| /* | |
| * 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; | |
| /** | |
| * The {@code QuadCurve2D} class defines a quadratic parametric curve | |
| * segment in {@code (x,y)} coordinate space. | |
| * <p> | |
| * This class is only the abstract superclass for all objects that | |
| * store a 2D quadratic curve segment. | |
| * The actual storage representation of the coordinates is left to | |
| * the subclass. | |
| * | |
| * @author Jim Graham | |
| * @since 1.2 | |
| */ | |
| public abstract class QuadCurve2D implements Shape, Cloneable { | |
| /** | |
| * A quadratic parametric curve segment specified with | |
| * {@code float} coordinates. | |
| * | |
| * @since 1.2 | |
| */ | |
| public static class Float extends QuadCurve2D implements Serializable { | |
| /** | |
| * The X coordinate of the start point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public float x1; | |
| /** | |
| * The Y coordinate of the start point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public float y1; | |
| /** | |
| * The X coordinate of the control point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public float ctrlx; | |
| /** | |
| * The Y coordinate of the control point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public float ctrly; | |
| /** | |
| * The X coordinate of the end point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public float x2; | |
| /** | |
| * The Y coordinate of the end point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public float y2; | |
| /** | |
| * Constructs and initializes a {@code QuadCurve2D} with | |
| * coordinates (0, 0, 0, 0, 0, 0). | |
| * @since 1.2 | |
| */ | |
| public Float() { | |
| } | |
| /** | |
| * Constructs and initializes a {@code QuadCurve2D} from the | |
| * specified {@code float} coordinates. | |
| * | |
| * @param x1 the X coordinate of the start point | |
| * @param y1 the Y coordinate of the start point | |
| * @param ctrlx the X coordinate of the control point | |
| * @param ctrly the Y coordinate of the control point | |
| * @param x2 the X coordinate of the end point | |
| * @param y2 the Y coordinate of the end point | |
| * @since 1.2 | |
| */ | |
| public Float(float x1, float y1, | |
| float ctrlx, float ctrly, | |
| float x2, float y2) | |
| { | |
| setCurve(x1, y1, ctrlx, ctrly, 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 getCtrlX() { | |
| return (double) ctrlx; | |
| } | |
| /** | |
| * {@inheritDoc} | |
| * @since 1.2 | |
| */ | |
| public double getCtrlY() { | |
| return (double) ctrly; | |
| } | |
| /** | |
| * {@inheritDoc} | |
| * @since 1.2 | |
| */ | |
| public Point2D getCtrlPt() { | |
| return new Point2D.Float(ctrlx, ctrly); | |
| } | |
| /** | |
| * {@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 ctrlx, double ctrly, | |
| double x2, double y2) | |
| { | |
| this.x1 = (float) x1; | |
| this.y1 = (float) y1; | |
| this.ctrlx = (float) ctrlx; | |
| this.ctrly = (float) ctrly; | |
| this.x2 = (float) x2; | |
| this.y2 = (float) y2; | |
| } | |
| /** | |
| * Sets the location of the end points and control point of this curve | |
| * to the specified {@code float} coordinates. | |
| * | |
| * @param x1 the X coordinate of the start point | |
| * @param y1 the Y coordinate of the start point | |
| * @param ctrlx the X coordinate of the control point | |
| * @param ctrly the Y coordinate of the control point | |
| * @param x2 the X coordinate of the end point | |
| * @param y2 the Y coordinate of the end point | |
| * @since 1.2 | |
| */ | |
| public void setCurve(float x1, float y1, | |
| float ctrlx, float ctrly, | |
| float x2, float y2) | |
| { | |
| this.x1 = x1; | |
| this.y1 = y1; | |
| this.ctrlx = ctrlx; | |
| this.ctrly = ctrly; | |
| this.x2 = x2; | |
| this.y2 = y2; | |
| } | |
| /** | |
| * Use serialVersionUID from JDK 1.6 for interoperability. | |
| */ | |
| @Serial | |
| private static final long serialVersionUID = -8511188402130719609L; | |
| } | |
| /** | |
| * A quadratic parametric curve segment specified with | |
| * {@code double} coordinates. | |
| * | |
| * @since 1.2 | |
| */ | |
| public static class Double extends QuadCurve2D implements Serializable { | |
| /** | |
| * The X coordinate of the start point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public double x1; | |
| /** | |
| * The Y coordinate of the start point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public double y1; | |
| /** | |
| * The X coordinate of the control point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public double ctrlx; | |
| /** | |
| * The Y coordinate of the control point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public double ctrly; | |
