Java tutorial
/* * Copyright (c) 1997, 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.awt.Rectangle; import java.util.Arrays; import java.io.Serializable; import sun.awt.geom.Curve; import static java.lang.Math.abs; import static java.lang.Math.max; import static java.lang.Math.ulp; /** * The {@code CubicCurve2D} class defines a cubic parametric curve * segment in {@code (x,y)} coordinate space. * <p> * This class is only the abstract superclass for all objects which * store a 2D cubic curve segment. * The actual storage representation of the coordinates is left to * the subclass. * * @author Jim Graham * @since 1.2 */ public abstract class CubicCurve2D implements Shape, Cloneable { /** * A cubic parametric curve segment specified with * {@code float} coordinates. * @since 1.2 */ public static class Float extends CubicCurve2D implements Serializable { /** * The X coordinate of the start point * of the cubic curve segment. * @since 1.2 * @serial */ public float x1; /** * The Y coordinate of the start point * of the cubic curve segment. * @since 1.2 * @serial */ public float y1; /** * The X coordinate of the first control point * of the cubic curve segment. * @since 1.2 * @serial */ public float ctrlx1; /** * The Y coordinate of the first control point * of the cubic curve segment. * @since 1.2 * @serial */ public float ctrly1; /** * The X coordinate of the second control point * of the cubic curve segment. * @since 1.2 * @serial */ public float ctrlx2; /** * The Y coordinate of the second control point * of the cubic curve segment. * @since 1.2 * @serial */ public float ctrly2; /** * The X coordinate of the end point * of the cubic curve segment. * @since 1.2 * @serial */ public float x2; /** * The Y coordinate of the end point * of the cubic curve segment. * @since 1.2 * @serial */ public float y2; /** * Constructs and initializes a CubicCurve with coordinates * (0, 0, 0, 0, 0, 0, 0, 0). * @since 1.2 */ public Float() { } /** * Constructs and initializes a {@code CubicCurve2D} from * the specified {@code float} coordinates. * * @param x1 the X coordinate for the start point * of the resulting {@code CubicCurve2D} * @param y1 the Y coordinate for the start point * of the resulting {@code CubicCurve2D} * @param ctrlx1 the X coordinate for the first control point * of the resulting {@code CubicCurve2D} * @param ctrly1 the Y coordinate for the first control point * of the resulting {@code CubicCurve2D} * @param ctrlx2 the X coordinate for the second control point * of the resulting {@code CubicCurve2D} * @param ctrly2 the Y coordinate for the second control point * of the resulting {@code CubicCurve2D} * @param x2 the X coordinate for the end point * of the resulting {@code CubicCurve2D} * @param y2 the Y coordinate for the end point * of the resulting {@code CubicCurve2D} * @since 1.2 */ public Float(float x1, float y1, float ctrlx1, float ctrly1, float ctrlx2, float ctrly2, float x2, float y2) { setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public double getX1() { return (double) x1; } /** * {@inheritDoc} * @since 1.2 */ public double getY1() { return (double) y1; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP1() { return new Point2D.Float(x1, y1); } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlX1() { return (double) ctrlx1; } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlY1() { return (double) ctrly1; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getCtrlP1() { return new Point2D.Float(ctrlx1, ctrly1); } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlX2() { return (double) ctrlx2; } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlY2() { return (double) ctrly2; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getCtrlP2() { return new Point2D.Float(ctrlx2, ctrly2); } /** * {@inheritDoc} * @since 1.2 */ public double getX2() { return (double) x2; } /** * {@inheritDoc} * @since 1.2 */ public double getY2() { return (double) y2; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP2() { return new Point2D.Float(x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public void setCurve(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) { this.x1 = (float) x1; this.y1 = (float) y1; this.ctrlx1 = (float) ctrlx1; this.ctrly1 = (float) ctrly1; this.ctrlx2 = (float) ctrlx2; this.ctrly2 = (float) ctrly2; this.x2 = (float) x2; this.y2 = (float) y2; } /** * Sets the location of the end points and control points * of this curve to the specified {@code float} coordinates. * * @param x1 the X coordinate used to set the start point * of this {@code CubicCurve2D} * @param y1 the Y coordinate used to set the start point * of this {@code CubicCurve2D} * @param ctrlx1 the X coordinate used to set the first control point * of this {@code CubicCurve2D} * @param ctrly1 the Y coordinate used to set the first control point * of this {@code CubicCurve2D} * @param ctrlx2 the X coordinate used to set the second control point * of this {@code CubicCurve2D} * @param ctrly2 the Y coordinate used to set the second control point * of this {@code CubicCurve2D} * @param