| /* |
| * Copyright (c) 1997, 2006, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| package java.awt.geom; |
| |
| import java.awt.Shape; |
| import java.awt.Rectangle; |
| import java.util.Arrays; |
| import java.io.Serializable; |
| import sun.awt.geom.Curve; |
| |
| /** |
| * The <code>CubicCurve2D</code> class defines a cubic parametric curve |
| * segment in {@code (x,y)} coordinate space. |
| * <p> |
| * This class is only the abstract superclass for all objects which |
| * store a 2D cubic curve segment. |
| * The actual storage representation of the coordinates is left to |
| * the subclass. |
| * |
| * @author Jim Graham |
| * @since 1.2 |
| */ |
| public abstract class CubicCurve2D implements Shape, Cloneable { |
| |
| /** |
| * A cubic parametric curve segment specified with |
| * {@code float} coordinates. |
| * @since 1.2 |
| */ |
| public static class Float extends CubicCurve2D implements Serializable { |
| /** |
| * The X coordinate of the start point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float x1; |
| |
| /** |
| * The Y coordinate of the start point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float y1; |
| |
| /** |
| * The X coordinate of the first control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float ctrlx1; |
| |
| /** |
| * The Y coordinate of the first control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float ctrly1; |
| |
| /** |
| * The X coordinate of the second control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float ctrlx2; |
| |
| /** |
| * The Y coordinate of the second control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float ctrly2; |
| |
| /** |
| * The X coordinate of the end point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float x2; |
| |
| /** |
| * The Y coordinate of the end point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public float y2; |
| |
| /** |
| * Constructs and initializes a CubicCurve with coordinates |
| * (0, 0, 0, 0, 0, 0, 0, 0). |
| * @since 1.2 |
| */ |
| public Float() { |
| } |
| |
| /** |
| * Constructs and initializes a {@code CubicCurve2D} from |
| * the specified {@code float} coordinates. |
| * |
| * @param x1 the X coordinate for the start point |
| * of the resulting {@code CubicCurve2D} |
| * @param y1 the Y coordinate for the start point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrlx1 the X coordinate for the first control point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrly1 the Y coordinate for the first control point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrlx2 the X coordinate for the second control point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrly2 the Y coordinate for the second control point |
| * of the resulting {@code CubicCurve2D} |
| * @param x2 the X coordinate for the end point |
| * of the resulting {@code CubicCurve2D} |
| * @param y2 the Y coordinate for the end point |
| * of the resulting {@code CubicCurve2D} |
| * @since 1.2 |
| */ |
| public Float(float x1, float y1, |
| float ctrlx1, float ctrly1, |
| float ctrlx2, float ctrly2, |
| float x2, float y2) |
| { |
| setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getX1() { |
| return (double) x1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getY1() { |
| return (double) y1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getP1() { |
| return new Point2D.Float(x1, y1); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlX1() { |
| return (double) ctrlx1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlY1() { |
| return (double) ctrly1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getCtrlP1() { |
| return new Point2D.Float(ctrlx1, ctrly1); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlX2() { |
| return (double) ctrlx2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlY2() { |
| return (double) ctrly2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getCtrlP2() { |
| return new Point2D.Float(ctrlx2, ctrly2); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getX2() { |
| return (double) x2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getY2() { |
| return (double) y2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getP2() { |
| return new Point2D.Float(x2, y2); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public void setCurve(double x1, double y1, |
| double ctrlx1, double ctrly1, |
| double ctrlx2, double ctrly2, |
| double x2, double y2) |
| { |
| this.x1 = (float) x1; |
| this.y1 = (float) y1; |
| this.ctrlx1 = (float) ctrlx1; |
