say about the values of the corresponding matrix
     * element fields.
     * Note that the rules governing the SCALE fields are slightly