x2 the X coordinate used to set the end point * of this {@code CubicCurve2D} * @param y2 the Y coordinate used to set the end point * of this {@code CubicCurve2D} * @since 1.2 */ public void setCurve(float x1, float y1, float ctrlx1, float ctrly1, float ctrlx2, float ctrly2, float x2, float y2) { this.x1 = x1; this.y1 = y1; this.ctrlx1 = ctrlx1; this.ctrly1 = ctrly1; this.ctrlx2 = ctrlx2; this.ctrly2 = ctrly2; this.x2 = x2; this.y2 = y2; } /** * {@inheritDoc} * @since 1.2 */ public Rectangle2D getBounds2D() { float left = Math.min(Math.min(x1, x2), Math.min(ctrlx1, ctrlx2)); float top = Math.min(Math.min(y1, y2), Math.min(ctrly1, ctrly2)); float right = Math.max(Math.max(x1, x2), Math.max(ctrlx1, ctrlx2)); float bottom = Math.max(Math.max(y1, y2), Math.max(ctrly1, ctrly2)); return new Rectangle2D.Float(left, top, right - left, bottom - top); } /* * JDK 1.6 serialVersionUID */ private static final long serialVersionUID = -1272015596714244385L; } /** * A cubic parametric curve segment specified with * {@code double} coordinates. * @since 1.2 */ public static class Double extends CubicCurve2D implements Serializable { /** * The X coordinate of the start point * of the cubic curve segment. * @since 1.2 * @serial */ public double x1; /** * The Y coordinate of the start point * of the cubic curve segment. * @since 1.2 * @serial */ public double y1; /** * The X coordinate of the first control point * of the cubic curve segment. * @since 1.2 * @serial */ public double ctrlx1; /** * The Y coordinate of the first control point * of the cubic curve segment. * @since 1.2 * @serial */ public double ctrly1; /** * The X coordinate of the second control point * of the cubic curve segment. * @since 1.2 * @serial */ public double ctrlx2; /** * The Y coordinate of the second control point * of the cubic curve segment. * @since 1.2 * @serial */ public double ctrly2; /** * The X coordinate of the end point * of the cubic curve segment. * @since 1.2 * @serial */ public double x2; /** * The Y coordinate of the end point * of the cubic curve segment. * @since 1.2 * @serial */ public double y2; /** * Constructs and initializes a CubicCurve with coordinates * (0, 0, 0, 0, 0, 0, 0, 0). * @since 1.2 */ public Double() { } /** * Constructs and initializes a {@code CubicCurve2D} from * the specified {@code double} coordinates. * * @param x1 the X coordinate for the start point * of the resulting {@code CubicCurve2D} * @param y1 the Y coordinate for the start point * of the resulting {@code CubicCurve2D} * @param ctrlx1 the X coordinate for the first control point * of the resulting {@code CubicCurve2D} * @param ctrly1 the Y coordinate for the first control point * of the resulting {@code CubicCurve2D} * @param ctrlx2 the X coordinate for the second control point * of the resulting {@code CubicCurve2D} * @param ctrly2 the Y coordinate for the second control point * of the resulting {@code CubicCurve2D} * @param x2 the X coordinate for the end point * of the resulting {@code CubicCurve2D} * @param y2 the Y coordinate for the end point * of the resulting {@code CubicCurve2D} * @since 1.2 */ public Double(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) { setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public double getX1() { return x1; } /** * {@inheritDoc} * @since 1.2 */ public double getY1() { return y1; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP1() { return new Point2D.Double(x1, y1); } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlX1() { return ctrlx1; } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlY1() { return ctrly1; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getCtrlP1() { return new Point2D.Double(ctrlx1, ctrly1); } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlX2() { return ctrlx2; } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlY2() { return ctrly2; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getCtrlP2() { return new Point2D.Double(ctrlx2, ctrly2); } /** * {@inheritDoc} * @since 1.2 */ public double getX2() { return x2; } /** * {@inheritDoc} * @since 1.2 */ public double getY2() { return y2; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP2() { return new Point2D.Double(x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public void setCurve(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) { this.x1 = x1; this.y1 = y1; this.ctrlx1 = ctrlx1; this.ctrly1 = ctrly1; this.ctrlx2 = ctrlx2; this.ctrly2 = ctrly2; this.x2 = x2; this.y2 = y2; } /** * {@inheritDoc} * @since 1.2 */ public Rectangle2D getBounds2D() { double left = Math.min(Math.min(x1, x2), Math.min(ctrlx1, ctrlx2)); double top = Math.min(Math.min(y1, y2), Math.min(ctrly1, ctrly2)); double right = Math.max(Math.max(x1, x2), Math.max(ctrlx1, ctrlx2)); double bottom = Math.max(Math.max(y1, y2), Math.max(ctrly1, ctrly2)); return new Rectangle2D.Double(left, top, right - left, bottom - top); } /* * JDK 1.6 serialVersionUID */ private static final long serialVersionUID = -4202960122839707295L; } /** * This is an abstract class that cannot be instantiated directly. * Type-specific