| this.ctrly1 = (float) ctrly1; |
| this.ctrlx2 = (float) ctrlx2; |
| this.ctrly2 = (float) ctrly2; |
| this.x2 = (float) x2; |
| this.y2 = (float) y2; |
| } |
| |
| /** |
| * Sets the location of the end points and control points |
| * of this curve to the specified {@code float} coordinates. |
| * |
| * @param x1 the X coordinate used to set the start point |
| * of this {@code CubicCurve2D} |
| * @param y1 the Y coordinate used to set the start point |
| * of this {@code CubicCurve2D} |
| * @param ctrlx1 the X coordinate used to set the first control point |
| * of this {@code CubicCurve2D} |
| * @param ctrly1 the Y coordinate used to set the first control point |
| * of this {@code CubicCurve2D} |
| * @param ctrlx2 the X coordinate used to set the second control point |
| * of this {@code CubicCurve2D} |
| * @param ctrly2 the Y coordinate used to set the second control point |
| * of this {@code CubicCurve2D} |
| * @param x2 the X coordinate used to set the end point |
| * of this {@code CubicCurve2D} |
| * @param y2 the Y coordinate used to set the end point |
| * of this {@code CubicCurve2D} |
| * @since 1.2 |
| */ |
| public void setCurve(float x1, float y1, |
| float ctrlx1, float ctrly1, |
| float ctrlx2, float ctrly2, |
| float x2, float y2) |
| { |
| this.x1 = x1; |
| this.y1 = y1; |
| this.ctrlx1 = ctrlx1; |
| this.ctrly1 = ctrly1; |
| this.ctrlx2 = ctrlx2; |
| this.ctrly2 = ctrly2; |
| this.x2 = x2; |
| this.y2 = y2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Rectangle2D getBounds2D() { |
| float left = Math.min(Math.min(x1, x2), |
| Math.min(ctrlx1, ctrlx2)); |
| float top = Math.min(Math.min(y1, y2), |
| Math.min(ctrly1, ctrly2)); |
| float right = Math.max(Math.max(x1, x2), |
| Math.max(ctrlx1, ctrlx2)); |
| float bottom = Math.max(Math.max(y1, y2), |
| Math.max(ctrly1, ctrly2)); |
| return new Rectangle2D.Float(left, top, |
| right - left, bottom - top); |
| } |
| |
| /* |
| * JDK 1.6 serialVersionUID |
| */ |
| private static final long serialVersionUID = -1272015596714244385L; |
| } |
| |
| /** |
| * A cubic parametric curve segment specified with |
| * {@code double} coordinates. |
| * @since 1.2 |
| */ |
| public static class Double extends CubicCurve2D implements Serializable { |
| /** |
| * The X coordinate of the start point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double x1; |
| |
| /** |
| * The Y coordinate of the start point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double y1; |
| |
| /** |
| * The X coordinate of the first control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double ctrlx1; |
| |
| /** |
| * The Y coordinate of the first control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double ctrly1; |
| |
| /** |
| * The X coordinate of the second control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double ctrlx2; |
| |
| /** |
| * The Y coordinate of the second control point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double ctrly2; |
| |
| /** |
| * The X coordinate of the end point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double x2; |
| |
| /** |
| * The Y coordinate of the end point |
| * of the cubic curve segment. |
| * @since 1.2 |
| * @serial |
| */ |
| public double y2; |
| |
| /** |
| * Constructs and initializes a CubicCurve with coordinates |
| * (0, 0, 0, 0, 0, 0, 0, 0). |
| * @since 1.2 |
| */ |
| public Double() { |
| } |
| |
| /** |
| * Constructs and initializes a {@code CubicCurve2D} from |
| * the specified {@code double} coordinates. |
| * |
| * @param x1 the X coordinate for the start point |
| * of the resulting {@code CubicCurve2D} |
| * @param y1 the Y coordinate for the start point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrlx1 the X coordinate for the first control point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrly1 the Y coordinate for the first control point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrlx2 the X coordinate for the second control point |
| * of the resulting {@code CubicCurve2D} |
| * @param ctrly2 the Y coordinate for the second control point |
| * of the resulting {@code CubicCurve2D} |
| * @param x2 the X coordinate for the end point |
| * of the resulting {@code CubicCurve2D} |
| * @param y2 the Y coordinate for the end point |
| * of the resulting {@code CubicCurve2D} |
| * @since 1.2 |
| */ |
| public Double(double x1, double y1, |
| double ctrlx1, double ctrly1, |
| double ctrlx2, double ctrly2, |
| double x2, double y2) |
| { |
| setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getX1() { |
| return x1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getY1() { |
| return y1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getP1() { |
| return new Point2D.Double(x1, y1); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlX1() { |
| return ctrlx1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlY1() { |
| return ctrly1; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getCtrlP1() { |
| return new Point2D.Double(ctrlx1, ctrly1); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlX2() { |
| return ctrlx2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getCtrlY2() { |
| return ctrly2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getCtrlP2() { |
| return new Point2D.Double(ctrlx2, ctrly2); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getX2() { |
| return x2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public double getY2() { |
| return y2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Point2D getP2() { |
| return new Point2D.Double(x2, y2); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public void setCurve(double x1, double y1, |
| double ctrlx1, double ctrly1, |
| double ctrlx2, double ctrly2, |
| double x2, double y2) |
| { |
| this.x1 = x1; |
| this.y1 = y1; |
| this.ctrlx1 = ctrlx1; |
| this.ctrly1 = ctrly1; |
| this.ctrlx2 = ctrlx2; |
| this.ctrly2 = ctrly2; |
| this.x2 = x2; |
| this.y2 = y2; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Rectangle2D getBounds2D() { |
| double left = Math.min(Math.min(x1, x2), |
| Math.min(ctrlx1, ctrlx2)); |
| double top = Math.min(Math.min(y1, y2), |
| Math.min(ctrly1, ctrly2)); |
| double right = Math.max(Math.max(x1, x2), |
| Math.max(ctrlx1, ctrlx2)); |
| double bottom = Math.max(Math.max(y1, y2), |
| Math.max(ctrly1, ctrly2)); |
| return new Rectangle2D.Double(left, top, |
| right - left, bottom - top); |
| } |
| |
| /* |
| * JDK 1.6 serialVersionUID |
| */ |
| private static final long serialVersionUID = -4202960122839707295L; |
| } |
| |
| /** |
| * This is an abstract class that cannot be instantiated directly. |
| * Type-specific implementation subclasses are available for |
| * instantiation and provide a number of formats for storing |
| * the information necessary to satisfy the various accessor |
| * methods below. |
| * |
| * @see java.awt.geom.CubicCurve2D.Float |
| * @see java.awt.geom.CubicCurve2D.Double |
| * @since 1.2 |
| */ |
| protected CubicCurve2D() { |
| } |
| |
| /** |
| * Returns the X coordinate of the start point in double precision. |
| * @return the X coordinate of the start point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getX1(); |
| |
| /** |
| * Returns the Y coordinate of the start point in double precision. |
| * @return the Y coordinate of the start point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getY1(); |
| |
| /** |
| * Returns the start point. |
| * @return a {@code Point2D} that is the start point of |
| * the {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract Point2D getP1(); |
| |
| /** |
| * Returns the X coordinate of the first control point in double precision. |
| * @return the X coordinate of the first control point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getCtrlX1(); |
| |
| /** |
| * Returns the Y coordinate of the first control point in double precision. |
| * @return the Y coordinate of the first control point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getCtrlY1(); |
| |
| /** |
| * Returns the first control point. |
| * @return a {@code Point2D} that is the first control point of |
| * the {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract Point2D getCtrlP1(); |
| |
| /** |
| * Returns the X coordinate of the second control point |
| * in double precision. |
| * @return the X coordinate of the second control point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getCtrlX2(); |
| |
| /** |
| * Returns the Y coordinate of the second control point |
| * in double precision. |
| * @return the Y coordinate of the second control point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getCtrlY2(); |
| |
| /** |
| * Returns the second control point. |
| * @return a {@code Point2D} that is the second control point of |
| * the {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract Point2D getCtrlP2(); |
| |
| /** |
| * Returns the X coordinate of the end point in double precision. |
| * @return the X coordinate of the end point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getX2(); |
| |