| /** | |
| * The X coordinate of the end point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public double x2; | |
| /** | |
| * The Y coordinate of the end point of the quadratic curve | |
| * segment. | |
| * @since 1.2 | |
| * @serial | |
| */ | |
| public double y2; | |
| /** | |
| * Constructs and initializes a {@code QuadCurve2D} with | |
| * coordinates (0, 0, 0, 0, 0, 0). | |
| * @since 1.2 | |
| */ | |
| public Double() { | |
| } | |
| /** | |
| * Constructs and initializes a {@code QuadCurve2D} from the | |
| * specified {@code double} coordinates. | |
| * | |
| * @param x1 the X coordinate of the start point | |
| * @param y1 the Y coordinate of the start point | |
| * @param ctrlx the X coordinate of the control point | |
| * @param ctrly the Y coordinate of the control point | |
| * @param x2 the X coordinate of the end point | |
| * @param y2 the Y coordinate of the end point | |
| * @since 1.2 | |
| */ | |
| public Double(double x1, double y1, | |
| double ctrlx, double ctrly, | |
| double x2, double y2) | |
| { | |
| setCurve(x1, y1, ctrlx, ctrly, 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 getCtrlX() { | |
| return ctrlx; | |
| } | |
| /** | |
| * {@inheritDoc} | |
| * @since 1.2 | |
| */ | |
| public double getCtrlY() { | |
| return ctrly; | |
| } | |
| /** | |
| * {@inheritDoc} | |
| * @since 1.2 | |
| */ | |
| public Point2D getCtrlPt() { | |
| return new Point2D.Double(ctrlx, ctrly); | |
| } | |
| /** | |
| * {@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 ctrlx, double ctrly, | |
| double x2, double y2) | |
| { | |
| this.x1 = x1; | |
| this.y1 = y1; | |
| this.ctrlx = ctrlx; | |
| this.ctrly = ctrly; | |
| this.x2 = x2; | |
| this.y2 = y2; | |
| } | |
| /** | |
| * Use serialVersionUID from JDK 1.6 for interoperability. | |
| */ | |
| @Serial | |
| private static final long serialVersionUID = 4217149928428559721L; | |
| } | |
| /** | |
| * 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.QuadCurve2D.Float | |
| * @see java.awt.geom.QuadCurve2D.Double | |
| * @since 1.2 | |
| */ | |
| protected QuadCurve2D() { | |
| } | |
| /** | |
| * Returns the X coordinate of the start point in | |
| * {@code double} in precision. | |
| * @return the X coordinate of the start point. | |
| * @since 1.2 | |
| */ | |
| public abstract double getX1(); | |
| /** | |
| * Returns the Y coordinate of the start point in | |
| * {@code double} precision. | |
| * @return the Y coordinate of the start point. | |
| * @since 1.2 | |
| */ | |
| public abstract double getY1(); | |
| /** | |
| * Returns the start point. | |
| * @return a {@code Point2D} that is the start point of this | |
| * {@code QuadCurve2D}. | |
| * @since 1.2 | |
| */ | |
| public abstract Point2D getP1(); | |
| /** | |
| * Returns the X coordinate of the control point in | |
| * {@code double} precision. | |
| * @return X coordinate the control point | |
| * @since 1.2 | |
| */ | |
| public abstract double getCtrlX(); | |
| /** | |
| * Returns the Y coordinate of the control point in | |
| * {@code double} precision. | |
| * @return the Y coordinate of the control point. | |
| * @since 1.2 | |
| */ | |
| public abstract double getCtrlY(); | |
| /** | |
| * Returns the control point. | |
| * @return a {@code Point2D} that is the control point of this | |
| * {@code Point2D}. | |
| * @since 1.2 | |
| */ | |
| public abstract Point2D getCtrlPt(); | |
| /** | |
| * Returns the X coordinate of the end point in | |
| * {@code double} precision. | |
| * @return the x coordinate of the end point. | |
| * @since 1.2 | |
| */ | |
| public abstract double getX2(); | |
| /** | |
| * Returns the Y coordinate of the end point in | |
| * {@code double} precision. | |
| * @return the Y coordinate of the end point. | |
| * @since 1.2 | |
| */ | |
| public abstract double getY2(); | |
| /** | |
| * Returns the end point. | |
| * @return a {@code Point} object that is the end point | |
| * of this {@code Point2D}. | |
| * @since 1.2 | |
| */ | |
| public abstract Point2D getP2(); | |
| /** | |
| * Sets the location of the end points and control point of this curve | |
| * to the specified {@code double} coordinates. | |
| * | |
| * @param x1 the X coordinate of the start point | |
| * @param y1 the Y coordinate of the start point | |
| * @param ctrlx the X coordinate of the control point | |
| * @param ctrly the Y coordinate of the control point | |
| * @param x2 the X coordinate of the end point | |
| * @param y2 the Y coordinate of the end point | |
| * @since 1.2 | |
| */ | |
| public abstract void setCurve(double x1, double y1, | |
| double ctrlx, double ctrly, | |
| double x2, double y2); | |