implementation subclasses are available for * instantiation and provide a number of formats for storing * the information necessary to satisfy the various accessor * methods below. * * @see java.awt.geom.CubicCurve2D.Float * @see java.awt.geom.CubicCurve2D.Double * @since 1.2 */ protected CubicCurve2D() { } /** * Returns the X coordinate of the start point in double precision. * @return the X coordinate of the start point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getX1(); /** * Returns the Y coordinate of the start point in double precision. * @return the Y coordinate of the start point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getY1(); /** * Returns the start point. * @return a {@code Point2D} that is the start point of * the {@code CubicCurve2D}. * @since 1.2 */ public abstract Point2D getP1(); /** * Returns the X coordinate of the first control point in double precision. * @return the X coordinate of the first control point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getCtrlX1(); /** * Returns the Y coordinate of the first control point in double precision. * @return the Y coordinate of the first control point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getCtrlY1(); /** * Returns the first control point. * @return a {@code Point2D} that is the first control point of * the {@code CubicCurve2D}. * @since 1.2 */ public abstract Point2D getCtrlP1(); /** * Returns the X coordinate of the second control point * in double precision. * @return the X coordinate of the second control point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getCtrlX2(); /** * Returns the Y coordinate of the second control point * in double precision. * @return the Y coordinate of the second control point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getCtrlY2(); /** * Returns the second control point. * @return a {@code Point2D} that is the second control point of * the {@code CubicCurve2D}. * @since 1.2 */ public abstract Point2D getCtrlP2(); /** * Returns the X coordinate of the end point in double precision. * @return the X coordinate of the end point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getX2(); /** * Returns the Y coordinate of the end point in double precision. * @return the Y coordinate of the end point of the * {@code CubicCurve2D}. * @since 1.2 */ public abstract double getY2(); /** * Returns the end point. * @return a {@code Point2D} that is the end point of * the {@code CubicCurve2D}. * @since 1.2 */ public abstract Point2D getP2(); /** * Sets the location of the end points and control points of this curve * to the specified double coordinates. * * @param x1 the X coordinate used to set the start point * of this {@code CubicCurve2D} * @param y1 the Y coordinate used to set the start point * of this {@code CubicCurve2D} * @param ctrlx1 the X coordinate used to set the first control point * of this {@code CubicCurve2D} * @param ctrly1 the Y coordinate used to set the first control point * of this {@code CubicCurve2D} * @param ctrlx2 the X coordinate used to set the second control point * of this {@code CubicCurve2D} * @param ctrly2 the Y coordinate used to set the second control point * of this {@code CubicCurve2D} * @param x2 the X coordinate used to set the end point * of this {@code CubicCurve2D} * @param y2 the Y coordinate used to set the end point * of this {@code CubicCurve2D} * @since 1.2 */ public abstract void setCurve(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2); /** * Sets the location of the end points and control points of this curve * to the double coordinates at the specified offset in the specified * array. * @param coords a double array containing coordinates * @param offset the index of {@code coords} from which to begin * setting the end points and control points of this curve * to the coordinates contained in {@code coords} * @since 1.2 */ public void setCurve(double[] coords, int offset) { setCurve(coords[offset + 0], coords[offset + 1], coords[offset + 2], coords[offset + 3], coords[offset + 4], coords[offset + 5], coords[offset + 6], coords[offset + 7]); } /** * Sets the location of the end points and control points of this curve * to the specified {@code Point2D} coordinates. * @param p1 the first specified {@code Point2D} used to set the * start point of this curve * @param cp1 the second specified {@code Point2D} used to set the * first control point of this curve * @param cp2 the third specified {@code Point2D} used to set the * second control point of this curve * @param p2 the fourth specified {@code Point2D} used to set the * end point of this curve * @since 1.2 */ public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) { setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(), cp2.getX(), cp2.getY(), p2.getX(), p2.getY()); } /** * Sets the location of the end points and control points of this curve * to the coordinates of the {@code Point2D} objects at the specified * offset in the specified array. * @param pts an array of {@code Point2D} objects * @param offset the index of {@code pts} from