| /** |
| * Returns the Y coordinate of the end point in double precision. |
| * @return the Y coordinate of the end point of the |
| * {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract double getY2(); |
| |
| /** |
| * Returns the end point. |
| * @return a {@code Point2D} that is the end point of |
| * the {@code CubicCurve2D}. |
| * @since 1.2 |
| */ |
| public abstract Point2D getP2(); |
| |
| /** |
| * Sets the location of the end points and control points of this curve |
| * to the specified double coordinates. |
| * |
| * @param x1 the X coordinate used to set the start point |
| * of this {@code CubicCurve2D} |
| * @param y1 the Y coordinate used to set the start point |
| * of this {@code CubicCurve2D} |
| * @param ctrlx1 the X coordinate used to set the first control point |
| * of this {@code CubicCurve2D} |
| * @param ctrly1 the Y coordinate used to set the first control point |
| * of this {@code CubicCurve2D} |
| * @param ctrlx2 the X coordinate used to set the second control point |
| * of this {@code CubicCurve2D} |
| * @param ctrly2 the Y coordinate used to set the second control point |
| * of this {@code CubicCurve2D} |
| * @param x2 the X coordinate used to set the end point |
| * of this {@code CubicCurve2D} |
| * @param y2 the Y coordinate used to set the end point |
| * of this {@code CubicCurve2D} |
| * @since 1.2 |
| */ |
| public abstract void setCurve(double x1, double y1, |
| double ctrlx1, double ctrly1, |
| double ctrlx2, double ctrly2, |
| double x2, double y2); |
| |
| /** |
| * Sets the location of the end points and control points of this curve |
| * to the double coordinates at the specified offset in the specified |
| * array. |
| * @param coords a double array containing coordinates |
| * @param offset the index of <code>coords</code> from which to begin |
| * setting the end points and control points of this curve |
| * to the coordinates contained in <code>coords</code> |
| * @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</code> coordinates. |
| * @param p1 the first specified <code>Point2D</code> used to set the |
| * start point of this curve |
| * @param cp1 the second specified <code>Point2D</code> used to set the |
| * first control point of this curve |
| * @param cp2 the third specified <code>Point2D</code> used to set the |
| * second control point of this curve |
| * @param p2 the fourth specified <code>Point2D</code> 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</code> objects at the specified |
| * offset in the specified array. |
| * @param pts an array of <code>Point2D</code> objects |
| * @param offset the index of <code>pts</code> from which to begin setting |
| * the end points and control points of this curve to the |
| * points contained in <code>pts</code> |
| * @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</code>. |
| * @param c the specified <code>CubicCurve2D</code> |
| * @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</code> from which to begin |
| * getting the end points and control points of the curve |
| * @return the square of the flatness of the <code>CubicCurve2D</code> |
| * specified by the coordinates in <code>coords</code> 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</code> from which to begin |
| * getting the end points and control points of the curve |
| * @return the flatness of the <code>CubicCurve2D</code> |
| * specified by the coordinates in <code>coords</code> 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</code> parameter |
| * and stores the resulting two subdivided curves into the |
| * <code>left</code> and <code>right</code> curve parameters. |
| * Either or both of the <code>left</code> and <code>right</code> objects |
| * may be the same as the <code>src</code> object or <code>null</code>. |
| * @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</code> array at indices <code>srcoff</code> |
| * through (<code>srcoff</code> + 7) and stores the |
| * resulting two subdivided curves into the two result arrays at the |
| * corresponding indices. |
| * Either or both of the <code>left</code> and <code>right</code> |
| * arrays may be <code>null</code> or a reference to the same array |
| * as the <code>src</code> 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</code> |
| * and <code>right</code> and to use offsets, such as <code>rightoff</code> |
| * equals (<code>leftoff</code> + 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</code> |
| * 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</code> |
