Java tutorial
/* * Copyright (c) 1996, 2018, Oracle and/or its affiliates. All rights reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. Oracle designates this * particular file as subject to the "Classpath" exception as provided * by Oracle in the LICENSE file that accompanied this code. * * This code is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License * version 2 for more details (a copy is included in the LICENSE file that * accompanied this code). * * You should have received a copy of the GNU General Public License version * 2 along with this work; if not, write to the Free Software Foundation, * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. * * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA * or visit www.oracle.com if you need additional information or have any * questions. */ package java.awt.geom; import java.awt.Shape; import java.beans.ConstructorProperties; /** * The {@code 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. * <p> * 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 {@code (x,y)} into * destination coordinates {@code (x',y')} by considering * them to be a column vector and multiplying the coordinate vector * by the matrix according to the following process: * <pre> * [ x'] [ m00 m01 m02 ] [ x ] [ m00x + m01y + m02 ] * [ y'] = [ m10 m11 m12 ] [ y ] = [ m10x + m11y + m12 ] * [ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ] * </pre> * <h2><a id="quadrantapproximation">Handling 90-Degree Rotations</a></h2> * <p> * In some variations of the {@code rotate} methods in the * {@code 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. * <p> * Since 90 degrees is represented as {@code 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 {@code PI/2} but never close enough * for the sine or cosine to be exactly 0.0, 1.0 or -1.0. * The implementations of {@code Math.sin()} and * {@code Math.cos()} correspondingly never return 0.0 * for any case other than {@code 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. * <p> * The net result of these issues is that if the * {@code Math.sin()} and {@code 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 {@code 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. * <p> * 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 <em>theta</em> as a quadrant * rotation if either <code>Math.sin(<em>theta</em>)</code> or * <code>Math.cos(<em>theta</em>)</code> 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 {@code Math.PI/2.0}. * * @author Jim Graham * @since 1.2 */ public class AffineTransform implements Cloneable, java.io.Serializable { /* * This constant is only useful for the cached type field. * It indicates that the type has been decached and must be recalculated. */ private static final int TYPE_UNKNOWN = -1; /** * 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. * @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 * @since 1.2 */ public static final int TYPE_IDENTITY = 0; /** * 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. * @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 * @since 1.2 */ public static final int TYPE_TRANSLATION = 1; /** * 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. * @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 #getType * @since 1.2 */ public static final int TYPE_UNIFORM_SCALE = 2; /** * 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. * @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 #getType * @since 1.2 */ public static final int TYPE_GENERAL_SCALE = 4; /** * This constant is a bit mask for any of the scale flag bits. * @see #TYPE_UNIFORM_SCALE * @see #TYPE_GENERAL_SCALE * @since 1.2 */ public static final int TYPE_MASK_SCALE = (TYPE_UNIFORM_SCALE | TYPE_GENERAL_SCALE); /** * 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. * @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 * @since 1.2 */ public static final int TYPE_FLIP = 64; /* NOTE: TYPE_FLIP was added after GENERAL_TRANSFORM was in public * circulation and the flag bits could no longer be conveniently * renumbered without introducing binary incompatibility in outside * code. */ /** * 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. * @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 #getType * @since 1.2 */ public static final int TYPE_QUADRANT_ROTATION = 8; /** * 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. * @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 #getType * @since 1.2 */ public static final int TYPE_GENERAL_ROTATION = 16; /** * This constant is a bit mask for any of the rotation flag bits. * @see #TYPE_QUADRANT_ROTATION * @see #TYPE_GENERAL_ROTATION * @since 1.2 */ public static final int TYPE_MASK_ROTATION = (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_ROTATION); /** * 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. * @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 * @since 1.2 */ public static final int TYPE_GENERAL_TRANSFORM = 32; /** * This constant is used for the internal state variable to indicate * that no calculations need to be performed and that the source * coordinates only need to be copied to their destinations to * complete the transformation equation of this transform. * @see #APPLY_TRANSLATE * @see #APPLY_SCALE * @see #APPLY_SHEAR * @see #state */ static final int APPLY_IDENTITY = 0; /** * This constant is used for the internal state variable to indicate * that the translation components of the matrix (m02 and m12) need * to be added to complete the transformation equation of this transform. * @see #APPLY_IDENTITY * @see #APPLY_SCALE * @see #APPLY_SHEAR * @see #state */ static final int APPLY_TRANSLATE = 1; /** * This constant is used for the internal state variable to indicate * that the scaling components of the matrix (m00 and m11) need * to be factored in to complete the transformation equation of * this transform. If the APPLY_SHEAR bit is also set then it * indicates that the scaling components are not both 0.0. If the * APPLY_SHEAR bit is not also set then it indicates that the * scaling components are not both 1.0. If neither the APPLY_SHEAR * nor the APPLY_SCALE bits are set then the scaling components * are both 1.0, which means that the x and y components contribute * to the transformed coordinate, but they are not multiplied by * any scaling factor. * @see #APPLY_IDENTITY * @see #APPLY_TRANSLATE * @see #APPLY_SHEAR * @see #state */ static final int APPLY_SCALE = 2; /** * This constant is used for the internal state variable to indicate * that the shearing components of the matrix (m01 and m10) need * to be factored in to complete the transformation equation of this * transform. The presence of this bit in the state variable changes * the interpretation of the APPLY_SCALE bit as indicated in its * documentation. * @see #APPLY_IDENTITY * @see #APPLY_TRANSLATE * @see #APPLY_SCALE * @see #state */ static final int APPLY_SHEAR = 4; /* * For methods which combine together the state of two separate * transforms and dispatch based upon the combination, these constants * specify how far to shift one of the states so that the two states * are mutually non-interfering and provide constants for testing the * bits of the shifted (HI) state. The methods in this class use * the convention that the state of "this" transform is unshifted and * the state of the "other" or "argument" transform is shifted (HI). */ private static final int HI_SHIFT = 3; private static final int HI_IDENTITY = APPLY_IDENTITY << HI_SHIFT; private static final int HI_TRANSLATE = APPLY_TRANSLATE << HI_SHIFT; private static final int HI_SCALE = APPLY_SCALE << HI_SHIFT; private static final int HI_SHEAR = APPLY_SHEAR << HI_SHIFT; /** * The X coordinate scaling element of the 3x3 * affine transformation matrix. * * @serial */ double m00; /** * The Y coordinate shearing element of the 3x3 * affine transformation matrix. * * @serial */ double m10; /** * The X coordinate shearing element of the 3x3 * affine transformation matrix. * * @serial */ double m01; /** * The Y coordinate scaling element of the 3x3 * affine transformation matrix. * * @serial */ double m11; /** * The X coordinate of the translation element of the * 3x3 affine transformation matrix. * * @serial */ double m02; /** * The Y coordinate of the translation element of the * 3x3 affine transformation matrix. * * @serial */ double m12; /** * This field keeps track of which components of the matrix need to * be applied when performing a transformation. * @see #APPLY_IDENTITY * @see #APPLY_TRANSLATE * @see #APPLY_SCALE * @see #APPLY_SHEAR */ transient int state; /** * This field caches the current transformation type of the matrix. * @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 #TYPE_GENERAL_TRANSFORM * @see #TYPE_UNKNOWN * @see #getType */ private transient int type; private AffineTransform(double m00, double m10, double m01, double m11, double m02, double m12, int state) { this.m00 = m00; this.m10 = m10; this.m01 = m01; this.m11 = m11; this.m02 = m02; this.m12 = m12; this.state = state; this.type = TYPE_UNKNOWN; } /** * Constructs a new {@code AffineTransform} representing the * Identity transformation. * @since 1.2 */ public AffineTransform() { m00 = m11 = 1.0; // m01 = m10 = m02 = m12 = 0.0; /* Not needed. */ // state = APPLY_IDENTITY; /* Not needed. */ // type = TYPE_IDENTITY; /* Not needed. */ } /** * Constructs a new {@code AffineTransform} that is a copy of * the specified {@code AffineTransform} object. * @param Tx the {@code AffineTransform} object to copy * @since 1.2 */ public AffineTransform(AffineTransform Tx) { this.m00 = Tx.m00; this.m10 = Tx.m10; this.m01 = Tx.m01; this.m11 = Tx.m11; this.m02 = Tx.m02; this.m12 = Tx.m12; this.state = Tx.state; this.type = Tx.type; } /** * Constructs a new {@code AffineTransform} from 6 floating point * values representing the 6 specifiable entries of the 3x3 * transformation matrix. * * @param m00 the X coordinate scaling element of the 3x3 matrix * @param m10 the Y coordinate shearing element of the 3x3 matrix * @param m01 the X coordinate shearing element of the 3x3 matrix * @param m11 the Y coordinate scaling element of the 3x3 matrix * @param m02 the X coordinate translation element of the 3x3 matrix * @param m12 the Y coordinate translation element of the 3x3 matrix * @since 1.2 */ @ConstructorProperties({ "scaleX", "shearY", "shearX", "scaleY", "translateX", "translateY" }) 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; updateState(); } /** * Constructs