which to begin setting * the end points and control points of this curve to the * points contained in {@code pts} * @since 1.2 */ public void setCurve(Point2D[] pts, int offset) { setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(), pts[offset + 1].getX(), pts[offset + 1].getY(), pts[offset + 2].getX(), pts[offset + 2].getY(), pts[offset + 3].getX(), pts[offset + 3].getY()); } /** * Sets the location of the end points and control points of this curve * to the same as those in the specified {@code CubicCurve2D}. * @param c the specified {@code CubicCurve2D} * @since 1.2 */ public void setCurve(CubicCurve2D c) { setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(), c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2()); } /** * Returns the square of the flatness of the cubic curve specified * by the indicated control points. The flatness is the maximum distance * of a control point from the line connecting the end points. * * @param x1 the X coordinate that specifies the start point * of a {@code CubicCurve2D} * @param y1 the Y coordinate that specifies the start point * of a {@code CubicCurve2D} * @param ctrlx1 the X coordinate that specifies the first control point * of a {@code CubicCurve2D} * @param ctrly1 the Y coordinate that specifies the first control point * of a {@code CubicCurve2D} * @param ctrlx2 the X coordinate that specifies the second control point * of a {@code CubicCurve2D} * @param ctrly2 the Y coordinate that specifies the second control point * of a {@code CubicCurve2D} * @param x2 the X coordinate that specifies the end point * of a {@code CubicCurve2D} * @param y2 the Y coordinate that specifies the end point * of a {@code CubicCurve2D} * @return the square of the flatness of the {@code CubicCurve2D} * represented by the specified coordinates. * @since 1.2 */ public static double getFlatnessSq(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) { return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1), Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2)); } /** * Returns the flatness of the cubic curve specified * by the indicated control points. The flatness is the maximum distance * of a control point from the line connecting the end points. * * @param x1 the X coordinate that specifies the start point * of a {@code CubicCurve2D} * @param y1 the Y coordinate that specifies the start point * of a {@code CubicCurve2D} * @param ctrlx1 the X coordinate that specifies the first control point * of a {@code CubicCurve2D} * @param ctrly1 the Y coordinate that specifies the first control point * of a {@code CubicCurve2D} * @param ctrlx2 the X coordinate that specifies the second control point * of a {@code CubicCurve2D} * @param ctrly2 the Y coordinate that specifies the second control point * of a {@code CubicCurve2D} * @param x2 the X coordinate that specifies the end point * of a {@code CubicCurve2D} * @param y2 the Y coordinate that specifies the end point * of a {@code CubicCurve2D} * @return the flatness of the {@code CubicCurve2D} * represented by the specified coordinates. * @since 1.2 */ public static double getFlatness(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) { return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2)); } /** * Returns the square of the flatness of the cubic curve specified * by the control points stored in the indicated array at the * indicated index. The flatness is the maximum distance * of a control point from the line connecting the end points. * @param coords an array containing coordinates * @param offset the index of {@code coords} from which to begin * getting the end points and control points of the curve * @return the square of the flatness of the {@code CubicCurve2D} * specified by the coordinates in {@code coords} at * the specified offset. * @since 1.2 */ public static double getFlatnessSq(double[] coords, int offset) { return getFlatnessSq(coords[offset + 0], coords[offset + 1], coords[offset + 2], coords[offset + 3], coords[offset + 4], coords[offset + 5], coords[offset + 6], coords[offset + 7]); } /** * Returns the flatness of the cubic curve specified * by the control points stored in the indicated array at the * indicated index. The flatness is the maximum distance * of a control point from the line connecting the end points. * @param coords an array containing coordinates * @param offset the index of {@code coords} from which to begin * getting the end points and control points of the curve * @return the flatness of the {@code CubicCurve2D} * specified by the coordinates in {@code coords} at * the specified offset. * @since 1.2 */ public static double getFlatness(double[] coords, int offset) { return getFlatness(coords[offset + 0], coords[offset + 1], coords[offset + 2], coords[offset + 3], coords[offset + 4], coords[offset + 5], coords[offset + 6], coords[offset + 7]); } /** * Returns the square of the flatness of this curve. The flatness is the * maximum distance of a control point from the line connecting the * end points. * @return the square of the flatness of this