| * array and place the non-complex roots into the <code>res</code> |
| * 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 Numerical Recipes, 5.6, Quadratic and Cubic Equations |
| double d = eqn[3]; |
| if (d == 0.0) { |
| // The cubic has degenerated to quadratic (or line or ...). |
| return QuadCurve2D.solveQuadratic(eqn, res); |
| } |
| double a = eqn[2] / d; |
| double b = eqn[1] / d; |
| double c = eqn[0] / d; |
| int roots = 0; |
| double Q = (a * a - 3.0 * b) / 9.0; |
| double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0; |
| double R2 = R * R; |
| double Q3 = Q * Q * Q; |
| a = a / 3.0; |
| if (R2 < Q3) { |
| double theta = Math.acos(R / Math.sqrt(Q3)); |
| Q = -2.0 * Math.sqrt(Q); |
| if (res == eqn) { |
| // Copy the eqn so that we don't clobber it with the |
| // roots. This is needed so that fixRoots can do its |
| // work with the original equation. |
| eqn = new double[4]; |
| System.arraycopy(res, 0, eqn, 0, 4); |
| } |
| res[roots++] = Q * Math.cos(theta / 3.0) - a; |
| res[roots++] = Q * Math.cos((theta + Math.PI * 2.0)/ 3.0) - a; |
| res[roots++] = Q * Math.cos((theta - Math.PI * 2.0)/ 3.0) - a; |
| fixRoots(res, eqn); |
| } else { |
| boolean neg = (R < 0.0); |
| double S = Math.sqrt(R2 - Q3); |
| if (neg) { |
| R = -R; |
| } |
| double A = Math.pow(R + S, 1.0 / 3.0); |
| if (!neg) { |
| A = -A; |
| } |
| double B = (A == 0.0) ? 0.0 : (Q / A); |
| res[roots++] = (A + B) - a; |
| } |
| return roots; |
| } |
| |
| /* |
| * This pruning step is necessary since solveCubic uses the |
| * cosine function to calculate the roots when there are 3 |
| * of them. Since the cosine method can have an error of |
| * +/- 1E-14 we need to make sure that we don't make any |
| * bad decisions due to an error. |
| * |
| * If the root is not near one of the endpoints, then we will |
| * only have a slight inaccuracy in calculating the x intercept |
| * which will only cause a slightly wrong answer for some |
| * points very close to the curve. While the results in that |
| * case are not as accurate as they could be, they are not |
| * disastrously inaccurate either. |
| * |
| * On the other hand, if the error happens near one end of |
| * the curve, then our processing to reject values outside |
| * of the t=[0,1] range will fail and the results of that |
| * failure will be disastrous since for an entire horizontal |
| * range of test points, we will either overcount or undercount |
| * the crossings and get a wrong answer for all of them, even |
| * when they are clearly and obviously inside or outside the |
| * curve. |
| * |
| * To work around this problem, we try a couple of Newton-Raphson |
| * iterations to see if the true root is closer to the endpoint |
| * or further away. If it is further away, then we can stop |
| * since we know we are on the right side of the endpoint. If |
| * we change direction, then either we are now being dragged away |
| * from the endpoint in which case the first condition will cause |
| * us to stop, or we have passed the endpoint and are headed back. |
| * In the second case, we simply evaluate the slope at the |
| * endpoint itself and place ourselves on the appropriate side |
| * of it or on it depending on that result. |
| */ |
| private static void fixRoots(double res[], double eqn[]) { |
| final double EPSILON = 1E-5; |
| for (int i = 0; i < 3; i++) { |
| double t = res[i]; |
| if (Math.abs(t) < EPSILON) { |
| res[i] = findZero(t, 0, eqn); |
| } else if (Math.abs(t - 1) < EPSILON) { |
| res[i] = findZero(t, 1, eqn); |
| } |
| } |
| } |
| |
| private static double solveEqn(double eqn[], int order, double t) { |
| double v = eqn[order]; |
| while (--order >= 0) { |
| v = v * t + eqn[order]; |
| } |
| return v; |
| } |
| |
| private static double findZero(double t, double target, double eqn[]) { |
| double slopeqn[] = {eqn[1], 2*eqn[2], 3*eqn[3]}; |
| double slope; |
| double origdelta = 0; |
| double origt = t; |
| while (true) { |
| slope = solveEqn(slopeqn, 2, t); |
| if (slope == 0) { |
| // At a local minima - must return |
| return t; |
| } |
| double y = solveEqn(eqn, 3, t); |
| if (y == 0) { |
| // Found it! - return it |
| return t; |
| } |
| // assert(slope != 0 && y != 0); |
| double delta = - (y / slope); |
| // assert(delta != 0); |
| if (origdelta == 0) { |
| origdelta = delta; |
| } |
| if (t < target) { |
| if (delta < 0) return t; |
| } else if (t > target) { |
| if (delta > 0) return t; |
| } else { /* t == target */ |
| return (delta > 0 |