| /** | |
| * Sets the location of the end points and control points of this | |
| * {@code QuadCurve2D} to the {@code double} coordinates at | |
| * the specified offset in the specified array. | |
| * @param coords the array containing coordinate values | |
| * @param offset the index into the array from which to start | |
| * getting the coordinate values and assigning them to this | |
| * {@code QuadCurve2D} | |
| * @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]); | |
| } | |
| /** | |
| * Sets the location of the end points and control point of this | |
| * {@code QuadCurve2D} to the specified {@code Point2D} | |
| * coordinates. | |
| * @param p1 the start point | |
| * @param cp the control point | |
| * @param p2 the end point | |
| * @since 1.2 | |
| */ | |
| public void setCurve(Point2D p1, Point2D cp, Point2D p2) { | |
| setCurve(p1.getX(), p1.getY(), | |
| cp.getX(), cp.getY(), | |
| p2.getX(), p2.getY()); | |
| } | |
| /** | |
| * Sets the location of the end points and control points of this | |
| * {@code QuadCurve2D} to the coordinates of the | |
| * {@code Point2D} objects at the specified offset in | |
| * the specified array. | |
| * @param pts an array containing {@code Point2D} that define | |
| * coordinate values | |
| * @param offset the index into {@code pts} from which to start | |
| * getting the coordinate values and assigning them to this | |
| * {@code QuadCurve2D} | |
| * @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()); | |
| } | |
| /** | |
| * Sets the location of the end points and control point of this | |
| * {@code QuadCurve2D} to the same as those in the specified | |
| * {@code QuadCurve2D}. | |
| * @param c the specified {@code QuadCurve2D} | |
| * @since 1.2 | |
| */ | |
| public void setCurve(QuadCurve2D c) { | |
| setCurve(c.getX1(), c.getY1(), | |
| c.getCtrlX(), c.getCtrlY(), | |
| c.getX2(), c.getY2()); | |
| } | |
| /** | |
| * Returns the square of the flatness, or maximum distance of a | |
| * control point from the line connecting the end points, of the | |
| * quadratic curve specified by the indicated control points. | |
| * | |
| * @param x1 the X coordinate of the start point | |
| * @param y1 the Y coordinate of the start point | |
| * @param ctrlx the X coordinate of the control point | |
| * @param ctrly the Y coordinate of the control point | |
| * @param x2 the X coordinate of the end point | |
| * @param y2 the Y coordinate of the end point | |
| * @return the square of the flatness of the quadratic curve | |
| * defined by the specified coordinates. | |
| * @since 1.2 | |
| */ | |
| public static double getFlatnessSq(double x1, double y1, | |
| double ctrlx, double ctrly, | |
| double x2, double y2) { | |
| return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly); | |
| } | |
| /** | |
| * Returns the flatness, or maximum distance of a | |
| * control point from the line connecting the end points, of the | |
| * quadratic curve specified by the indicated control points. | |
| * | |
| * @param x1 the X coordinate of the start point | |
| * @param y1 the Y coordinate of the start point | |
| * @param ctrlx the X coordinate of the control point | |
| * @param ctrly the Y coordinate of the control point | |
| * @param x2 the X coordinate of the end point | |
| * @param y2 the Y coordinate of the end point | |
| * @return the flatness of the quadratic curve defined by the | |
| * specified coordinates. | |
| * @since 1.2 | |
| */ | |
| public static double getFlatness(double x1, double y1, | |
| double ctrlx, double ctrly, | |
| double x2, double y2) { | |
| return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly); | |
| } | |
| /** | |
| * Returns the square of the flatness, or maximum distance of a | |
| * control point from the line connecting the end points, of the | |
| * quadratic curve specified by the control points stored in the | |
| * indicated array at the indicated index. | |
| * @param coords an array containing coordinate values | |
| * @param offset the index into {@code coords} from which to | |
| * to start getting the values from the array | |
| * @return the flatness of the quadratic curve that is defined by the | |
| * values in the specified array at the specified index. | |
| * @since 1.2 | |
| */ | |
| public static double getFlatnessSq(double[] coords, int offset) { | |
| return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1], | |
| coords[offset + 4], coords[offset + 5], | |
| coords[offset + 2], coords[offset + 3]); | |
| } | |
| /** | |
| * Returns the flatness, or maximum distance of a | |
| * control point from the line connecting the end points, of the | |