a new {@code AffineTransform} from an array of * floating point 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]}. * @param flatmatrix the float array containing the values to be set * in the new {@code AffineTransform} object. The length of the * array is assumed to be at least 4. If the length of the array is * less than 6, only the first 4 values are taken. If the length of * the array is greater than 6, the first 6 values are taken. * @since 1.2 */ 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} from 6 double * precision values representing the 6 specifiable entries of the 3x3 * transformation matrix. * * @param m00 the X coordinate scaling element of the 3x3 matrix * @param m10 the Y coordinate shearing element of the 3x3 matrix * @param m01 the X coordinate shearing element of the 3x3 matrix * @param m11 the Y coordinate scaling element of the 3x3 matrix * @param m02 the X coordinate translation element of the 3x3 matrix * @param m12 the Y coordinate translation element of the 3x3 matrix * @since 1.2 */ 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} 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]}. * @param flatmatrix the double array containing the values to be set * in the new {@code AffineTransform} object. The length of the * array is assumed to be at least 4. If the length of the array is * less than 6, only the first 4 values are taken. If the length of * the array is greater than 6, the first 6 values are taken. * @since 1.2 */ 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} object that represents a * translation transformation, created with the specified vector. * @since 1.2 */ 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 by a positive angle theta rotates points on the positive * X axis toward the positive Y axis. * Note also the discussion of * <a href="#quadrantapproximation">Handling 90-Degree Rotations</a> * above. * @param theta the angle of rotation measured in radians * @return an {@code AffineTransform} object that is a rotation * transformation, created with the specified angle of rotation. * @since 1.2 */ 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.translate(anchorx, anchory); // S3: final translation * Tx.rotate(theta); // S2: rotate around anchor * Tx.translate(-anchorx, -anchory); // 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 by a positive angle theta rotates points on the positive * X axis toward the positive Y axis. * Note also the discussion of * <a href="#quadrantapproximation">Handling 90-Degree Rotations</a> * above. * * @param theta the angle of rotation measured in radians * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @return an {@code AffineTransform} object that rotates * coordinates around the specified point by the specified angle of * rotation. * @since 1.2 */ public static AffineTransform getRotateInstance(double theta, double anchorx, double anchory) { AffineTransform Tx = new AffineTransform(); Tx.setToRotation(theta, anchorx, anchory); return Tx; } /** * 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 {@code vecx} and {@code vecy} are 0.0, * an identity transform is returned. * This operation is equivalent to calling: * <pre> * AffineTransform.getRotateInstance(Math.atan2(vecy, vecx)); * </pre> * * @param vecx the X coordinate of the rotation vector * @param vecy the Y coordinate of the rotation vector * @return an {@code AffineTransform} object that rotates * coordinates according to the specified rotation vector. * @since 1.6 */ public static AffineTransform getRotateInstance(double vecx, double vecy) { AffineTransform Tx = new AffineTransform(); Tx.setToRotation(vecx, vecy); return Tx; } /** * Returns 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 {@code vecx} and {@code vecy} are 0.0, * an identity transform is returned. * This operation is equivalent to calling: * <pre> * AffineTransform.getRotateInstance(Math.atan2(vecy, vecx), * anchorx, anchory); * </pre> * * @param vecx the X coordinate of the rotation vector * @param vecy the Y coordinate of the rotation vector * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @return an {@code AffineTransform} object that rotates * coordinates around the specified point according to the * specified rotation vector. * @since 1.6 */ public static AffineTransform getRotateInstance(double vecx, double vecy, double anchorx, double anchory) { AffineTransform Tx = new AffineTransform(); Tx.setToRotation(vecx, vecy, anchorx, anchory); return Tx; } /** * Returns a transform that rotates coordinates by the specified * number of quadrants. * This operation is equivalent to calling: * <pre> * AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0); * </pre> * Rotating by a positive number of quadrants rotates points on * the positive X axis toward the positive Y axis. * @param numquadrants the number of 90 degree arcs to rotate by * @return an {@code AffineTransform} object that rotates * coordinates by the specified number of quadrants. * @since 1.6 */ public static AffineTransform getQuadrantRotateInstance(int numquadrants) { AffineTransform Tx = new AffineTransform(); Tx.setToQuadrantRotation(numquadrants); return Tx; } /** * Returns a transform that rotates coordinates by the specified * number of quadrants around the specified anchor point. * This operation is equivalent to calling: * <pre> * AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0, * anchorx, anchory); * </pre> * Rotating by a positive number of quadrants rotates points on * the positive X axis toward the positive Y axis. * * @param numquadrants the number of 90 degree arcs to rotate by * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @return an {@code AffineTransform} object that rotates * coordinates by the specified number of quadrants around the * specified anchor point. * @since 1.6 */ public static AffineTransform getQuadrantRotateInstance(int numquadrants, double anchorx, double anchory) { AffineTransform Tx = new AffineTransform(); Tx.setToQuadrantRotation(numquadrants, anchorx, anchory); 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} object that scales * coordinates by the specified factors. * @since 1.2 */ 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} object that shears * coordinates by the specified multipliers. * @since 1.2 */ 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 * appropriate 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 * @since 1.2 */ 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 */ @SuppressWarnings("fallthrough") private void calculateType() { int ret = TYPE_IDENTITY; boolean sgn0, sgn1; double M0, M1, M2, M3; updateState(); switch (state) { default: stateError(); /* 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} 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 * @since 1.2 */ @SuppressWarnings("fallthrough") public double getDeterminant() { switch (state) { default: stateError(); /* 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 * different depending on whether the SHEAR flag is also set. * <pre> * SCALE SHEAR TRANSLATE * m00/m11 m01/m10 m02/m12 * * IDENTITY 1.0 0.0 0.0 * TRANSLATE (TR) 1.0 0.0 not both 0.0 * SCALE (SC) not both 1.0 0.0 0.0 * TR | SC not both 1.0 0.0 not both 0.0 * SHEAR (SH) 0.0 not both 0.0 0.0 * TR | SH 0.0 not both 0.0 not both 0.0 * SC | SH not both 0.0 not both 0.0 0.0 * TR | SC | SH not both 0.0 not both 0.0 not both 0.0 * </pre> */ void updateState() { if (m01 == 0.0 && m10 == 0.0) { if (m00 == 1.0 && m11 == 1.0) { if (m02 == 0.0 && m12 == 0.0) { state = APPLY_IDENTITY; type = TYPE_IDENTITY; } else { state = APPLY_TRANSLATE; type = TYPE_TRANSLATION; } } else { if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SCALE; type = TYPE_UNKNOWN; } else { state = (APPLY_SCALE | APPLY_TRANSLATE); type = TYPE_UNKNOWN; } } } else { if (m00 == 0.0 && m11 == 0.0) { if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SHEAR; type = TYPE_UNKNOWN; } else { state = (APPLY_SHEAR | APPLY_TRANSLATE); type = TYPE_UNKNOWN; } } else { if (m02 == 0.0 && m12 == 0.0) { state = (APPLY_SHEAR | APPLY_SCALE); type = TYPE_UNKNOWN; } else { state = (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE); type = TYPE_UNKNOWN; } } } } /* * Convenience method used internally to throw exceptions when * a case was forgotten in a switch statement. */ private void stateError() { throw new InternalError("missing case in transform state switch"); } /** * 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 } * @param flatmatrix the double array used to store the returned * values. * @see #getScaleX * @see #getScaleY * @see #getShearX * @see #getShearY * @see #getTranslateX * @see #getTranslateY * @since 1.2 */ public void getMatrix(double[] flatmatrix) { flatmatrix[0] = m00; flatmatrix[1] = m10; flatmatrix[2] = m01; flatmatrix[3] = m11; if (flatmatrix.length > 5) { flatmatrix[4] = m02; flatmatrix[5] = m12; } } /** * Returns the {@code m00} element of the 3x3 affine transformation matrix. * This matrix factor determines how input X coordinates will affect output * X coordinates and is one element of the scale of the transform. * To measure the full amount by which X coordinates are stretched or * contracted by this transform, use the following code: * <pre> * Point2D p = new Point2D.Double(1, 0); * p = tx.deltaTransform(p, p); * double scaleX = p.distance(0, 0); * </pre> * @return a double value that is {@code m00} element of the * 3x3 affine transformation matrix. * @see #getMatrix * @since 1.2 */ public double getScaleX() { return m00; } /** * Returns the {@code m11} element of the 3x3 affine transformation matrix. * This matrix factor determines how input Y coordinates will affect output * Y coordinates and is one element of the scale of the transform. * To measure the full amount by which Y coordinates are stretched or * contracted by this transform, use the following code: * <pre> * Point2D p = new Point2D.Double(0, 1); * p = tx.deltaTransform(p, p); * double scaleY = p.distance(0, 0); * </pre> * @return a double value that is {@code m11} element of the * 3x3 affine transformation matrix. * @see #getMatrix * @since 1.2 */ public double getScaleY() { return m11; } /** * Returns the X coordinate shearing element (m01) of the 3x3 * affine transformation matrix. * @return a double value that is the X coordinate of the shearing * element of the affine transformation matrix. * @see #getMatrix * @since 1.2 */ public double getShearX() { return m01; } /** * Returns the Y coordinate shearing element (m10) of the 3x3 * affine transformation matrix. * @return a double value that is the Y coordinate of the shearing * element of the affine transformation matrix. * @see #getMatrix * @since 1.2 */ public double getShearY() { return m10; } /** * Returns the X coordinate of the translation element (m02) of the * 3x3 affine transformation matrix. * @return a double value that is the X coordinate of the translation * element of the affine transformation matrix. * @see #getMatrix * @since 1.2 */ public double getTranslateX() { return m02; } /** * Returns the Y coordinate of the translation element (m12) of the * 3x3 affine transformation matrix. * @return a double value that is the Y coordinate of the translation * element of the affine transformation matrix. * @see #getMatrix * @since 1.2 */ public double getTranslateY() { return m12; } /** * Concatenates this transform with a translation transformation. * This is equivalent to calling concatenate(T), where T is an * {@code AffineTransform} represented by the following matrix: * <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 * @since 1.2 */ public void translate(double tx, double ty) { switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): m02 = tx * m00 + ty * m01 + m02; m12 = tx * m10 + ty * m11 + m12; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SHEAR | APPLY_SCALE; if (type != TYPE_UNKNOWN) { type -= TYPE_TRANSLATION; } } return; case (APPLY_SHEAR | APPLY_SCALE): m02 = tx * m00 + ty * m01; m12 = tx * m10 + ty * m11; if (m02 != 0.0 || m12 != 0.0) { state = APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE; type |= TYPE_TRANSLATION; } return; case (APPLY_SHEAR | APPLY_TRANSLATE): m02 = ty * m01 + m02; m12 = tx * m10 + m12; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SHEAR; if (type != TYPE_UNKNOWN) { type -= TYPE_TRANSLATION; } } return; case (APPLY_SHEAR): m02 = ty * m01; m12 = tx * m10; if (m02 != 0.0 || m12 != 0.0) { state = APPLY_SHEAR | APPLY_TRANSLATE; type |= TYPE_TRANSLATION; } return; case (APPLY_SCALE | APPLY_TRANSLATE): m02 = tx * m00 + m02; m12 = ty * m11 + m12; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SCALE; if (type != TYPE_UNKNOWN) { type -= TYPE_TRANSLATION; } } return; case (APPLY_SCALE): m02 = tx * m00; m12 = ty * m11; if (m02 != 0.0 || m12 != 0.0) { state = APPLY_SCALE | APPLY_TRANSLATE; type |= TYPE_TRANSLATION; } return; case (APPLY_TRANSLATE): m02 = tx + m02; m12 = ty + m12; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_IDENTITY; type = TYPE_IDENTITY; } return; case (APPLY_IDENTITY): m02 = tx; m12 = ty; if (tx != 0.0 || ty != 0.0) { state = APPLY_TRANSLATE; type = TYPE_TRANSLATION; } return; } } // Utility methods to optimize rotate methods. // These tables translate the flags during predictable quadrant // rotations where the shear and scale values are swapped and negated. private static final int[] rot90conversion = { /* IDENTITY => */ APPLY_SHEAR, /* TRANSLATE (TR) => */ APPLY_SHEAR | APPLY_TRANSLATE, /* SCALE (SC) => */ APPLY_SHEAR, /* SC | TR => */ APPLY_SHEAR | APPLY_TRANSLATE, /* SHEAR (SH) => */ APPLY_SCALE, /* SH | TR => */ APPLY_SCALE | APPLY_TRANSLATE, /* SH | SC => */ APPLY_SHEAR | APPLY_SCALE, /* SH | SC | TR => */ APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE, }; private void rotate90() { double M0 = m00; m00 = m01; m01 = -M0; M0 = m10; m10 = m11; m11 = -M0; int state = rot90conversion[this.state]; if ((state & (APPLY_SHEAR | APPLY_SCALE)) == APPLY_SCALE && m00 == 1.0 && m11 == 1.0) { state -= APPLY_SCALE; } this.state = state; type = TYPE_UNKNOWN; } private void rotate180() { m00 = -m00; m11 = -m11; int state = this.state; if ((state & (APPLY_SHEAR)) != 0) { // If there was a shear, then this rotation has no // effect on the state. m01 = -m01; m10 = -m10; } else { // No shear means the SCALE state may toggle when // m00 and m11 are negated. if (m00 == 1.0 && m11 == 1.0) { this.state = state & ~APPLY_SCALE; } else { this.state = state | APPLY_SCALE; } } type = TYPE_UNKNOWN; } private void rotate270() { double M0 = m00; m00 = -m01; m01 = M0; M0 = m10; m10 = -m11; m11 = M0; int state = rot90conversion[this.state]; if ((state & (APPLY_SHEAR | APPLY_SCALE)) == APPLY_SCALE && m00 == 1.0 && m11 == 1.0) { state -= APPLY_SCALE; } this.state = state; type = TYPE_UNKNOWN; } /** * Concatenates this transform with a rotation transformation. * This is equivalent to calling concatenate(R), where R is an * {@code AffineTransform} represented by the following matrix: * <pre> * [ cos(theta) -sin(theta) 0 ] * [ sin(theta) cos(theta) 0 ] * [ 0 0 1 ] * </pre> * Rotating by a positive angle theta rotates points on the positive * X axis toward the positive Y axis. * Note also the discussion of * <a href="#quadrantapproximation">Handling 90-Degree Rotations</a> * above. * @param theta the angle of rotation measured in radians * @since 1.2 */ public void rotate(double theta) { double sin = Math.sin(theta); if (sin == 1.0) { rotate90(); } else if (sin == -1.0) { rotate270(); } else { double cos = Math.cos(theta); if (cos == -1.0) { rotate180(); } else if (cos != 1.0) { double M0, M1; M0 = m00; M1 = m01; m00 = cos * M0 + sin * M1; m01 = -sin * M0 + cos * M1; M0 = m10; M1 = m11; m10 = cos * M0 + sin * M1; m11 = -sin * M0 + cos * M1; updateState(); } } } /** * 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). * <p> * This operation is equivalent to the following sequence of calls: * <pre> * translate(anchorx, anchory); // S3: final translation * rotate(theta); // S2: rotate around anchor * translate(-anchorx, -anchory); // S1: translate anchor to origin * </pre> * Rotating by a positive angle theta rotates points on the positive * X axis toward the positive Y axis. * Note also the discussion of * <a href="#quadrantapproximation">Handling 90-Degree Rotations</a> * above. * * @param theta the angle of rotation measured in radians * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @since 1.2 */ public void rotate(double theta, double anchorx, double anchory) { // REMIND: Simple for now - optimize later translate(anchorx, anchory); rotate(theta); translate(-anchorx, -anchory); } /** * 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 {@code vecx} and {@code vecy} are 0.0, * no additional rotation is added to this transform. * This operation is equivalent to calling: * <pre> * rotate(Math.atan2(vecy, vecx)); * </pre> * * @param vecx the X coordinate of the rotation vector * @param vecy the Y coordinate of the rotation vector * @since 1.6 */ public void rotate(double vecx, double vecy) { if (vecy == 0.0) { if (vecx < 0.0) { rotate180(); } // If vecx > 0.0 - no rotation // If vecx == 0.0 - undefined rotation - treat as no rotation } else if (vecx == 0.0) { if (vecy > 0.0) { rotate90(); } else { // vecy must be < 0.0 rotate270(); } } else { double len = Math.sqrt(vecx * vecx + vecy * vecy); double sin = vecy / len; double cos = vecx / len; double M0, M1; M0 = m00; M1 = m01; m00 = cos * M0 + sin * M1; m01 = -sin * M0 + cos * M1; M0 = m10; M1 = m11; m10 = cos * M0 + sin * M1; m11 = -sin * M0 + cos * M1; updateState(); } } /** * 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 {@code vecx} and {@code vecy} are 0.0, * the transform is not modified in any way. * This method is equivalent to calling: * <pre> * rotate(Math.atan2(vecy, vecx), anchorx, anchory); * </pre> * * @param vecx the X coordinate of the rotation vector * @param vecy the Y coordinate of the rotation vector * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @since 1.6 */ public void rotate(double vecx, double vecy, double anchorx, double anchory) { // REMIND: Simple for now - optimize later translate(anchorx, anchory); rotate(vecx, vecy); translate(-anchorx, -anchory); } /** * Concatenates this transform with a transform that rotates * coordinates by the specified number of quadrants. * This is equivalent to calling: * <pre> * rotate(numquadrants * Math.PI / 2.0); * </pre> * Rotating by a positive number of quadrants rotates points on * the positive X axis toward the positive Y axis. * @param numquadrants the number of 90 degree arcs to rotate by * @since 1.6 */ public void quadrantRotate(int numquadrants) { switch (numquadrants & 3) { case 0: break; case 1: rotate90(); break; case 2: rotate180(); break; case 3: rotate270(); break; } } /** * 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: * <pre> * rotate(numquadrants * Math.PI / 2.0, anchorx, anchory); * </pre> * Rotating by a positive number of quadrants rotates points on * the positive X axis toward the positive Y axis. * * @param numquadrants the number of 90 degree arcs to rotate by * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @since 1.6 */ public void quadrantRotate(int numquadrants, double anchorx, double anchory) { switch (numquadrants & 3) { case 0: return; case 1: m02 += anchorx * (m00 - m01) + anchory * (m01 + m00); m12 += anchorx * (m10 - m11) + anchory * (m11 + m10); rotate90(); break; case 2: m02 += anchorx * (m00 + m00) + anchory * (m01 + m01); m12 += anchorx * (m10 + m10) + anchory * (m11 + m11); rotate180(); break; case 3: m02 += anchorx * (m00 + m01) + anchory * (m01 - m00); m12 += anchorx * (m10 + m11) + anchory * (m11 - m10); rotate270(); break; } if (m02 == 0.0 && m12 == 0.0) { state &= ~APPLY_TRANSLATE; } else { state |= APPLY_TRANSLATE; } } /** * Concatenates this transform with a scaling transformation. * This is equivalent to calling concatenate(S), where S is an * {@code AffineTransform} represented by the following matrix: * <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 * @since 1.2 */ @SuppressWarnings("fallthrough") public void scale(double sx, double sy) { int state = this.state; switch (state) { default: stateError(); /* NOTREACHED */ case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SHEAR | APPLY_SCALE): m00 *= sx; m11 *= sy; /* NOBREAK */ case (APPLY_SHEAR | APPLY_TRANSLATE): case (APPLY_SHEAR): m01 *= sy; m10 *= sx; if (m01 == 0 && m10 == 0) { state &= APPLY_TRANSLATE; if (m00 == 1.0 && m11 == 1.0) { this.type = (state == APPLY_IDENTITY ? TYPE_IDENTITY : TYPE_TRANSLATION); } else { state |= APPLY_SCALE; this.type = TYPE_UNKNOWN; } this.state = state; } return; case (APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SCALE): m00 *= sx; m11 *= sy; if (m00 == 1.0 && m11 == 1.0) { this.state = (state &= APPLY_TRANSLATE); this.type = (state == APPLY_IDENTITY ? TYPE_IDENTITY : TYPE_TRANSLATION); } else { this.type = TYPE_UNKNOWN; } return; case (APPLY_TRANSLATE): case (APPLY_IDENTITY): m00 = sx; m11 = sy; if (sx != 1.0 || sy != 1.0) { this.state = state | APPLY_SCALE; this.type = TYPE_UNKNOWN; } return; } } /** * Concatenates this transform with a shearing transformation. * This is equivalent to calling concatenate(SH), where SH is an * {@code AffineTransform} represented by the following matrix: * <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 * @since 1.2 */ public void shear(double shx, double shy) { int state = this.state; switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SHEAR | APPLY_SCALE): double M0, M1; M0 = m00; M1 = m01; m00 = M0 + M1 * shy; m01 = M0 * shx + M1; M0 = m10; M1 = m11; m10 = M0 + M1 * shy; m11 = M0 * shx + M1; updateState(); return; case (APPLY_SHEAR | APPLY_TRANSLATE): case (APPLY_SHEAR): m00 = m01 * shy; m11 = m10 * shx; if (m00 != 0.0 || m11 != 0.0) { this.state = state | APPLY_SCALE; } this.type = TYPE_UNKNOWN; return; case (APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SCALE): m01 = m00 * shx; m10 = m11 * shy; if (m01 != 0.0 || m10 != 0.0) { this.state = state | APPLY_SHEAR; } this.type = TYPE_UNKNOWN; return; case (APPLY_TRANSLATE): case (APPLY_IDENTITY): m01 = shx; m10 = shy; if (m01 != 0.0 || m10 != 0.0) { this.state = state | APPLY_SCALE | APPLY_SHEAR; this.type = TYPE_UNKNOWN; } return; } } /** * Resets this transform to the Identity transform. * @since 1.2 */ public void setToIdentity() { m00 = m11 = 1.0; m10 = m01 = m02 = m12 = 0.0; state = APPLY_IDENTITY; type = TYPE_IDENTITY; } /** * Sets this transform to a translation transformation. * The matrix representing this transform becomes: * <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 * @since 1.2 */ public void setToTranslation(double tx, double ty) { m00 = 1.0; m10 = 0.0; m01 = 0.0; m11 = 1.0; m02 = tx; m12 = ty; if (tx != 0.0 || ty != 0.0) { state = APPLY_TRANSLATE; type = TYPE_TRANSLATION; } else { state = APPLY_IDENTITY; type = TYPE_IDENTITY; } } /** * Sets this transform to a rotation transformation. * The matrix representing this transform becomes: * <pre> * [ cos(theta) -sin(theta) 0 ] * [ sin(theta) cos(theta) 0 ] * [ 0 0 1 ] * </pre> * Rotating by a positive angle theta rotates points on the positive * X axis toward the positive Y axis. * Note also the discussion of * <a href="#quadrantapproximation">Handling 90-Degree Rotations</a> * above. * @param theta the angle of rotation measured in radians * @since 1.2 */ public void setToRotation(double theta) { double sin = Math.sin(theta); double cos; if (sin == 1.0 || sin == -1.0) { cos = 0.0; state = APPLY_SHEAR; type = TYPE_QUADRANT_ROTATION; } else { cos = Math.cos(theta); if (cos == -1.0) { sin = 0.0; state = APPLY_SCALE; type = TYPE_QUADRANT_ROTATION; } else if (cos == 1.0) { sin = 0.0; state = APPLY_IDENTITY; type = TYPE_IDENTITY; } else { state = APPLY_SHEAR | APPLY_SCALE; type = TYPE_GENERAL_ROTATION; } } m00 = cos; m10 = sin; m01 = -sin; m11 = cos; m02 = 0.0; m12 = 0.0; } /** * 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). * <p> * This operation is equivalent to the following sequence of calls: * <pre> * setToTranslation(anchorx, anchory); // S3: final translation * rotate(theta); // S2: rotate around anchor * translate(-anchorx, -anchory); // S1: translate anchor to origin * </pre> * The matrix representing this transform becomes: * <pre> * [ cos(theta) -sin(theta) x-x*cos+y*sin ] * [ sin(theta) cos(theta) y-x*sin-y*cos ] * [ 0 0 1 ] * </pre> * Rotating by a positive angle theta rotates points on the positive * X axis toward the positive Y axis. * Note also the discussion of * <a href="#quadrantapproximation">Handling 90-Degree Rotations</a> * above. * * @param theta the angle of rotation measured in radians * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @since 1.2 */ public void setToRotation(double theta, double anchorx, double anchory) { setToRotation(theta); double sin = m10; double oneMinusCos = 1.0 - m00; m02 = anchorx * oneMinusCos + anchory * sin; m12 = anchory * oneMinusCos - anchorx * sin; if (m02 != 0.0 || m12 != 0.0) { state |= APPLY_TRANSLATE; type |= TYPE_TRANSLATION; } } /** * 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 {@code vecx} and {@code vecy} are 0.0, * the transform is set to an identity transform. * This operation is equivalent to calling: * <pre> * setToRotation(Math.atan2(vecy, vecx)); * </pre> * * @param vecx the X coordinate of the rotation vector * @param vecy the Y coordinate of the rotation vector * @since 1.6 */ public void setToRotation(double vecx, double vecy) { double sin, cos; if (vecy == 0) { sin = 0.0; if (vecx < 0.0) { cos = -1.0; state = APPLY_SCALE; type = TYPE_QUADRANT_ROTATION; } else { cos = 1.0; state = APPLY_IDENTITY; type = TYPE_IDENTITY; } } else if (vecx == 0) { cos = 0.0; sin = (vecy > 0.0) ? 1.0 : -1.0; state = APPLY_SHEAR; type = TYPE_QUADRANT_ROTATION; } else { double len = Math.sqrt(vecx * vecx + vecy * vecy); cos = vecx / len; sin = vecy / len; state = APPLY_SHEAR | APPLY_SCALE; type = TYPE_GENERAL_ROTATION; } m00 = cos; m10 = sin; m01 = -sin; m11 = cos; m02 = 0.0; m12 = 0.0; } /** * 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 {@code vecx} and {@code vecy} are 0.0, * the transform is set to an identity transform. * This operation is equivalent to calling: * <pre> * setToTranslation(Math.atan2(vecy, vecx), anchorx, anchory); * </pre> * * @param vecx the X coordinate of the rotation vector * @param vecy the Y coordinate of the rotation vector * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @since 1.6 */ public void setToRotation(double vecx, double vecy, double anchorx, double anchory) { setToRotation(vecx, vecy); double sin = m10; double oneMinusCos = 1.0 - m00; m02 = anchorx * oneMinusCos + anchory * sin; m12 = anchory * oneMinusCos - anchorx * sin; if (m02 != 0.0 || m12 != 0.0) { state |= APPLY_TRANSLATE; type |= TYPE_TRANSLATION; } } /** * Sets this transform to a rotation transformation that rotates * coordinates by the specified number of quadrants. * This operation is equivalent to calling: * <pre> * setToRotation(numquadrants * Math.PI / 2.0); * </pre> * Rotating by a positive number of quadrants rotates points on * the positive X axis toward the positive Y axis. * @param numquadrants the number of 90 degree arcs to rotate by * @since 1.6 */ public void setToQuadrantRotation(int numquadrants) { switch (numquadrants & 3) { case 0: m00 = 1.0; m10 = 0.0; m01 = 0.0; m11 = 1.0; m02 = 0.0; m12 = 0.0; state = APPLY_IDENTITY; type = TYPE_IDENTITY; break; case 1: m00 = 0.0; m10 = 1.0; m01 = -1.0; m11 = 0.0; m02 = 0.0; m12 = 0.0; state = APPLY_SHEAR; type = TYPE_QUADRANT_ROTATION; break; case 2: m00 = -1.0; m10 = 0.0; m01 = 0.0; m11 = -1.0; m02 = 0.0; m12 = 0.0; state = APPLY_SCALE; type = TYPE_QUADRANT_ROTATION; break; case 3: m00 = 0.0; m10 = -1.0; m01 = 1.0; m11 = 0.0; m02 = 0.0; m12 = 0.0; state = APPLY_SHEAR; type = TYPE_QUADRANT_ROTATION; break; } } /** * 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: * <pre> * setToRotation(numquadrants * Math.PI / 2.0, anchorx, anchory); * </pre> * Rotating by a positive number of quadrants rotates points on * the positive X axis toward the positive Y axis. * * @param numquadrants the number of 90 degree arcs to rotate by * @param anchorx the X coordinate of the rotation anchor point * @param anchory the Y coordinate of the rotation anchor point * @since 1.6 */ public void setToQuadrantRotation(int numquadrants, double anchorx, double anchory) { switch (numquadrants & 3) { case 0: m00 = 1.0; m10 = 0.0; m01 = 0.0; m11 = 1.0; m02 = 0.0; m12 = 0.0; state = APPLY_IDENTITY; type = TYPE_IDENTITY; break; case 1: m00 = 0.0; m10 = 1.0; m01 = -1.0; m11 = 0.0; m02 = anchorx + anchory; m12 = anchory - anchorx; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SHEAR; type = TYPE_QUADRANT_ROTATION; } else { state = APPLY_SHEAR | APPLY_TRANSLATE; type = TYPE_QUADRANT_ROTATION | TYPE_TRANSLATION; } break; case 2: m00 = -1.0; m10 = 0.0; m01 = 0.0; m11 = -1.0; m02 = anchorx + anchorx; m12 = anchory + anchory; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SCALE; type = TYPE_QUADRANT_ROTATION; } else { state = APPLY_SCALE | APPLY_TRANSLATE; type = TYPE_QUADRANT_ROTATION | TYPE_TRANSLATION; } break; case 3: m00 = 0.0; m10 = -1.0; m01 = 1.0; m11 = 0.0; m02 = anchorx - anchory; m12 = anchory + anchorx; if (m02 == 0.0 && m12 == 0.0) { state = APPLY_SHEAR; type = TYPE_QUADRANT_ROTATION; } else { state = APPLY_SHEAR | APPLY_TRANSLATE; type = TYPE_QUADRANT_ROTATION | TYPE_TRANSLATION; } break; } } /** * Sets this transform to a scaling transformation. * The matrix representing this transform becomes: * <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 * @since 1.2 */ public void setToScale(double sx, double sy) { m00 = sx; m10 = 0.0; m01 = 0.0; m11 = sy; m02 = 0.0; m12 = 0.0; if (sx != 1.0 || sy != 1.0) { state = APPLY_SCALE; type = TYPE_UNKNOWN; } else { state = APPLY_IDENTITY; type = TYPE_IDENTITY; } } /** * Sets this transform to a shearing transformation. * The matrix representing this transform becomes: * <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 * @since 1.2 */ public void setToShear(double shx, double shy) { m00 = 1.0; m01 = shx; m10 = shy; m11 = 1.0; m02 = 0.0; m12 = 0.0; if (shx != 0.0 || shy != 0.0) { state = (APPLY_SHEAR | APPLY_SCALE); type = TYPE_UNKNOWN; } else { state = APPLY_IDENTITY; type = TYPE_IDENTITY; } } /** * Sets this transform to a copy of the transform in the specified * {@code AffineTransform} object. * @param Tx the {@code AffineTransform} object from which to * copy the transform * @since 1.2 */ public void setTransform(AffineTransform Tx) { this.m00 = Tx.m00; this.m10 = Tx.m10; this.m01 = Tx.m01; this.m11 = Tx.m11; this.m02 = Tx.m02; this.m12 = Tx.m12; this.state = Tx.state; this.type = Tx.type; } /** * Sets this transform to the matrix specified by the 6 * double precision values. * * @param m00 the X coordinate scaling element of the 3x3 matrix * @param m10 the Y coordinate shearing element of the 3x3 matrix * @param m01 the X coordinate shearing element of the 3x3 matrix * @param m11 the Y coordinate scaling element of the 3x3 matrix * @param m02 the X coordinate translation element of the 3x3 matrix * @param m12 the Y coordinate translation element of the 3x3 matrix * @since 1.2 */ 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; updateState(); } /** * Concatenates