| ? (target + java.lang.Double.MIN_VALUE) |
| : (target - java.lang.Double.MIN_VALUE)); |
| } |
| double newt = t + delta; |
| if (t == newt) { |
| // The deltas are so small that we aren't moving... |
| return t; |
| } |
| if (delta * origdelta < 0) { |
| // We have reversed our path. |
| int tag = (origt < t |
| ? getTag(target, origt, t) |
| : getTag(target, t, origt)); |
| if (tag != INSIDE) { |
| // Local minima found away from target - return the middle |
| return (origt + t) / 2; |
| } |
| // Local minima somewhere near target - move to target |
| // and let the slope determine the resulting t. |
| t = target; |
| } else { |
| t = newt; |
| } |
| } |
| } |
| |
| /** |
| * {@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()); |
| } |
| |
| /* |
| * Fill an array with the coefficients of the parametric equation |
| * in t, ready for solving against val with solveCubic. |
| * We currently have: |
| * <pre> |
| * val = P(t) = C1(1-t)^3 + 3CP1 t(1-t)^2 + 3CP2 t^2(1-t) + C2 t^3 |
| * = C1 - 3C1t + 3C1t^2 - C1t^3 + |
| * 3CP1t - 6CP1t^2 + 3CP1t^3 + |
| * 3CP2t^2 - 3CP2t^3 + |
| * C2t^3 |
| * 0 = (C1 - val) + |
| * (3CP1 - 3C1) t + |
| * (3C1 - 6CP1 + 3CP2) t^2 + |
| * (C2 - 3CP2 + 3CP1 - C1) t^3 |
| * 0 = C + Bt + At^2 + Dt^3 |
| * C = C1 - val |
| * B = 3*CP1 - 3*C1 |
| * A = 3*CP2 - 6*CP1 + 3*C1 |
| * D = C2 - 3*CP2 + 3*CP1 - C1 |
| * </pre> |
| */ |
| private static void fillEqn(double eqn[], double val, |
| double c1, double cp1, double cp2, double c2) { |
| eqn[0] = c1 - val; |
| eqn[1] = (cp1 - c1) * 3.0; |
| eqn[2] = (cp2 - cp1 - cp1 + c1) * 3.0; |
| eqn[3] = c2 + (cp1 - cp2) * 3.0 - c1; |
| 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 |
| * cubic equation are also ignored. |
| */ |
| private static int evalCubic(double vals[], int num, |
| boolean include0, |
| boolean include1, |
| double inflect[], |
| double c1, double cp1, |
| double cp2, 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] + 3*inflect[3]*t)*t != 0)) |
| { |
| double u = 1 - t; |
| vals[j++] = c1*u*u*u + 3*cp1*t*u*u + 3*cp2*t*t*u + c2*t*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-existant 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 ctrlx1 = getCtrlX1(); |
| double ctrly1 = getCtrlY1(); |
| double ctrlx2 = getCtrlX2(); |
| double ctrly2 = getCtrlY2(); |
| int ctrlx1tag = getTag(ctrlx1, x, x+w); |
| int ctrly1tag = getTag(ctrly1, y, y+h); |
| int ctrlx2tag = getTag(ctrlx2, x, x+w); |
| int ctrly2tag = getTag(ctrly2, y, y+h); |
| |
| // Trivially reject if all points are entirely to one side of |
| // the rectangle. |
| if (x1tag < INSIDE && x2tag < INSIDE && |
| ctrlx1tag < INSIDE && ctrlx2tag < INSIDE) |
| { |
| return false; // All points left |
| } |
| if (y1tag < INSIDE && y2tag < INSIDE && |
| ctrly1tag < INSIDE && ctrly2tag < INSIDE) |
| { |
| return false; // All points above |
| } |
| if (x1tag > INSIDE && x2tag > INSIDE && |
| ctrlx1tag > INSIDE && ctrlx2tag > INSIDE) |
| { |
| return false; // All points right |
| } |
| if (y1tag > INSIDE && y2tag > INSIDE && |
| ctrly1tag > INSIDE && ctrly2tag > 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, ctrlx1tag) && |
| inwards(y1tag, y2tag, ctrly1tag)) |
| { |
| // First endpoint on border with either edge moving inside |
| return true; |
| } |
| if (inwards(x2tag, x1tag, ctrlx2tag) && |
| inwards(y2tag, y1tag, ctrly2tag)) |
| { |
| // 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 4 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[4]; |
| double[] res = new double[4]; |
| 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, ctrly1, ctrly2, y2); |
| int num = solveCubic(eqn, res); |
| num = evalCubic(res, num, true, true, null, |
| x1, ctrlx1, ctrlx2, x2); |
| // odd counts imply the crossing was out of [0,1] bounds |
| // otherwise there is no way for that part of the curve to |
| // "return" to meet its endpoint |
| return (num == 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, ctrlx1, ctrlx2, x2); |
| int num = solveCubic(eqn, res); |
| num = evalCubic(res, num, true, true, null, |
| y1, ctrly1, ctrly2, y2); |
| // odd counts imply the crossing was out of [0,1] bounds |
| // otherwise there is no way for that part of the curve to |
| // "return" to meet its endpoint |
| return (num == 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 may |
| // get one or three intersections of the curve with the vertical |
| // side of the rectangle. This is because the endpoint segment |
| // accounts for the other intersection in an even pairing. Thus, |