| * quadratic curve specified by the control points stored in the | |
| * indicated array at the indicated index. | |
| * @param coords an array containing coordinate values | |
| * @param offset the index into {@code coords} from which to | |
| * start getting the coordinate values | |
| * @return the flatness of a quadratic curve defined by the | |
| * specified array at the specified offset. | |
| * @since 1.2 | |
| */ | |
| public static double getFlatness(double[] coords, int offset) { | |
| return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1], | |
| coords[offset + 4], coords[offset + 5], | |
| coords[offset + 2], coords[offset + 3]); | |
| } | |
| /** | |
| * Returns the square of the flatness, or maximum distance of a | |
| * control point from the line connecting the end points, of this | |
| * {@code QuadCurve2D}. | |
| * @return the square of the flatness of this | |
| * {@code QuadCurve2D}. | |
| * @since 1.2 | |
| */ | |
| public double getFlatnessSq() { | |
| return Line2D.ptSegDistSq(getX1(), getY1(), | |
| getX2(), getY2(), | |
| getCtrlX(), getCtrlY()); | |
| } | |
| /** | |
| * Returns the flatness, or maximum distance of a | |
| * control point from the line connecting the end points, of this | |
| * {@code QuadCurve2D}. | |
| * @return the flatness of this {@code QuadCurve2D}. | |
| * @since 1.2 | |
| */ | |
| public double getFlatness() { | |
| return Line2D.ptSegDist(getX1(), getY1(), | |
| getX2(), getY2(), | |
| getCtrlX(), getCtrlY()); | |
| } | |
| /** | |
| * Subdivides this {@code QuadCurve2D} 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 can be the same as this {@code QuadCurve2D} or | |
| * {@code null}. | |
| * @param left the {@code QuadCurve2D} object for storing the | |
| * left or first half of the subdivided curve | |
| * @param right the {@code QuadCurve2D} object for storing the | |
| * right or second half of the subdivided curve | |
| * @since 1.2 | |
| */ | |
| public void subdivide(QuadCurve2D left, QuadCurve2D right) { | |
| subdivide(this, left, right); | |
| } | |
| /** | |
| * Subdivides the quadratic 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 can be the same as the {@code src} object or | |
| * {@code null}. | |
| * @param src the quadratic curve to be subdivided | |
| * @param left the {@code QuadCurve2D} object for storing the | |
| * left or first half of the subdivided curve | |
| * @param right the {@code QuadCurve2D} object for storing the | |
| * right or second half of the subdivided curve | |
| * @since 1.2 | |
| */ | |
| public static void subdivide(QuadCurve2D src, | |
| QuadCurve2D left, | |
| QuadCurve2D right) { | |
| double x1 = src.getX1(); | |
| double y1 = src.getY1(); | |
| double ctrlx = src.getCtrlX(); | |
| double ctrly = src.getCtrlY(); | |
| double x2 = src.getX2(); | |
| double y2 = src.getY2(); | |
| double ctrlx1 = (x1 + ctrlx) / 2.0; | |
| double ctrly1 = (y1 + ctrly) / 2.0; | |
| double ctrlx2 = (x2 + ctrlx) / 2.0; | |
| double ctrly2 = (y2 + ctrly) / 2.0; | |
| ctrlx = (ctrlx1 + ctrlx2) / 2.0; | |
| ctrly = (ctrly1 + ctrly2) / 2.0; | |
| if (left != null) { | |
| left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly); | |
| } | |
| if (right != null) { | |
| right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2); | |
| } | |
| } | |
| /** | |
| * Subdivides the quadratic curve specified by the coordinates | |
| * stored in the {@code src} array at indices | |
| * {@code srcoff} through {@code srcoff} + 5 | |
| * 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 can be {@code null} or a reference to the same array | |
| * and offset 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 that | |
| * {@code rightoff} equals {@code leftoff} + 4 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 ctrlx = src[srcoff + 2]; | |
| double ctrly = src[srcoff + 3]; | |
| double x2 = src[srcoff + 4]; | |
| double y2 = src[srcoff + 5]; | |
| if (left != null) { | |
| left[leftoff + 0] = x1; | |
| left[leftoff + 1] = y1; | |
| } | |
| if (right != null) { | |
| right[rightoff + 4] = x2; | |
| right[rightoff + 5] = y2; | |
| } | |
| x1 = (x1 + ctrlx) / 2.0; | |
| y1 = (y1 + ctrly) / 2.0; | |
| x2 = (x2 + ctrlx) / 2.0; | |
| y2 = (y2 + ctrly) / 2.0; | |
| ctrlx = (x1 + x2) / 2.0; | |
| ctrly = (y1 + y2) / 2.0; | |
| if (left != null) { | |
| left[leftoff + 2] = x1; | |
| left[leftoff + 3] = y1; | |
| left[leftoff + 4] = ctrlx; | |
| left[leftoff + 5] = ctrly; | |
| } | |
| if (right != null) { | |
| right[rightoff + 0] = ctrlx; | |
| right[rightoff + 1] = ctrly; | |
| right[rightoff + 2] = x2; | |
| right[rightoff + 3] = y2; | |
| } | |
| } | |
| /** | |