an {@code AffineTransform Tx} to * this {@code AffineTransform} Cx in the most commonly useful * way to provide a new user space * that is mapped to the former user space by {@code 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 {@code 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 {@code Tx} is represented * by the matrix [Tx] then this method does the following: * <pre> * [this] = [this] x [Tx] * </pre> * @param Tx the {@code AffineTransform} object to be * concatenated with this {@code AffineTransform} object. * @see #preConcatenate * @since 1.2 */ @SuppressWarnings("fallthrough") public void concatenate(AffineTransform Tx) { double M0, M1; double T00, T01, T10, T11; double T02, T12; int mystate = state; int txstate = Tx.state; switch ((txstate << HI_SHIFT) | mystate) { /* ---------- Tx == IDENTITY cases ---------- */ case (HI_IDENTITY | APPLY_IDENTITY): case (HI_IDENTITY | APPLY_TRANSLATE): case (HI_IDENTITY | APPLY_SCALE): case (HI_IDENTITY | APPLY_SCALE | APPLY_TRANSLATE): case (HI_IDENTITY | APPLY_SHEAR): case (HI_IDENTITY | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE): case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): return; /* ---------- this == IDENTITY cases ---------- */ case (HI_SHEAR | HI_SCALE | HI_TRANSLATE | APPLY_IDENTITY): m01 = Tx.m01; m10 = Tx.m10; /* NOBREAK */ case (HI_SCALE | HI_TRANSLATE | APPLY_IDENTITY): m00 = Tx.m00; m11 = Tx.m11; /* NOBREAK */ case (HI_TRANSLATE | APPLY_IDENTITY): m02 = Tx.m02; m12 = Tx.m12; state = txstate; type = Tx.type; return; case (HI_SHEAR | HI_SCALE | APPLY_IDENTITY): m01 = Tx.m01; m10 = Tx.m10; /* NOBREAK */ case (HI_SCALE | APPLY_IDENTITY): m00 = Tx.m00; m11 = Tx.m11; state = txstate; type = Tx.type; return; case (HI_SHEAR | HI_TRANSLATE | APPLY_IDENTITY): m02 = Tx.m02; m12 = Tx.m12; /* NOBREAK */ case (HI_SHEAR | APPLY_IDENTITY): m01 = Tx.m01; m10 = Tx.m10; m00 = m11 = 0.0; state = txstate; type = Tx.type; return; /* ---------- Tx == TRANSLATE cases ---------- */ case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE): case (HI_TRANSLATE | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_TRANSLATE | APPLY_SHEAR): case (HI_TRANSLATE | APPLY_SCALE | APPLY_TRANSLATE): case (HI_TRANSLATE | APPLY_SCALE): case (HI_TRANSLATE | APPLY_TRANSLATE): translate(Tx.m02, Tx.m12); return; /* ---------- Tx == SCALE cases ---------- */ case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE): case (HI_SCALE | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_SCALE | APPLY_SHEAR): case (HI_SCALE | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SCALE | APPLY_SCALE): case (HI_SCALE | APPLY_TRANSLATE): scale(Tx.m00, Tx.m11); return; /* ---------- Tx == SHEAR cases ---------- */ case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE): T01 = Tx.m01; T10 = Tx.m10; M0 = m00; m00 = m01 * T10; m01 = M0 * T01; M0 = m10; m10 = m11 * T10; m11 = M0 * T01; type = TYPE_UNKNOWN; return; case (HI_SHEAR | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_SHEAR): m00 = m01 * Tx.m10; m01 = 0.0; m11 = m10 * Tx.m01; m10 = 0.0; state = mystate ^ (APPLY_SHEAR | APPLY_SCALE); type = TYPE_UNKNOWN; return; case (HI_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_SCALE): m01 = m00 * Tx.m01; m00 = 0.0; m10 = m11 * Tx.m10; m11 = 0.0; state = mystate ^ (APPLY_SHEAR | APPLY_SCALE); type = TYPE_UNKNOWN; return; case (HI_SHEAR | APPLY_TRANSLATE): m00 = 0.0; m01 = Tx.m01; m10 = Tx.m10; m11 = 0.0; state = APPLY_TRANSLATE | APPLY_SHEAR; type = TYPE_UNKNOWN; return; } // If Tx has more than one attribute, it is not worth optimizing // all of those cases... T00 = Tx.m00; T01 = Tx.m01; T02 = Tx.m02; T10 = Tx.m10; T11 = Tx.m11; T12 = Tx.m12; switch (mystate) { default: stateError(); /* NOTREACHED */ case (APPLY_SHEAR | APPLY_SCALE): state = mystate | txstate; /* NOBREAK */ case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M0 = m00; M1 = m01; m00 = T00 * M0 + T10 * M1; m01 = T01 * M0 + T11 * M1; m02 += T02 * M0 + T12 * M1; M0 = m10; M1 = m11; m10 = T00 * M0 + T10 * M1; m11 = T01 * M0 + T11 * M1; m12 += T02 * M0 + T12 * M1; type = TYPE_UNKNOWN; return; case (APPLY_SHEAR | APPLY_TRANSLATE): case (APPLY_SHEAR): M0 = m01; m00 = T10 * M0; m01 = T11 * M0; m02 += T12 * M0; M0 = m10; m10 = T00 * M0; m11 = T01 * M0; m12 += T02 * M0; break; case (APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SCALE): M0 = m00; m00 = T00 * M0; m01 = T01 * M0; m02 += T02 * M0; M0 = m11; m10 = T10 * M0; m11 = T11 * M0; m12 += T12 * M0; break; case (APPLY_TRANSLATE): m00 = T00; m01 = T01; m02 += T02; m10 = T10; m11 = T11; m12 += T12; state = txstate | APPLY_TRANSLATE; type = TYPE_UNKNOWN; return; } updateState(); } /** * Concatenates an {@code AffineTransform Tx} to * this {@code AffineTransform} Cx * in a less commonly used way such that {@code 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 * {@code Tx} like this: * Cx'(p) = Tx(Cx(p)) * In matrix notation, if this transform Cx * is represented by the matrix [this] and {@code Tx} is * represented by the matrix [Tx] then this method does the * following: * <pre> * [this] = [Tx] x [this] * </pre> * @param Tx the {@code AffineTransform} object to be * concatenated with this {@code AffineTransform} object. * @see #concatenate * @since 1.2 */ @SuppressWarnings("fallthrough") public void preConcatenate(AffineTransform Tx) { double M0, M1; double T00, T01, T10, T11; double T02, T12; int mystate = state; int txstate = Tx.state; switch ((txstate << HI_SHIFT) | mystate) { case (HI_IDENTITY | APPLY_IDENTITY): case (HI_IDENTITY | APPLY_TRANSLATE): case (HI_IDENTITY | APPLY_SCALE): case (HI_IDENTITY | APPLY_SCALE | APPLY_TRANSLATE): case (HI_IDENTITY | APPLY_SHEAR): case (HI_IDENTITY | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE): case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): // Tx is IDENTITY... return; case (HI_TRANSLATE | APPLY_IDENTITY): case (HI_TRANSLATE | APPLY_SCALE): case (HI_TRANSLATE | APPLY_SHEAR): case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE): // Tx is TRANSLATE, this has no TRANSLATE m02 = Tx.m02; m12 = Tx.m12; state = mystate | APPLY_TRANSLATE; type |= TYPE_TRANSLATION; return; case (HI_TRANSLATE | APPLY_TRANSLATE): case (HI_TRANSLATE | APPLY_SCALE | APPLY_TRANSLATE): case (HI_TRANSLATE | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): // Tx is TRANSLATE, this has one too m02 = m02 + Tx.m02; m12 = m12 + Tx.m12; return; case (HI_SCALE | APPLY_TRANSLATE): case (HI_SCALE | APPLY_IDENTITY): // Only these two existing states need a new state state = mystate | APPLY_SCALE; /* NOBREAK */ case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE): case (HI_SCALE | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_SCALE | APPLY_SHEAR): case (HI_SCALE | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SCALE | APPLY_SCALE): // Tx is SCALE, this is anything T00 = Tx.m00; T11 = Tx.m11; if ((mystate & APPLY_SHEAR) != 0) { m01 = m01 * T00; m10 = m10 * T11; if ((mystate & APPLY_SCALE) != 0) { m00 = m00 * T00; m11 = m11 * T11; } } else { m00 = m00 * T00; m11 = m11 * T11; } if ((mystate & APPLY_TRANSLATE) != 0) { m02 = m02 * T00; m12 = m12 * T11; } type = TYPE_UNKNOWN; return; case (HI_SHEAR | APPLY_SHEAR | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_SHEAR): mystate = mystate | APPLY_SCALE; /* NOBREAK */ case (HI_SHEAR | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_IDENTITY): case (HI_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_SCALE): state = mystate ^ APPLY_SHEAR; /* NOBREAK */ case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE): // Tx is SHEAR, this is anything T01 = Tx.m01; T10 = Tx.m10; M0 = m00; m00 = m10 * T01; m10 = M0 * T10; M0 = m01; m01 = m11 * T01; m11 = M0 * T10; M0 = m02; m02 = m12 * T01; m12 = M0 * T10; type = TYPE_UNKNOWN; return; } // If Tx has more than one attribute, it is not worth optimizing // all of those cases... T00 = Tx.m00; T01 = Tx.m01; T02 = Tx.m02; T10 = Tx.m10; T11 = Tx.m11; T12 = Tx.m12; switch (mystate) { default: stateError(); /* NOTREACHED */ case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M0 = m02; M1 = m12; T02 += M0 * T00 + M1 * T01; T12 += M0 * T10 + M1 * T11; /* NOBREAK */ case (APPLY_SHEAR | APPLY_SCALE): m02 = T02; m12 = T12; M0 = m00; M1 = m10; m00 = M0 * T00 + M1 * T01; m10 = M0 * T10 + M1 * T11; M0 = m01; M1 = m11; m01 = M0 * T00 + M1 * T01; m11 = M0 * T10 + M1 * T11; break; case (APPLY_SHEAR | APPLY_TRANSLATE): M0 = m02; M1 = m12; T02 += M0 * T00 + M1 * T01; T12 += M0 * T10 + M1 * T11; /* NOBREAK */ case (APPLY_SHEAR): m02 = T02; m12 = T12; M0 = m10; m00 = M0 * T01; m10 = M0 * T11; M0 = m01; m01 = M0 * T00; m11 = M0 * T10; break; case (APPLY_SCALE | APPLY_TRANSLATE): M0 = m02; M1 = m12; T02 += M0 * T00 + M1 * T01; T12 += M0 * T10 + M1 * T11; /* NOBREAK */ case (APPLY_SCALE): m02 = T02; m12 = T12; M0 = m00; m00 = M0 * T00; m10 = M0 * T10; M0 = m11; m01 = M0 * T01; m11 = M0 * T11; break; case (APPLY_TRANSLATE): M0 = m02; M1 = m12; T02 += M0 * T00 + M1 * T01; T12 += M0 * T10 + M1 * T11; /* NOBREAK */ case (APPLY_IDENTITY): m02 = T02; m12 = T12; m00 = T00; m10 = T10; m01 = T01; m11 = T11; state = mystate | txstate; type = TYPE_UNKNOWN; return; } updateState(); } /** * Returns an {@code 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)). * <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 {@code getDeterminant} method can be used to determine if this * transform has no inverse, in which case an exception will be * thrown if the {@code createInverse} method is called. * @return a new {@code AffineTransform} object representing the * inverse transformation. * @see #getDeterminant * @exception NoninvertibleTransformException * if the matrix cannot be inverted. * @since 1.2 */ public AffineTransform createInverse() throws NoninvertibleTransformException { double det; switch (state) { default: stateError(); /* NOTREACHED */ return null; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): det = m00 * m11 - m01 * m10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } return new AffineTransform(m11 / det, -m10 / det, -m01 / det, m00 / det, (m01 * m12 - m11 * m02) / det, (m10 * m02 - m00 * m12) / det, (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE)); case (APPLY_SHEAR | APPLY_SCALE): det = m00 * m11 - m01 * m10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } return new AffineTransform(m11 / det, -m10 / det, -m01 / det, m00 / det, 0.0, 0.0, (APPLY_SHEAR | APPLY_SCALE)); case (APPLY_SHEAR | APPLY_TRANSLATE): if (m01 == 0.0 || m10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } return new AffineTransform(0.0, 1.0 / m01, 1.0 / m10, 0.0, -m12 / m10, -m02 / m01, (APPLY_SHEAR | APPLY_TRANSLATE)); case (APPLY_SHEAR): if (m01 == 0.0 || m10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } return new AffineTransform(0.0, 1.0 / m01, 1.0 / m10, 0.0, 0.0, 0.0, (APPLY_SHEAR)); case (APPLY_SCALE | APPLY_TRANSLATE): if (m00 == 0.0 || m11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } return new AffineTransform(1.0 / m00, 0.0, 0.0, 1.0 / m11, -m02 / m00, -m12 / m11, (APPLY_SCALE | APPLY_TRANSLATE)); case (APPLY_SCALE): if (m00 == 0.0 || m11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } return new AffineTransform(1.0 / m00, 0.0, 0.0, 1.0 / m11, 0.0, 0.0, (APPLY_SCALE)); case (APPLY_TRANSLATE): return new AffineTransform(1.0, 0.0, 0.0, 1.0, -m02, -m12, (APPLY_TRANSLATE)); case (APPLY_IDENTITY): return new AffineTransform(); } /* NOTREACHED */ } /** * 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)). * <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 {@code getDeterminant} method can be used to determine if this * transform has no inverse, in which case an exception will be * thrown if the {@code invert} method is called. * @see #getDeterminant * @exception NoninvertibleTransformException * if the matrix cannot be inverted. * @since 1.6 */ public void invert() throws NoninvertibleTransformException { double M00, M01, M02; double M10, M11, M12; double det; switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M01 = m01; M02 = m02; M10 = m10; M11 = m11; M12 = m12; det = M00 * M11 - M01 * M10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } m00 = M11 / det; m10 = -M10 / det; m01 = -M01 / det; m11 = M00 / det; m02 = (M01 * M12 - M11 * M02) / det; m12 = (M10 * M02 - M00 * M12) / det; break; case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; det = M00 * M11 - M01 * M10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } m00 = M11 / det; m10 = -M10 / det; m01 = -M01 / det; m11 = M00 / det; // m02 = 0.0; // m12 = 0.0; break; case (APPLY_SHEAR | APPLY_TRANSLATE): M01 = m01; M02 = m02; M10 = m10; M12 = m12; if (M01 == 0.0 || M10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } // m00 = 0.0; m10 = 1.0 / M01; m01 = 1.0 / M10; // m11 = 0.0; m02 = -M12 / M10; m12 = -M02 / M01; break; case (APPLY_SHEAR): M01 = m01; M10 = m10; if (M01 == 0.0 || M10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } // m00 = 0.0; m10 = 1.0 / M01; m01 = 1.0 / M10; // m11 = 0.0; // m02 = 0.0; // m12 = 0.0; break; case (APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M02 = m02; M11 = m11; M12 = m12; if (M00 == 0.0 || M11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } m00 = 1.0 / M00; // m10 = 0.0; // m01 = 0.0; m11 = 1.0 / M11; m02 = -M02 / M00; m12 = -M12 / M11; break; case (APPLY_SCALE): M00 = m00; M11 = m11; if (M00 == 0.0 || M11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } m00 = 1.0 / M00; // m10 = 0.0; // m01 = 0.0; m11 = 1.0 / M11; // m02 = 0.0; // m12 = 0.0; break; case (APPLY_TRANSLATE): // m00 = 1.0; // m10 = 0.0; // m01 = 0.0; // m11 = 1.0; m02 = -m02; m12 = -m12; break; case (APPLY_IDENTITY): // m00 = 1.0; // m10 = 0.0; // m01 = 0.0; // m11 = 1.0; // m02 = 0.0; // m12 = 0.0; break; } } /** * Transforms the specified {@code ptSrc} and stores the result * in {@code ptDst}. * If {@code ptDst} is {@code null}, a new {@link Point2D} * object is allocated and then the result of the transformation is * stored in this object. * In either case, {@code ptDst}, which contains the * transformed point, is returned for convenience. * If {@code ptSrc} and {@code ptDst} are the same * object, the input point is correctly overwritten with * the transformed point. * @param ptSrc the specified {@code Point2D} to be transformed * @param ptDst the specified {@code Point2D} that stores the * result of transforming {@code ptSrc} * @return the {@code ptDst} after transforming * {@code ptSrc} and storing the result in {@code ptDst}. * @since 1.2 */ public Point2D transform(Point2D ptSrc, Point2D ptDst) { if (ptDst == null) { if (ptSrc instanceof Point2D.Double) { ptDst = new Point2D.Double(); } else { ptDst = new Point2D.Float(); } } // Copy source coords into local variables in case src == dst double x = ptSrc.getX(); double y = ptSrc.getY(); switch (state) { default: stateError(); /* NOTREACHED */ return null; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): ptDst.setLocation(x * m00 + y * m01 + m02, x * m10 + y * m11 + m12); return ptDst; case (APPLY_SHEAR | APPLY_SCALE): ptDst.setLocation(x * m00 + y * m01, x * m10 + y * m11); return ptDst; case (APPLY_SHEAR | APPLY_TRANSLATE): ptDst.setLocation(y * m01 + m02, x * m10 + m12); return ptDst; case (APPLY_SHEAR): ptDst.setLocation(y * m01, x * m10); return ptDst; case (APPLY_SCALE | APPLY_TRANSLATE): ptDst.setLocation(x * m00 + m02, y * m11 + m12); return ptDst; case (APPLY_SCALE): ptDst.setLocation(x * m00, y * m11); return ptDst; case (APPLY_TRANSLATE): ptDst.setLocation(x + m02, y + m12); return ptDst; case (APPLY_IDENTITY): ptDst.setLocation(x, y); return ptDst; } /* NOTREACHED */ } /** * Transforms an array of point objects by this transform. * If any element of the {@code ptDst} array is * {@code null}, a new {@code Point2D} object is allocated * and stored into that element before storing the results of the * transformation. * <p> * Note that this method does not take any precautions to * avoid problems caused by storing results into {@code Point2D} * objects that will be used as the source for calculations * further down the source array. * This method does guarantee that if a specified {@code 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 {@code Point2D} object for one * operation is the same object as the source {@code Point2D} * object for another operation further down the source array then * the original coordinates in that point are overwritten before * they can be converted. * @param ptSrc the array containing the source point objects * @param ptDst the array into which the transform point objects are * returned * @param srcOff the offset to the first point object to be * transformed in the source array * @param dstOff the offset to the location of the first * transformed point object that is stored in the destination array * @param numPts the number of point objects to be transformed * @since 1.2 */ public void transform(Point2D[] ptSrc, int srcOff, Point2D[] ptDst, int dstOff, int numPts) { int state = this.state; while (--numPts >= 0) { // Copy source coords into local variables in case src == dst Point2D src = ptSrc[srcOff++]; double x = src.getX(); double y = src.getY(); Point2D dst = ptDst[dstOff++]; if (dst == null) { if (src instanceof Point2D.Double) { dst = new Point2D.Double(); } else { dst = new Point2D.Float(); } ptDst[dstOff - 1] = dst; } switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): dst.setLocation(x * m00 + y * m01 + m02, x * m10 + y * m11 + m12); break; case (APPLY_SHEAR | APPLY_SCALE): dst.setLocation(x * m00 + y * m01, x * m10 + y * m11); break; case (APPLY_SHEAR | APPLY_TRANSLATE): dst.setLocation(y * m01 + m02, x * m10 + m12); break; case (APPLY_SHEAR): dst.setLocation(y * m01, x * m10); break; case (APPLY_SCALE | APPLY_TRANSLATE): dst.setLocation(x * m00 + m02, y * m11 + m12); break; case (APPLY_SCALE): dst.setLocation(x * m00, y * m11); break; case (APPLY_TRANSLATE): dst.setLocation(x + m02, y + m12); break; case (APPLY_IDENTITY): dst.setLocation(x, y); break; } } /* NOTREACHED */ } /** * 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 {@code [x0, y0, x1, y1, ..., xn, yn]}. * @param srcPts the array containing the source point coordinates. * Each point is stored as a pair of x, y coordinates. * @param dstPts the array into which the transformed point coordinates * are returned. Each point is stored as a pair of x, y * coordinates. * @param srcOff the offset to the first point to be transformed * in the source array * @param dstOff the offset to the location of the first * transformed point that is stored in the destination array * @param numPts the number of points to be transformed * @since 1.2 */ public void transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) { double M00, M01, M02, M10, M11, M12; // For caching if (dstPts == srcPts && dstOff > srcOff && dstOff < srcOff + numPts * 2) { // If the arrays overlap partially with the destination higher // than the source and we transform the coordinates normally // we would overwrite some of the later source coordinates // with results of previous transformations. // To get around this we use arraycopy to copy the points // to their final destination with correct overwrite // handling and then transform them in place in the new // safer location. System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); // srcPts = dstPts; // They are known to be equal. srcOff = dstOff; } switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M01 = m01; M02 = m02; M10 = m10; M11 = m11; M12 = m12; while (--numPts >= 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); } return; case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = (float) (M00 * x + M01 * y); dstPts[dstOff++] = (float) (M10 * x + M11 * y); } return; case (APPLY_SHEAR | APPLY_TRANSLATE): M01 = m01; M02 = m02; M10 = m10; M12 = m12; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++] + M02); dstPts[dstOff++] = (float) (M10 * x + M12); } return; case (APPLY_SHEAR): M01 = m01; M10 = m10; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++]); dstPts[dstOff++] = (float) (M10 * x); } return; case (APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M02 = m02; M11 = m11; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++] + M02); dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++] + M12); } return; case (APPLY_SCALE): M00 = m00; M11 = m11; while (--numPts >= 0) { dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++]); dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++]); } return; case (APPLY_TRANSLATE): M02 = m02; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = (float) (srcPts[srcOff++] + M02); dstPts[dstOff++] = (float) (srcPts[srcOff++] + M12); } return; case (APPLY_IDENTITY): if (srcPts != dstPts || srcOff != dstOff) { System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); } return; } /* NOTREACHED */ } /** * 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 {@code [x0, y0, x1, y1, ..., xn, yn]}. * @param srcPts the array containing the source point coordinates. * Each point is stored as a pair of x, y coordinates. * @param dstPts the array into which the transformed point * coordinates are returned. Each point is stored as a pair of * x, y coordinates. * @param srcOff the offset to the first point to be transformed * in the source array * @param dstOff the offset to the location of the first * transformed point that is stored in the destination array * @param numPts the number of point objects to be transformed * @since 1.2 */ public void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) { double M00, M01, M02, M10, M11, M12; // For caching if (dstPts == srcPts && dstOff > srcOff && dstOff < srcOff + numPts * 2) { // If the arrays overlap partially with the destination higher // than the source and we transform the coordinates normally // we would overwrite some of the later source coordinates // with results of previous transformations. // To get around this we use arraycopy to copy the points // to their final destination with correct overwrite // handling and then transform them in place in the new // safer location. System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); // srcPts = dstPts; // They are known to be equal. srcOff = dstOff; } switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M01 = m01; M02 = m02; M10 = m10; M11 = m11; M12 = m12; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = M00 * x + M01 * y + M02; dstPts[dstOff++] = M10 * x + M11 * y + M12; } return; case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = M00 * x + M01 * y; dstPts[dstOff++] = M10 * x + M11 * y; } return; case (APPLY_SHEAR | APPLY_TRANSLATE): M01 = m01; M02 = m02; M10 = m10; M12 = m12; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = M01 * srcPts[srcOff++] + M02; dstPts[dstOff++] = M10 * x + M12; } return; case (APPLY_SHEAR): M01 = m01; M10 = m10; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = M01 * srcPts[srcOff++]; dstPts[dstOff++] = M10 * x; } return; case (APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M02 = m02; M11 = m11; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = M00 * srcPts[srcOff++] + M02; dstPts[dstOff++] = M11 * srcPts[srcOff++] + M12; } return; case (APPLY_SCALE): M00 = m00; M11 = m11; while (--numPts >= 0) { dstPts[dstOff++] = M00 * srcPts[srcOff++]; dstPts[dstOff++] = M11 * srcPts[srcOff++]; } return; case (APPLY_TRANSLATE): M02 = m02; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = srcPts[srcOff++] + M02; dstPts[dstOff++] = srcPts[srcOff++] + M12; } return; case (APPLY_IDENTITY): if (srcPts != dstPts || srcOff != dstOff) { System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); } return; } /* NOTREACHED */ } /** * 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 {@code [x0, y0, x1, y1, ..., xn, yn]}. * @param srcPts the array containing the source point coordinates. * Each point is stored as a pair of x, y coordinates. * @param dstPts the array into which the transformed point coordinates * are returned. Each point is stored as a pair of x, y * coordinates. * @param srcOff the offset to the first point to be transformed * in the source array * @param dstOff the offset to the location of the first * transformed point that is stored in the destination array * @param numPts the number of points to be transformed * @since 1.2 */ public void transform(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) { double M00, M01, M02, M10, M11, M12; // For caching switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M01 = m01; M02 = m02; M10 = m10; M11 = m11; M12 = m12; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = M00 * x + M01 * y + M02; dstPts[dstOff++] = M10 * x + M11 * y + M12; } return; case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = M00 * x + M01 * y; dstPts[dstOff++] = M10 * x + M11 * y; } return; case (APPLY_SHEAR | APPLY_TRANSLATE): M01 = m01; M02 = m02; M10 = m10; M12 = m12; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = M01 * srcPts[srcOff++] + M02; dstPts[dstOff++] = M10 * x + M12; } return; case (APPLY_SHEAR): M01 = m01; M10 = m10; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = M01 * srcPts[srcOff++]; dstPts[dstOff++] = M10 * x; } return; case (APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M02 = m02; M11 = m11; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = M00 * srcPts[srcOff++] + M02; dstPts[dstOff++] = M11 * srcPts[srcOff++] + M12; } return; case (APPLY_SCALE): M00 = m00; M11 = m11; while (--numPts >= 0) { dstPts[dstOff++] = M00 * srcPts[srcOff++]; dstPts[dstOff++] = M11 * srcPts[srcOff++]; } return; case (APPLY_TRANSLATE): M02 = m02; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = srcPts[srcOff++] + M02; dstPts[dstOff++] = srcPts[srcOff++] + M12; } return; case (APPLY_IDENTITY): while (--numPts >= 0) { dstPts[dstOff++] = srcPts[srcOff++]; dstPts[dstOff++] = srcPts[srcOff++]; } return; } /* NOTREACHED */ } /** * 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 {@code [x0, y0, x1, y1, ..., xn, yn]}. * @param srcPts the array containing the source point coordinates. * Each point is stored as a pair of x, y coordinates. * @param dstPts the array into which the transformed point * coordinates are returned. Each point is stored as a pair of * x, y coordinates. * @param srcOff the offset to the first point to be transformed * in the source array * @param dstOff the offset to the location of the first * transformed point that is stored in the destination array * @param numPts the number of point objects to be transformed * @since 1.2 */ public void transform(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) { double M00, M01, M02, M10, M11, M12; // For caching switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M01 = m01; M02 = m02; M10 = m10; M11 = m11; M12 = m12; while (--numPts >= 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); } return; case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = (float) (M00 * x + M01 * y); dstPts[dstOff++] = (float) (M10 * x + M11 * y); } return; case (APPLY_SHEAR | APPLY_TRANSLATE): M01 = m01; M02 = m02; M10 = m10; M12 = m12; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++] + M02); dstPts[dstOff++] = (float) (M10 * x + M12); } return; case (APPLY_SHEAR): M01 = m01; M10 = m10; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++]); dstPts[dstOff++] = (float) (M10 * x); } return; case (APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M02 = m02; M11 = m11; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++] + M02); dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++] + M12); } return; case (APPLY_SCALE): M00 = m00; M11 = m11; while (--numPts >= 0) { dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++]); dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++]); } return; case (APPLY_TRANSLATE): M02 = m02; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = (float) (srcPts[srcOff++] + M02); dstPts[dstOff++] = (float) (srcPts[srcOff++] + M12); } return; case (APPLY_IDENTITY): while (--numPts >= 0) { dstPts[dstOff++] = (float) (srcPts[srcOff++]); dstPts[dstOff++] = (float) (srcPts[srcOff++]); } return; } /* NOTREACHED */ } /** * Inverse transforms the specified {@code ptSrc} and stores the * result in {@code ptDst}. * If {@code ptDst} is {@code null}, a new * {@code Point2D} object is allocated and then the result of the * transform is stored in this object. * In either case, {@code ptDst}, which contains the transformed * point, is returned for convenience. * If {@code ptSrc} and {@code ptDst} are the same * object, the input point is correctly overwritten with the * transformed point. * @param ptSrc the point to be inverse transformed * @param ptDst the resulting transformed point * @return {@code ptDst}, which contains the result of the * inverse transform. * @exception NoninvertibleTransformException if the matrix cannot be * inverted. * @since 1.2 */ @SuppressWarnings("fallthrough") public Point2D inverseTransform(Point2D ptSrc, Point2D ptDst) throws NoninvertibleTransformException { if (ptDst == null) { if (ptSrc instanceof Point2D.Double) { ptDst = new Point2D.Double(); } else { ptDst = new Point2D.Float(); } } // Copy source coords into local variables in case src == dst double x = ptSrc.getX(); double y = ptSrc.getY(); switch (state) { default: stateError(); /* NOTREACHED */ case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): x -= m02; y -= m12; /* NOBREAK */ case (APPLY_SHEAR | APPLY_SCALE): double det = m00 * m11 - m01 * m10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } ptDst.setLocation((x * m11 - y * m01) / det, (y * m00 - x * m10) / det); return ptDst; case (APPLY_SHEAR | APPLY_TRANSLATE): x -= m02; y -= m12; /* NOBREAK */ case (APPLY_SHEAR): if (m01 == 0.0 || m10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } ptDst.setLocation(y / m10, x / m01); return ptDst; case (APPLY_SCALE | APPLY_TRANSLATE): x -= m02; y -= m12; /* NOBREAK */ case (APPLY_SCALE): if (m00 == 0.0 || m11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } ptDst.setLocation(x / m00, y / m11); return ptDst; case (APPLY_TRANSLATE): ptDst.setLocation(x - m02, y - m12); return ptDst; case (APPLY_IDENTITY): ptDst.setLocation(x, y); return ptDst; } /* NOTREACHED */ } /** * 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 {@code [x0, y0, x1, y1, ..., xn, yn]}. * @param srcPts the array containing the source point coordinates. * Each point is stored as a pair of x, y coordinates. * @param dstPts the array into which the transformed point * coordinates are returned. Each point is stored as a pair of * x, y coordinates. * @param srcOff the offset to the first point to be transformed * in the source array * @param dstOff the offset to the location of the first * transformed point that is stored in the destination array * @param numPts the number of point objects to be transformed * @exception NoninvertibleTransformException if the matrix cannot be * inverted. * @since 1.2 */ public void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws NoninvertibleTransformException { double M00, M01, M02, M10, M11, M12; // For caching double det; if (dstPts == srcPts && dstOff > srcOff && dstOff < srcOff + numPts * 2) { // If the arrays overlap partially with the destination higher // than the source and we transform the coordinates normally // we would overwrite some of the later