| // with the endpoint crossing we end up with 2 or 4 total crossings. |
| // |
| // (Remember there is overlap in both the X and Y ranges which |
| // means that the segment itself must cross at least one vertical |
| // edge of the rectangle - in particular, the "near vertical side" |
| // - leaving an odd number of intersections for the curve.) |
| // |
| // Now we calculate the y tags of all the intersections on the |
| // "near vertical side" of the rectangle. We will have one with |
| // the endpoint segment, and one or three with the curve. If |
| // any pair of those 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); |
| |
| // Now we have to calculate an array of solutions of the curve |
| // with the "near vertical side" of the rectangle. Then we |
| // need to sort the tags and do a pairwise range test to see |
| // if either of the pairs of crossings spans the Y range of |
| // the rectangle. |
| // |
| // Note that the c2tag can still tell us which vertical edge |
| // to test against. |
| fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2); |
| int num = solveCubic(eqn, res); |
| num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2); |
| |
| // Now put all of the tags into a bucket and sort them. There |
| // is an intersection iff one of the pairs of tags "spans" the |
| // Y range of the rectangle. |
| int tags[] = new int[num+1]; |
| for (int i = 0; i < num; i++) { |
| tags[i] = getTag(res[i], y, y+h); |
| } |
| tags[num] = c1tag; |
| Arrays.sort(tags); |
| return ((num >= 1 && tags[0] * tags[1] <= 0) || |
| (num >= 3 && tags[2] * tags[3] <= 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: Cubic curves closed by connecting their |
| // endpoints form either one or two convex halves with |
| // the closing line segment as an edge of both sides. |
| if (!(contains(x, y) && |
| contains(x + w, y) && |
| contains(x + w, y + h) && |
| contains(x, y + h))) { |
| return false; |
| } |
| // Either the rectangle is entirely inside one of the convex |
| // halves or it crosses from one to the other, in which case |
| // it must intersect the closing line segment. |
| Rectangle2D rect = new Rectangle2D.Double(x, y, w, h); |
| return !rect.intersectsLine(getX1(), getY1(), getX2(), getY2()); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public boolean contains(Rectangle2D r) { |
| return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight()); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * @since 1.2 |
| */ |
| public Rectangle getBounds() { |
| return getBounds2D().getBounds(); |
| } |
| |
| /** |
| * Returns an iteration object that defines the boundary of the |
| * shape. |
| * The iterator for this class is not multi-threaded safe, |
| * which means that this <code>CubicCurve2D</code> class does not |
| * guarantee that modifications to the geometry of this |
| * <code>CubicCurve2D</code> object do not affect any iterations of |
| * that geometry that are already in process. |
| * @param at an optional <code>AffineTransform</code> to be applied to the |
| * coordinates as they are returned in the iteration, or <code>null</code> |
| * if untransformed coordinates are desired |
| * @return the <code>PathIterator</code> object that returns the |
| * geometry of the outline of this <code>CubicCurve2D</code>, 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</code> class does not |
| * guarantee that modifications to the geometry of this |
| * <code>CubicCurve2D</code> object do not affect any iterations of |
| * that geometry that are already in process. |
| * @param at an optional <code>AffineTransform</code> to be applied to the |
| * coordinates as they are returned in the iteration, or <code>null</code> |
| * 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</code> object that returns the |
| * geometry of the outline of this <code>CubicCurve2D</code>, |
| * one segment at a time. |
| * @since 1.2 |
| */ |
| public PathIterator getPathIterator(AffineTransform at, double flatness) { |
| return new FlatteningPathIterator(getPathIterator(at), flatness); |
| } |
| |
| /** |
| * Creates a new object of the same class as this object. |
| * |
| * @return a clone of this instance. |
| * @exception OutOfMemoryError if there is not enough memory. |
| * @see java.lang.Cloneable |
| * @since 1.2 |
| */ |
| public Object clone() { |
| try { |
| return super.clone(); |
| } catch (CloneNotSupportedException e) { |
| // this shouldn't happen, since we are Cloneable |
| throw new InternalError(); |
| } |
| } |
| } |