| * Solves the quadratic 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 quadratic solved is represented | |
| * by the equation: | |
| * <pre> | |
| * eqn = {C, B, A}; | |
| * ax^2 + bx + c = 0 | |
| * </pre> | |
| * A return value of {@code -1} is used to distinguish a constant | |
| * equation, which might be always 0 or never 0, from an equation that | |
| * has no zeroes. | |
| * @param eqn the array that contains the quadratic coefficients | |
| * @return the number of roots, or {@code -1} if the equation is | |
| * a constant | |
| * @since 1.2 | |
| */ | |
| public static int solveQuadratic(double[] eqn) { | |
| return solveQuadratic(eqn, eqn); | |
| } | |
| /** | |
| * Solves the quadratic whose coefficients are in the {@code eqn} | |
| * array and places the non-complex roots into the {@code res} | |
| * array, returning the number of roots. | |
| * The quadratic solved is represented by the equation: | |
| * <pre> | |
| * eqn = {C, B, A}; | |
| * ax^2 + bx + c = 0 | |
| * </pre> | |
| * A return value of {@code -1} is used to distinguish a constant | |
| * equation, which might be always 0 or never 0, from an equation that | |
| * has no zeroes. | |
| * @param eqn the specified array of coefficients to use to solve | |
| * the quadratic equation | |
| * @param res the array that contains the non-complex roots | |
| * resulting from the solution of the quadratic equation | |
| * @return the number of roots, or {@code -1} if the equation is | |
| * a constant. | |
| * @since 1.3 | |
| */ | |
| public static int solveQuadratic(double[] eqn, double[] res) { | |
| double a = eqn[2]; | |
| double b = eqn[1]; | |
| double c = eqn[0]; | |
| int roots = 0; | |
| if (a == 0.0) { | |
| // The quadratic parabola has degenerated to a line. | |
| if (b == 0.0) { | |
| // The line has degenerated to a constant. | |
| return -1; | |
| } | |
| res[roots++] = -c / b; | |
| } else { | |
| // From Numerical Recipes, 5.6, Quadratic and Cubic Equations | |
| double d = b * b - 4.0 * a * c; | |
| if (d < 0.0) { | |
| // If d < 0.0, then there are no roots | |
| return 0; | |
| } | |
| d = Math.sqrt(d); | |
| // For accuracy, calculate one root using: | |
| // (-b +/- d) / 2a | |
| // and the other using: | |
| // 2c / (-b +/- d) | |
| // Choose the sign of the +/- so that b+d gets larger in magnitude | |
| if (b < 0.0) { | |
| d = -d; | |
| } | |
| double q = (b + d) / -2.0; | |
| // We already tested a for being 0 above | |
| res[roots++] = q / a; | |
| if (q != 0.0) { | |
| res[roots++] = c / q; | |
| } | |
| } | |
| return roots; | |
| } | |
| /** | |
| * {@inheritDoc} | |
| * @since 1.2 | |
| */ | |
| public boolean contains(double x, double y) { | |
| double x1 = getX1(); | |
| double y1 = getY1(); | |
| double xc = getCtrlX(); | |
| double yc = getCtrlY(); | |
| double x2 = getX2(); | |
| double y2 = getY2(); | |
| /* | |
| * We have a convex shape bounded by quad curve Pc(t) | |
| * and ine Pl(t). | |
| * | |
| * P1 = (x1, y1) - start point of curve | |
| * P2 = (x2, y2) - end point of curve | |
| * Pc = (xc, yc) - control point | |
| * | |
| * Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 = | |
| * = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1 | |
| * Pl(t) = P1*(1 - t) + P2*t | |
| * t = [0:1] | |
| * | |
| * P = (x, y) - point of interest | |
| * | |
| * Let's look at second derivative of quad curve equation: | |
| * | |
| * Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq'' | |
| * It's constant vector. | |
| * | |
| * Let's draw a line through P to be parallel to this | |
| * vector and find the intersection of the quad curve | |
| * and the line. | |
| * | |
| * Pq(t) is point of intersection if system of equations | |
| * below has the solution. | |
| * | |
| * L(s) = P + Pq''*s == Pq(t) | |
| * Pq''*s + (P - Pq(t)) == 0 | |
| * | |
| * | xq''*s + (x - xq(t)) == 0 | |
| * | yq''*s + (y - yq(t)) == 0 | |
| * | |
| * This system has the solution if rank of its matrix equals to 1. | |
| * That is, determinant of the matrix should be zero. | |
| * | |
| * (y - yq(t))*xq'' == (x - xq(t))*yq'' | |
| * | |
| * Let's solve this equation with 't' variable. | |
| * Also let kx = x1 - 2*xc + x2 | |
| * ky = y1 - 2*yc + y2 | |
| * | |
| * t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) / | |
| * ((xc - x1)*ky - (yc - y1)*kx) | |
| * | |
| * Let's do the same for our line Pl(t): | |
| * | |
| * t0l = ((x - x1)*ky - (y - y1)*kx) / | |
| * ((x2 - x1)*ky - (y2 - y1)*kx) | |
| * | |
| * It's easy to check that t0q == t0l. This fact means | |
| * we can compute t0 only one time. | |
| * | |
| * In case t0 < 0 or t0 > 1, we have an intersections outside | |
| * of shape bounds. So, P is definitely out of shape. | |
| * | |
