| /* | |
| * Copyright (c) 1997, 2021, 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.Rectangle; | |
| import java.awt.Shape; | |
| import java.io.Serial; | |
| import java.io.Serializable; | |
| import java.util.Arrays; | |
| 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; | |
| } | |
| /** | |
| * Use serialVersionUID from JDK 1.6 for interoperability. | |
| */ | |
| @Serial | |
| 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; | |
| } | |
| /** | |
| * Use serialVersionUID from JDK 1.6 for interoperability. | |
| */ | |
| @Serial | |
| 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-existent 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 Rectangle2D getBounds2D() { | |
| return Path2D.getBounds2D(getPathIterator(null)); | |
| } | |
| /** | |
| * {@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. | |
| * @throws 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); | |
| } | |
| } | |
| } |