curve. * @since 1.2 */ public double getFlatnessSq() { return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(), getCtrlX2(), getCtrlY2(), getX2(), getY2()); } /** * Returns the flatness of this curve. The flatness is the * maximum distance of a control point from the line connecting the * end points. * @return the flatness of this curve. * @since 1.2 */ public double getFlatness() { return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(), getCtrlX2(), getCtrlY2(), getX2(), getY2()); } /** * Subdivides this cubic curve and stores the resulting two * subdivided curves into the left and right curve parameters. * Either or both of the left and right objects may be the same * as this object or null. * @param left the cubic curve object for storing for the left or * first half of the subdivided curve * @param right the cubic curve object for storing for the right or * second half of the subdivided curve * @since 1.2 */ public void subdivide(CubicCurve2D left, CubicCurve2D right) { subdivide(this, left, right); } /** * Subdivides the cubic curve specified by the {@code src} parameter * and stores the resulting two subdivided curves into the * {@code left} and {@code right} curve parameters. * Either or both of the {@code left} and {@code right} objects * may be the same as the {@code src} object or {@code null}. * @param src the cubic curve to be subdivided * @param left the cubic curve object for storing the left or * first half of the subdivided curve * @param right the cubic curve object for storing the right or * second half of the subdivided curve * @since 1.2 */ public static void subdivide(CubicCurve2D src, CubicCurve2D left, CubicCurve2D right) { double x1 = src.getX1(); double y1 = src.getY1(); double ctrlx1 = src.getCtrlX1(); double ctrly1 = src.getCtrlY1(); double ctrlx2 = src.getCtrlX2(); double ctrly2 = src.getCtrlY2(); double x2 = src.getX2(); double y2 = src.getY2(); double centerx = (ctrlx1 + ctrlx2) / 2.0; double centery = (ctrly1 + ctrly2) / 2.0; ctrlx1 = (x1 + ctrlx1) / 2.0; ctrly1 = (y1 + ctrly1) / 2.0; ctrlx2 = (x2 + ctrlx2) / 2.0; ctrly2 = (y2 + ctrly2) / 2.0; double ctrlx12 = (ctrlx1 + centerx) / 2.0; double ctrly12 = (ctrly1 + centery) / 2.0; double ctrlx21 = (ctrlx2 + centerx) / 2.0; double ctrly21 = (ctrly2 + centery) / 2.0; centerx = (ctrlx12 + ctrlx21) / 2.0; centery = (ctrly12 + ctrly21) / 2.0; if (left != null) { left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx12, ctrly12, centerx, centery); } if (right != null) { right.setCurve(centerx, centery, ctrlx21, ctrly21, ctrlx2, ctrly2, x2, y2); } } /** * Subdivides the cubic curve specified by the coordinates * stored in the {@code src} array at indices {@code srcoff} * through ({@code srcoff} + 7) and stores the * resulting two subdivided curves into the two result arrays at the * corresponding indices. * Either or both of the {@code left} and {@code right} * arrays may be {@code null} or a reference to the same array * as the {@code src} array. * Note that the last point in the first subdivided curve is the * same as the first point in the second subdivided curve. Thus, * it is possible to pass the same array for {@code left} * and {@code right} and to use offsets, such as {@code rightoff} * equals ({@code leftoff} + 6), in order * to avoid allocating extra storage for this common point. * @param src the array holding the coordinates for the source curve * @param srcoff the offset into the array of the beginning of the * the 6 source coordinates * @param left the array for storing the coordinates for the first * half of the subdivided curve * @param leftoff the offset into the array of the beginning of the * the 6 left coordinates * @param right the array for storing the coordinates for the second * half of the subdivided curve * @param rightoff the offset into the array of the beginning of the * the 6 right coordinates * @since 1.2 */ public static void subdivide(double[] src, int srcoff, double[] left, int leftoff, double[] right, int rightoff) { double x1 = src[srcoff + 0]; double y1 = src[srcoff + 1]; double ctrlx1 = src[srcoff + 2]; double ctrly1 = src[srcoff + 3]; double ctrlx2 = src[srcoff + 4]; double ctrly2 = src[srcoff + 5]; double x2 = src[srcoff + 6]; double y2 = src[srcoff + 7]; if (left != null) { left[leftoff + 0] = x1; left[leftoff + 1] = y1; } if (right != null) { right[rightoff + 6] = x2; right[rightoff + 7] = y2; } x1 = (x1 + ctrlx1) / 2.0; y1 = (y1 + ctrly1) / 2.0; x2 = (x2 + ctrlx2) / 2.0; y2 = (y2 + ctrly2) / 2.0; double centerx = (ctrlx1 + ctrlx2) / 2.0; double centery = (ctrly1 + ctrly2) / 2.0; ctrlx1 = (x1 + centerx) / 2.0; ctrly1 = (y1 + centery) / 2.0; ctrlx2 = (x2 + centerx) / 2.0; ctrly2 = (y2 + centery) / 2.0; centerx = (ctrlx1 + ctrlx2) / 2.0; centery = (ctrly1 + ctrly2) / 2.0; if (left != null) { left[leftoff + 2] = x1; left[leftoff + 3] = y1; left[leftoff + 4] = ctrlx1; left[leftoff + 5] = ctrly1; left[leftoff + 6] = centerx; left[leftoff + 7] = centery; } if (right != null) { right[rightoff + 0] = centerx; right[rightoff + 1] = centery; right[rightoff + 2] = ctrlx2; right[rightoff + 3] = ctrly2; right[rightoff + 4] = x2; right[rightoff + 5] = y2; } } /** * Solves the cubic whose coefficients are in the {@code eqn} * array and places the non-complex roots back into the same array, * returning the number of roots. The solved cubic is represented * by the equation: * <pre> * eqn = {c, b, a, d} * dx^3 + ax^2 + bx + c = 0 * </pre> * A return value of -1 is used to distinguish a constant equation * that might be always 0 or never 0 from an equation that has no * zeroes. * @param eqn an array containing coefficients for a cubic * @return the number of roots, or -1 if the equation is a constant. * @since 1.2 */ public static int solveCubic(double[] eqn) { return solveCubic(eqn, eqn); } /** * Solve the cubic whose coefficients are in the {@code eqn} * array and place the non-complex roots into the {@code res} * array, returning the number of roots. * The cubic solved is represented by the equation: * eqn = {c, b, a, d} * dx^3 + ax^2 + bx + c = 0 * A return value of -1 is used to distinguish a constant equation, * which may be always 0 or never 0, from an equation which has no * zeroes. * @param eqn the specified array of coefficients to use to solve * the cubic equation * @param res the array that contains the non-complex roots * resulting from the solution of the cubic equation * @return the number of roots, or -1 if the equation is a constant * @since 1.3 */ public static int solveCubic(double[] eqn, double[] res) { // From Graphics Gems: // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c final double d = eqn[3]; if (d == 0) { return QuadCurve2D.solveQuadratic(eqn, res); } /* normal form: x^3 + Ax^2 + Bx + C = 0 */ final double A = eqn[2] / d; final double B = eqn[1] / d; final double C = eqn[0] / d; // substitute x = y - A/3 to eliminate quadratic term: // x^3 +Px + Q = 0 // // Since we actually need P/3 and Q/2 for all of the // calculations that follow, we will calculate // p = P/3 // q = Q/2 // instead and use those values for simplicity of the code. double sq_A = A * A; double p = 1.0 / 3 * (-1.0 / 3 * sq_A + B); double q = 1.0 / 2 * (2.0 / 27 * A * sq_A - 1.0 / 3 * A * B + C); /* use Cardano's formula */ double cb_p = p * p * p; double D = q * q + cb_p; final double sub = 1.0 / 3 * A; int num; if (D < 0) { /* Casus irreducibilis: three real solutions */ // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method double phi = 1.0 / 3 * Math.acos(-q / Math.sqrt(-cb_p)); double t = 2 * Math.sqrt(-p); if (res == eqn) { eqn = Arrays.copyOf(eqn, 4); } res[0] = (t * Math.cos(phi)); res[1] = (-t * Math.cos(phi + Math.PI / 3)); res[2] = (-t * Math.cos(phi - Math.PI / 3)); num = 3; for (int i = 0; i < num; ++i) { res[i] -= sub; } } else { // Please see the comment in fixRoots marked 'XXX' before changing // any of the code in this case. double sqrt_D = Math.sqrt(D); double u = Math.cbrt(sqrt_D - q); double v = -Math.cbrt(sqrt_D + q); double uv = u + v; num = 1; double err = 1200000000 * ulp(abs(uv) + abs(sub)); if (iszero(D, err) || within(u, v, err)) { if (res == eqn) { eqn = Arrays.copyOf(eqn, 4); } res[1] = -(uv / 2) - sub; num = 2; } // this must be done after the potential Arrays.copyOf res[0] = uv - sub; } if (num > 1) { // num == 3 || num == 2 num = fixRoots(eqn, res, num); } if (num > 2 && (res[2] == res[1] || res[2] == res[0])) { num--; } if (num > 1 && res[1] == res[0]) { res[1] = res[--num]; // Copies res[2] to res[1] if needed } return num; } // preconditions: eqn != res && eqn[3] != 0 && num > 1 // This method tries to improve the accuracy of the roots of eqn (which // should be in res). It also might eliminate roots in res if it decideds // that they're not real roots. It will not check for roots that the // computation of res might have missed, so this method should only be // used when the roots in res have been computed using an algorithm // that never underestimates the number of roots (such as solveCubic above) private static int fixRoots(double[] eqn, double[] res, int num) { double[] intervals = { eqn[1], 2 * eqn[2], 3 * eqn[3] }; int critCount = QuadCurve2D.solveQuadratic(intervals, intervals); if (critCount == 2 && intervals[0] == intervals[1]) { critCount--; } if (critCount == 2 && intervals[0] > intervals[1]) { double tmp = intervals[0]; intervals[0] = intervals[1]; intervals[1] = tmp; } // below we use critCount to possibly filter out roots that shouldn't // have been computed. We require that eqn[3] != 0, so eqn is a proper // cubic, which means that its limits at -/+inf are -/+inf or +/-inf. // Therefore, if critCount==2, the curve is shaped like a sideways S, // and it could have 1-3 roots. If critCount==0 it is monotonic, and // if critCount==1 it is monotonic with a single point where it is // flat. In the last 2 cases there can only be 1 root. So in cases // where num > 1 but critCount < 2, we eliminate all roots in res // except one. if (num == 3) { double xe = getRootUpperBound(eqn); double x0 = -xe; Arrays.sort(res, 0, num); if (critCount == 2) { // this just tries to improve the accuracy of the computed // roots using