| * In case t0 is inside [0:1], we should calculate Pq(t0) | |
| * and Pl(t0). We have three points for now, and all of them | |
| * lie on one line. So, we just need to detect, is our point | |
| * of interest between points of intersections or not. | |
| * | |
| * If the denominator in the t0q and t0l equations is | |
| * zero, then the points must be collinear and so the | |
| * curve is degenerate and encloses no area. Thus the | |
| * result is false. | |
| */ | |
| double kx = x1 - 2 * xc + x2; | |
| double ky = y1 - 2 * yc + y2; | |
| double dx = x - x1; | |
| double dy = y - y1; | |
| double dxl = x2 - x1; | |
| double dyl = y2 - y1; | |
| double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx); | |
| if (t0 < 0 || t0 > 1 || t0 != t0) { | |
| return false; | |
| } | |
| double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1; | |
| double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1; | |
| double xl = dxl * t0 + x1; | |
| double yl = dyl * t0 + y1; | |
| return (x >= xb && x < xl) || | |
| (x >= xl && x < xb) || | |
| (y >= yb && y < yl) || | |
| (y >= yl && y < yb); | |
| } | |
| /** | |
| * {@inheritDoc} | |
| * @since 1.2 | |
| */ | |
| public boolean contains(Point2D p) { | |
| return contains(p.getX(), p.getY()); | |
| } | |
| /** | |
| * Fill an array with the coefficients of the parametric equation | |
| * in t, ready for solving against val with solveQuadratic. | |
| * We currently have: | |
| * val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2 | |
| * = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2 | |
| * = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 | |
| * 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 | |
| * 0 = C + Bt + At^2 | |
| * C = C1 - val | |
| * B = 2*CP - 2*C1 | |
| * A = C1 - 2*CP + C2 | |
| */ | |
| private static void fillEqn(double[] eqn, double val, | |
| double c1, double cp, double c2) { | |
| eqn[0] = c1 - val; | |
| eqn[1] = cp + cp - c1 - c1; | |
| eqn[2] = c1 - cp - cp + c2; | |
| return; | |
| } | |
| /** | |
| * Evaluate the t values in the first num slots of the vals[] array | |
| * and place the evaluated values back into the same array. Only | |
| * evaluate t values that are within the range <0, 1>, including | |
| * the 0 and 1 ends of the range iff the include0 or include1 | |
| * booleans are true. If an "inflection" equation is handed in, | |
| * then any points which represent a point of inflection for that | |
| * quadratic equation are also ignored. | |
| */ | |
| private static int evalQuadratic(double[] vals, int num, | |
| boolean include0, | |
| boolean include1, | |
| double[] inflect, | |
| double c1, double ctrl, double c2) { | |
| int j = 0; | |
| for (int i = 0; i < num; i++) { | |
| double t = vals[i]; | |
| if ((include0 ? t >= 0 : t > 0) && | |
| (include1 ? t <= 1 : t < 1) && | |
| (inflect == null || | |
| inflect[1] + 2*inflect[2]*t != 0)) | |
| { | |
| double u = 1 - t; | |
| vals[j++] = c1*u*u + 2*ctrl*t*u + c2*t*t; | |
| } | |
| } | |
| return j; | |
| } | |
| private static final int BELOW = -2; | |
| private static final int LOWEDGE = -1; | |
| private static final int INSIDE = 0; | |
| private static final int HIGHEDGE = 1; | |
| private static final int ABOVE = 2; | |
| /** | |
| * Determine where coord lies with respect to the range from | |
| * low to high. It is assumed that low <= high. The return | |
| * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE, | |
| * or ABOVE. | |
| */ | |
| private static int getTag(double coord, double low, double high) { | |
| if (coord <= low) { | |
| return (coord < low ? BELOW : LOWEDGE); | |
| } | |
| if (coord >= high) { | |
| return (coord > high ? ABOVE : HIGHEDGE); | |
| } | |
| return INSIDE; | |
| } | |
| /** | |
| * Determine if the pttag represents a coordinate that is already | |
| * in its test range, or is on the border with either of the two | |
| * opttags representing another coordinate that is "towards the | |
| * inside" of that test range. In other words, are either of the | |
| * two "opt" points "drawing the pt inward"? | |
| */ | |
| private static boolean inwards(int pttag, int opt1tag, int opt2tag) { | |
| switch (pttag) { | |
| case BELOW: | |
| case ABOVE: | |
| default: | |
| return false; | |
| case LOWEDGE: | |
| return (opt1tag >= INSIDE || opt2tag >= INSIDE); | |
| case INSIDE: | |
| return true; | |
| case HIGHEDGE: | |
| return (opt1tag <= INSIDE || opt2tag <= INSIDE); | |
| } | |
| } | |
| /** | |
| * {@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; | |
| } | |
| // Trivially accept if either endpoint is inside the rectangle | |
| // (not on its border since it may end there and not go inside) | |