source coordinates // with results of previous transformations. // To get around this we use arraycopy to copy the points // to their final destination with correct overwrite // handling and then transform them in place in the new // safer location. System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); // srcPts = dstPts; // They are known to be equal. srcOff = dstOff; } switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M01 = m01; M02 = m02; M10 = m10; M11 = m11; M12 = m12; det = M00 * M11 - M01 * M10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } while (--numPts >= 0) { double x = srcPts[srcOff++] - M02; double y = srcPts[srcOff++] - M12; dstPts[dstOff++] = (x * M11 - y * M01) / det; dstPts[dstOff++] = (y * M00 - x * M10) / det; } return; case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; det = M00 * M11 - M01 * M10; if (Math.abs(det) <= Double.MIN_VALUE) { throw new NoninvertibleTransformException("Determinant is " + det); } while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = (x * M11 - y * M01) / det; dstPts[dstOff++] = (y * M00 - x * M10) / det; } return; case (APPLY_SHEAR | APPLY_TRANSLATE): M01 = m01; M02 = m02; M10 = m10; M12 = m12; if (M01 == 0.0 || M10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } while (--numPts >= 0) { double x = srcPts[srcOff++] - M02; dstPts[dstOff++] = (srcPts[srcOff++] - M12) / M10; dstPts[dstOff++] = x / M01; } return; case (APPLY_SHEAR): M01 = m01; M10 = m10; if (M01 == 0.0 || M10 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = srcPts[srcOff++] / M10; dstPts[dstOff++] = x / M01; } return; case (APPLY_SCALE | APPLY_TRANSLATE): M00 = m00; M02 = m02; M11 = m11; M12 = m12; if (M00 == 0.0 || M11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } while (--numPts >= 0) { dstPts[dstOff++] = (srcPts[srcOff++] - M02) / M00; dstPts[dstOff++] = (srcPts[srcOff++] - M12) / M11; } return; case (APPLY_SCALE): M00 = m00; M11 = m11; if (M00 == 0.0 || M11 == 0.0) { throw new NoninvertibleTransformException("Determinant is 0"); } while (--numPts >= 0) { dstPts[dstOff++] = srcPts[srcOff++] / M00; dstPts[dstOff++] = srcPts[srcOff++] / M11; } return; case (APPLY_TRANSLATE): M02 = m02; M12 = m12; while (--numPts >= 0) { dstPts[dstOff++] = srcPts[srcOff++] - M02; dstPts[dstOff++] = srcPts[srcOff++] - M12; } return; case (APPLY_IDENTITY): if (srcPts != dstPts || srcOff != dstOff) { System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); } return; } /* NOTREACHED */ } /** * Transforms the relative distance vector specified by * {@code ptSrc} and stores the result in {@code ptDst}. * A relative distance vector is transformed without applying the * translation components of the affine transformation matrix * using the following equations: * <pre> * [ x' ] [ m00 m01 (m02) ] [ x ] [ m00x + m01y ] * [ y' ] = [ m10 m11 (m12) ] [ y ] = [ m10x + m11y ] * [ (1) ] [ (0) (0) ( 1 ) ] [ (1) ] [ (1) ] * </pre> * If {@code ptDst} is {@code null}, a new * {@code Point2D} object is allocated and then the result of the * transform is stored in this object. * In either case, {@code ptDst}, which contains the * transformed point, is returned for convenience. * If {@code ptSrc} and {@code ptDst} are the same object, * the input point is correctly overwritten with the transformed * point. * @param ptSrc the distance vector to be delta transformed * @param ptDst the resulting transformed distance vector * @return {@code ptDst}, which contains the result of the * transformation. * @since 1.2 */ public Point2D deltaTransform(Point2D ptSrc, Point2D ptDst) { if (ptDst == null) { if (ptSrc instanceof Point2D.Double) { ptDst = new Point2D.Double(); } else { ptDst = new Point2D.Float(); } } // Copy source coords into local variables in case src == dst double x = ptSrc.getX(); double y = ptSrc.getY(); switch (state) { default: stateError(); /* NOTREACHED */ return null; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SHEAR | APPLY_SCALE): ptDst.setLocation(x * m00 + y * m01, x * m10 + y * m11); return ptDst; case (APPLY_SHEAR | APPLY_TRANSLATE): case (APPLY_SHEAR): ptDst.setLocation(y * m01, x * m10); return ptDst; case (APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SCALE): ptDst.setLocation(x * m00, y * m11); return ptDst; case (APPLY_TRANSLATE): case (APPLY_IDENTITY): ptDst.setLocation(x, y); return ptDst; } /* NOTREACHED */ } /** * 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: * <pre> * [ x' ] [ m00 m01 (m02) ] [ x ] [ m00x + m01y ] * [ y' ] = [ m10 m11 (m12) ] [ y ] = [ m10x + m11y ] * [ (1) ] [ (0) (0) ( 1 ) ] [ (1) ] [ (1) ] * </pre> * 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 {@code [x0, y0, x1, y1, ..., xn, yn]}. * @param srcPts the array containing the source distance vectors. * Each vector is stored as a pair of relative x, y coordinates. * @param dstPts the array into which the transformed distance vectors * are returned. Each vector is stored as a pair of relative * x, y coordinates. * @param srcOff the offset to the first vector to be transformed * in the source array * @param dstOff the offset to the location of the first * transformed vector that is stored in the destination array * @param numPts the number of vector coordinate pairs to be * transformed * @since 1.2 */ public void deltaTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) { double M00, M01, M10, M11; // For caching if (dstPts == srcPts && dstOff > srcOff && dstOff < srcOff + numPts * 2) { // If the arrays overlap partially with the destination higher // than the source and we transform the coordinates normally // we would overwrite some of the later source coordinates // with results of previous transformations. // To get around this we use arraycopy to copy the points // to their final destination with correct overwrite // handling and then transform them in place in the new // safer location. System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); // srcPts = dstPts; // They are known to be equal. srcOff = dstOff; } switch (state) { default: stateError(); /* NOTREACHED */ return; case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SHEAR | APPLY_SCALE): M00 = m00; M01 = m01; M10 = m10; M11 = m11; while (--numPts >= 0) { double x = srcPts[srcOff++]; double y = srcPts[srcOff++]; dstPts[dstOff++] = x * M00 + y * M01; dstPts[dstOff++] = x * M10 + y * M11; } return; case (APPLY_SHEAR | APPLY_TRANSLATE): case (APPLY_SHEAR): M01 = m01; M10 = m10; while (--numPts >= 0) { double x = srcPts[srcOff++]; dstPts[dstOff++] = srcPts[srcOff++] * M01; dstPts[dstOff++] = x * M10; } return; case (APPLY_SCALE | APPLY_TRANSLATE): case (APPLY_SCALE): M00 = m00; M11 = m11; while (--numPts >= 0) { dstPts[dstOff++] = srcPts[srcOff++] * M00; dstPts[dstOff++] = srcPts[srcOff++] * M11; } return; case (APPLY_TRANSLATE): case (APPLY_IDENTITY): if (srcPts != dstPts || srcOff != dstOff) { System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2); } return; } /* NOTREACHED */ } /** * Returns a new {@link Shape} object defined by the geometry of the * specified {@code Shape} after it has been transformed by * this transform. * @param pSrc the specified {@code Shape} object to be * transformed by this transform. * @return a new {@code Shape} object that defines the geometry * of the transformed {@code Shape}, or null if {@code pSrc} is null. * @since 1.2 */ public Shape createTransformedShape(Shape pSrc) { if (pSrc == null) { return null; } return new Path2D.Double(pSrc, this); } // Round values to sane precision for printing // Note that Math.sin(Math.PI) has an error of about 10^-16 private static double _matround(double matval) { return Math.rint(matval * 1E15) / 1E15; } /** * Returns a {@code String} that represents the value of this * {@link Object}. * @return a {@code String} representing the value of this * {@code Object}. * @since 1.2 */ public String toString() { return ("AffineTransform[[" + _matround(m00) + ", " + _matround(m01) + ", " + _matround(m02) + "], [" + _matround(m10) + ", " + _matround(m11) + ", " + _matround(m12) + "]]"); } /** * Returns {@code true} if this {@code AffineTransform} is * an identity transform. * @return {@code true} if this {@code AffineTransform} is * an identity transform; {@code false} otherwise. * @since 1.2 */ public boolean isIdentity() { return (state == APPLY_IDENTITY || (getType() == TYPE_IDENTITY)); } /** * Returns a copy of this {@code AffineTransform} object. * @return an {@code Object} that is a copy of this * {@code AffineTransform} object. * @since 1.2 */ public Object clone() { try { return super.clone(); } catch (CloneNotSupportedException e) { // this shouldn't happen, since we are Cloneable throw new InternalError(e); } } /** * Returns the hashcode for this transform. * @return a hash code for this transform. * @since 1.2 */ public int hashCode() { long bits = Double.doubleToLongBits(m00); bits = bits * 31 + Double.doubleToLongBits(m01); bits = bits * 31 + Double.doubleToLongBits(m02); bits = bits * 31 + Double.doubleToLongBits(m10); bits = bits * 31 + Double.doubleToLongBits(m11); bits = bits * 31 + Double.doubleToLongBits(m12); return (((int) bits) ^ ((int) (bits >> 32))); } /** * Returns {@code true} if this {@code AffineTransform} * represents the same affine coordinate transform as the specified * argument. * @param obj the {@code Object} to test for equality with this * {@code AffineTransform} * @return {@code true} if {@code obj} equals this * {@code AffineTransform} object; {@code false} otherwise. * @since 1.2 */ public boolean equals(Object obj) { if (!(obj instanceof AffineTransform)) { return false; } AffineTransform a = (AffineTransform) obj; return ((m00 == a.m00) && (m01 == a.m01) && (m02 == a.m02) && (m10 == a.m10) && (m11 == a.m11) && (m12 == a.m12)); } /* Serialization support. A readObject method is neccessary because * the state field is part of the implementation of this particular * AffineTransform and not part of the public specification. The * state variable's value needs to be recalculated on the fly by the * readObject method as it is in the 6-argument matrix constructor. */ /* * JDK 1.2 serialVersionUID */ private static final long serialVersionUID = 1330973210523860834L; private void writeObject(java.io.ObjectOutputStream s) throws java.io.IOException { s.defaultWriteObject(); } private void readObject(java.io.ObjectInputStream s) throws java.lang.ClassNotFoundException, java.io.IOException { s.defaultReadObject(); updateState(); } }