Newton's method. res[0] = refineRootWithHint(eqn, x0, intervals[0], res[0]); res[1] = refineRootWithHint(eqn, intervals[0], intervals[1], res[1]); res[2] = refineRootWithHint(eqn, intervals[1], xe, res[2]); return 3; } else if (critCount == 1) { // we only need fx0 and fxe for the sign of the polynomial // at -inf and +inf respectively, so we don't need to do // fx0 = solveEqn(eqn, 3, x0); fxe = solveEqn(eqn, 3, xe) double fxe = eqn[3]; double fx0 = -fxe; double x1 = intervals[0]; double fx1 = solveEqn(eqn, 3, x1); // if critCount == 1 or critCount == 0, but num == 3 then // something has gone wrong. This branch and the one below // would ideally never execute, but if they do we can't know // which of the computed roots is closest to the real root; // therefore, we can't use refineRootWithHint. But even if // we did know, being here most likely means that the // curve is very flat close to two of the computed roots // (or maybe even all three). This might make Newton's method // fail altogether, which would be a pain to detect and fix. // This is why we use a very stable bisection method. if (oppositeSigns(fx0, fx1)) { res[0] = bisectRootWithHint(eqn, x0, x1, res[0]); } else if (oppositeSigns(fx1, fxe)) { res[0] = bisectRootWithHint(eqn, x1, xe, res[2]); } else /* fx1 must be 0 */ { res[0] = x1; } // return 1 } else if (critCount == 0) { res[0] = bisectRootWithHint(eqn, x0, xe, res[1]); // return 1 } } else if (num == 2 && critCount == 2) { // XXX: here we assume that res[0] has better accuracy than res[1]. // This is true because this method is only used from solveCubic // which puts in res[0] the root that it would compute anyway even // if num==1. If this method is ever used from any other method, or // if the solveCubic implementation changes, this assumption should // be reevaluated, and the choice of goodRoot might have to become // goodRoot = (abs(eqn'(res[0])) > abs(eqn'(res[1]))) ? res[0] : res[1] // where eqn' is the derivative of eqn. double goodRoot = res[0]; double badRoot = res[1]; double x1 = intervals[0]; double x2 = intervals[1]; // If a cubic curve really has 2 roots, one of those roots must be // at a critical point. That can't be goodRoot, so we compute x to // be the farthest critical point from goodRoot. If there are two // roots, x must be the second one, so we evaluate eqn at x, and if // it is zero (or close enough) we put x in res[1] (or badRoot, if // |solveEqn(eqn, 3, badRoot)| < |solveEqn(eqn, 3, x)| but this // shouldn't happen often). double x = abs(x1 - goodRoot) > abs(x2 - goodRoot) ? x1 : x2; double fx = solveEqn(eqn, 3, x); if (iszero(fx, 10000000 * ulp(x))) { double badRootVal = solveEqn(eqn, 3, badRoot); res[1] = abs(badRootVal) < abs(fx) ? badRoot : x; return 2; } } // else there can only be one root - goodRoot, and it is already in res[0] return 1; } // use newton's method. private static double refineRootWithHint(double[] eqn, double min, double max, double t) { if (!inInterval(t, min, max)) { return t; } double[] deriv = { eqn[1], 2 * eqn[2], 3 * eqn[3] }; double origt = t; for (int i = 0; i < 3; i++) { double slope = solveEqn(deriv, 2, t); double y = solveEqn(eqn, 3, t); double delta = -(y / slope); double newt = t + delta; if (slope == 0 || y == 0 || t == newt) { break; } t = newt; } if (within(t, origt, 1000 * ulp(origt)) && inInterval(t, min, max)) { return t; } return origt; } private static double bisectRootWithHint(double[] eqn, double x0, double xe, double hint) { double delta1 = Math.min(abs(hint - x0) / 64, 0.0625); double delta2 = Math.min(abs(hint - xe) / 64, 0.0625); double x02 = hint - delta1; double xe2 = hint + delta2; double fx02 = solveEqn(eqn, 3, x02); double fxe2 = solveEqn(eqn, 3, xe2); while (oppositeSigns(fx02, fxe2)) { if (x02 >= xe2) { return x02; } x0 = x02; xe = xe2; delta1 /= 64; delta2 /= 64; x02 = hint - delta1; xe2 = hint + delta2; fx02 = solveEqn(eqn, 3, x02); fxe2 = solveEqn(eqn, 3, xe2); } if (fx02 == 0) { return x02; } if (fxe2 == 0) { return xe2; } return bisectRoot(eqn, x0, xe); } private static double bisectRoot(double[] eqn, double x0, double xe) { double fx0 = solveEqn(eqn, 3, x0); double m = x0 + (xe - x0) / 2; while (m != x0 && m != xe) { double fm = solveEqn(eqn, 3, m); if (fm == 0) { return m; } if (oppositeSigns(fx0, fm)) { xe = m; } else { fx0 = fm; x0 = m; } m = x0 + (xe - x0) / 2; } return m; } private static boolean inInterval(double t, double min, double max) { return min <= t && t <= max; } private static boolean within(double x, double y, double err) { double d = y - x; return (d <= err && d >= -err); } private static boolean iszero(double x, double err) { return within(x, 0, err); } private static boolean oppositeSigns(double x1, double x2) { return (x1 < 0 && x2 > 0) || (x1 > 0 && x2 < 0); } private static double solveEqn(double[] eqn, int order, double t) { double v = eqn[order]; while (--order >= 0) { v = v * t + eqn[order]; } return v; } /* * Computes M+1 where M is an upper bound for all the roots in of eqn. * See: http://en.wikipedia.org/wiki/Sturm%27s_theorem#Applications. * The above link doesn't contain a proof, but I [dlila] proved it myself * so the result is reliable. The proof isn't difficult, but it's a bit * long to include here. * Precondition: eqn must represent a cubic polynomial */ private static double getRootUpperBound(double[] eqn) { double d = eqn[3]; double a = eqn[2]; double b = eqn[1]; double c = eqn[0]; double M = 1 + max(max(abs(a), abs(b)), abs(c)) / abs(d); M += ulp(M) + 1; return M; } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(double x, double y) { if (!