| // Record where they lie with respect to the rectangle. | |
| // -1 => left, 0 => inside, 1 => right | |
| double x1 = getX1(); | |
| double y1 = getY1(); | |
| int x1tag = getTag(x1, x, x+w); | |
| int y1tag = getTag(y1, y, y+h); | |
| if (x1tag == INSIDE && y1tag == INSIDE) { | |
| return true; | |
| } | |
| double x2 = getX2(); | |
| double y2 = getY2(); | |
| int x2tag = getTag(x2, x, x+w); | |
| int y2tag = getTag(y2, y, y+h); | |
| if (x2tag == INSIDE && y2tag == INSIDE) { | |
| return true; | |
| } | |
| double ctrlx = getCtrlX(); | |
| double ctrly = getCtrlY(); | |
| int ctrlxtag = getTag(ctrlx, x, x+w); | |
| int ctrlytag = getTag(ctrly, y, y+h); | |
| // Trivially reject if all points are entirely to one side of | |
| // the rectangle. | |
| if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) { | |
| return false; // All points left | |
| } | |
| if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) { | |
| return false; // All points above | |
| } | |
| if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) { | |
| return false; // All points right | |
| } | |
| if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) { | |
| return false; // All points below | |
| } | |
| // Test for endpoints on the edge where either the segment | |
| // or the curve is headed "inwards" from them | |
| // Note: These tests are a superset of the fast endpoint tests | |
| // above and thus repeat those tests, but take more time | |
| // and cover more cases | |
| if (inwards(x1tag, x2tag, ctrlxtag) && | |
| inwards(y1tag, y2tag, ctrlytag)) | |
| { | |
| // First endpoint on border with either edge moving inside | |
| return true; | |
| } | |
| if (inwards(x2tag, x1tag, ctrlxtag) && | |
| inwards(y2tag, y1tag, ctrlytag)) | |
| { | |
| // Second endpoint on border with either edge moving inside | |
| return true; | |
| } | |
| // Trivially accept if endpoints span directly across the rectangle | |
| boolean xoverlap = (x1tag * x2tag <= 0); | |
| boolean yoverlap = (y1tag * y2tag <= 0); | |
| if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) { | |
| return true; | |
| } | |
| if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) { | |
| return true; | |
| } | |
| // We now know that both endpoints are outside the rectangle | |
| // but the 3 points are not all on one side of the rectangle. | |
| // Therefore the curve cannot be contained inside the rectangle, | |
| // but the rectangle might be contained inside the curve, or | |
| // the curve might intersect the boundary of the rectangle. | |
| double[] eqn = new double[3]; | |
| double[] res = new double[3]; | |
| if (!yoverlap) { | |
| // Both Y coordinates for the closing segment are above or | |
| // below the rectangle which means that we can only intersect | |
| // if the curve crosses the top (or bottom) of the rectangle | |
| // in more than one place and if those crossing locations | |
| // span the horizontal range of the rectangle. | |
| fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2); | |
| return (solveQuadratic(eqn, res) == 2 && | |
| evalQuadratic(res, 2, true, true, null, | |
| x1, ctrlx, x2) == 2 && | |
| getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0); | |
| } | |
| // Y ranges overlap. Now we examine the X ranges | |
| if (!xoverlap) { | |
| // Both X coordinates for the closing segment are left of | |
| // or right of the rectangle which means that we can only | |
| // intersect if the curve crosses the left (or right) edge | |
| // of the rectangle in more than one place and if those | |
| // crossing locations span the vertical range of the rectangle. | |
| fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2); | |
| return (solveQuadratic(eqn, res) == 2 && | |
| evalQuadratic(res, 2, true, true, null, | |
| y1, ctrly, y2) == 2 && | |
| getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0); | |
| } | |
| // The X and Y ranges of the endpoints overlap the X and Y | |
| // ranges of the rectangle, now find out how the endpoint | |
| // line segment intersects the Y range of the rectangle | |
| double dx = x2 - x1; | |
| double dy = y2 - y1; | |
| double k = y2 * x1 - x2 * y1; | |
| int c1tag, c2tag; | |
| if (y1tag == INSIDE) { | |
| c1tag = x1tag; | |
| } else { | |
| c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w); | |
| } | |
| if (y2tag == INSIDE) { | |
| c2tag = x2tag; | |
| } else { | |
| c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w); | |
| } | |
| // If the part of the line segment that intersects the Y range | |
| // of the rectangle crosses it horizontally - trivially accept | |
| if (c1tag * c2tag <= 0) { | |
| return true; | |