(x * 0.0 + y * 0.0 == 0.0)) { /* Either x or y was infinite or NaN. * A NaN always produces a negative response to any test * and Infinity values cannot be "inside" any path so * they should return false as well. */ return false; } // We count the "Y" crossings to determine if the point is // inside the curve bounded by its closing line. double x1 = getX1(); double y1 = getY1(); double x2 = getX2(); double y2 = getY2(); int crossings = (Curve.pointCrossingsForLine(x, y, x1, y1, x2, y2) + Curve.pointCrossingsForCubic(x, y, x1, y1, getCtrlX1(), getCtrlY1(), getCtrlX2(), getCtrlY2(), x2, y2, 0)); return ((crossings & 1) == 1); } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(Point2D p) { return contains(p.getX(), p.getY()); } /** * {@inheritDoc} * @since 1.2 */ public boolean intersects(double x, double y, double w, double h) { // Trivially reject non-existant rectangles if (w <= 0 || h <= 0) { return false; } int numCrossings = rectCrossings(x, y, w, h); // the intended return value is // numCrossings != 0 || numCrossings == Curve.RECT_INTERSECTS // but if (numCrossings != 0) numCrossings == INTERSECTS won't matter // and if !(numCrossings != 0) then numCrossings == 0, so // numCrossings != RECT_INTERSECT return numCrossings != 0; } /** * {@inheritDoc} * @since 1.2 */ public boolean intersects(Rectangle2D r) { return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight()); } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(double x, double y, double w, double h) { if (w <= 0 || h <= 0) { return false; } int numCrossings = rectCrossings(x, y, w, h); return !(numCrossings == 0 || numCrossings == Curve.RECT_INTERSECTS); } private int rectCrossings(double x, double y, double w, double h) { int crossings = 0; if (!(getX1() == getX2() && getY1() == getY2())) { crossings = Curve.rectCrossingsForLine(crossings, x, y, x + w, y + h, getX1(), getY1(), getX2(), getY2()); if (crossings == Curve.RECT_INTERSECTS) { return crossings; } } // we call this with the curve's direction reversed, because we wanted // to call rectCrossingsForLine first, because it's cheaper. return Curve.rectCrossingsForCubic(crossings, x, y, x + w, y + h, getX2(), getY2(), getCtrlX2(), getCtrlY2(), getCtrlX1(), getCtrlY1(), getX1(), getY1(), 0); } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(Rectangle2D r) { return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight()); } /** * {@inheritDoc} * @since 1.2 */ public Rectangle getBounds() { return getBounds2D().getBounds(); } /** * Returns an iteration object that defines the boundary of the * shape. * The iterator for this class is not multi-threaded safe, * which means that this {@code CubicCurve2D} class does not * guarantee that modifications to the geometry of this * {@code CubicCurve2D} object do not affect any iterations of * that geometry that are already in process. * @param at an optional {@code AffineTransform} to be applied to the * coordinates as they are returned in the iteration, or {@code null} * if untransformed coordinates are desired * @return the {@code PathIterator} object that returns the * geometry of the outline of this {@code CubicCurve2D}, one * segment at a time. * @since 1.2 */ public PathIterator getPathIterator(AffineTransform at) { return new CubicIterator(this, at); } /** * Return an iteration object that defines the boundary of the * flattened shape. * The iterator for this class is not multi-threaded safe, * which means that this {@code CubicCurve2D} class does not * guarantee that modifications to the geometry of this * {@code CubicCurve2D} object do not affect any iterations of * that geometry that are already in process. * @param at an optional {@code AffineTransform} to be applied to the * coordinates as they are returned in the iteration, or {@code null} * if untransformed coordinates are desired * @param flatness the maximum amount that the control points * for a given curve can vary from colinear before a subdivided * curve is replaced by a straight line connecting the end points * @return the {@code PathIterator} object that returns the * geometry of the outline of this {@code CubicCurve2D}, * one segment at a time. * @since 1.2 */ public PathIterator getPathIterator(AffineTransform at, double flatness) { return new FlatteningPathIterator(getPathIterator(at), flatness); } /** * Creates a new object of the same class as this object. * * @return a clone of this instance. * @exception OutOfMemoryError if there is not enough memory. * @see java.lang.Cloneable * @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); } } }