| } | |
| // Now we know that both the X and Y ranges intersect and that | |
| // the endpoint line segment does not directly cross the rectangle. | |
| // | |
| // We can almost treat this case like one of the cases above | |
| // where both endpoints are to one side, except that we will | |
| // only get one intersection of the curve with the vertical | |
| // side of the rectangle. This is because the endpoint segment | |
| // accounts for the other intersection. | |
| // | |
| // (Remember there is overlap in both the X and Y ranges which | |
| // means that the segment must cross at least one vertical edge | |
| // of the rectangle - in particular, the "near vertical side" - | |
| // leaving only one intersection for the curve.) | |
| // | |
| // Now we calculate the y tags of the two intersections on the | |
| // "near vertical side" of the rectangle. We will have one with | |
| // the endpoint segment, and one with the curve. If those two | |
| // vertical intersections overlap the Y range of the rectangle, | |
| // we have an intersection. Otherwise, we don't. | |
| // c1tag = vertical intersection class of the endpoint segment | |
| // | |
| // Choose the y tag of the endpoint that was not on the same | |
| // side of the rectangle as the subsegment calculated above. | |
| // Note that we can "steal" the existing Y tag of that endpoint | |
| // since it will be provably the same as the vertical intersection. | |
| c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag); | |
| // c2tag = vertical intersection class of the curve | |
| // | |
| // We have to calculate this one the straightforward way. | |
| // Note that the c2tag can still tell us which vertical edge | |
| // to test against. | |
| fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2); | |
| int num = solveQuadratic(eqn, res); | |
| // Note: We should be able to assert(num == 2); since the | |
| // X range "crosses" (not touches) the vertical boundary, | |
| // but we pass num to evalQuadratic for completeness. | |
| evalQuadratic(res, num, true, true, null, y1, ctrly, y2); | |
| // Note: We can assert(num evals == 1); since one of the | |
| // 2 crossings will be out of the [0,1] range. | |
| c2tag = getTag(res[0], y, y+h); | |
| // Finally, we have an intersection if the two crossings | |
| // overlap the Y range of the rectangle. | |
| return (c1tag * c2tag <= 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; | |
| } | |
| // Assertion: Quadratic curves closed by connecting their | |
| // endpoints are always convex. | |
| return (contains(x, y) && | |
| contains(x + w, y) && | |
| contains(x + w, y + h) && | |
| contains(x, y + h)); | |
| } | |
| /** | |
| * {@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 of this {@code QuadCurve2D}. | |
| * The iterator for this class is not multi-threaded safe, | |
| * which means that this {@code QuadCurve2D} class does not | |
| * guarantee that modifications to the geometry of this | |
| * {@code QuadCurve2D} object do not affect any iterations of | |
| * that geometry that are already in process. | |
| * @param at an optional {@link AffineTransform} to apply to the | |
| * shape boundary | |
| * @return a {@link PathIterator} object that defines the boundary | |
| * of the shape. | |
| * @since 1.2 | |
| */ | |
| public PathIterator getPathIterator(AffineTransform at) { | |
| return new QuadIterator(this, at); | |
| } | |
| /** | |
| * Returns an iteration object that defines the boundary of the | |
| * flattened shape of this {@code QuadCurve2D}. | |
| * The iterator for this class is not multi-threaded safe, | |
| * which means that this {@code QuadCurve2D} class does not | |
| * guarantee that modifications to the geometry of this | |
| * {@code QuadCurve2D} object do not affect any iterations of | |
| * that geometry that are already in process. | |
| * @param at an optional {@code AffineTransform} to apply | |
| * to the boundary of the shape | |
| * @param flatness the maximum distance that the control points for a | |
| * subdivided curve can be with respect to a line connecting | |
| * the end points of this curve before this curve is | |
| * replaced by a straight line connecting the end points. | |
| * @return a {@code PathIterator} object that defines the | |
| * flattened boundary of the shape. | |
| * @since 1.2 | |
| */ | |
| public PathIterator getPathIterator(AffineTransform at, double flatness) { | |
| return new FlatteningPathIterator(getPathIterator(at), flatness); | |
| } | |
| /** | |
| * Creates a new object of the same class and with the same contents | |
| * 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); | |
| } | |
| } | |
| } |