https://openjdk.java.net/ 
/*
 * Copyright (c) 1997, 2011, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.awt.geom;

import java.awt.Shape;
import java.awt.Rectangle;
import java.util.Arrays;
import java.io.Serializable;
import sun.awt.geom.Curve;

import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.ulp;


The CubicCurve2D class defines a cubic parametric curve segment in (x,y) coordinate space. 

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
/**
 * The {@code CubicCurve2D} class defines a cubic parametric curve
 * segment in {@code (x,y)} coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects which
 * store a 2D cubic curve segment.
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @author      Jim Graham
 * @since 1.2
 */
public abstract class CubicCurve2D implements Shape, Cloneable {

    
A cubic parametric curve segment specified with float coordinates. 
Since:1.2
/**
     * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * Constructs and initializes a CubicCurve with coordinates
         * (0, 0, 0, 0, 0, 0, 0, 0).
         * @since 1.2
         */
        public Float() {
        }

        
Constructs and initializes a CubicCurve2D from the specified float coordinates. 
Params:
  • x1 – the X coordinate for the start point of the resulting CubicCurve2D
  • y1 – the Y coordinate for the start point of the resulting CubicCurve2D
  • ctrlx1 – the X coordinate for the first control point of the resulting CubicCurve2D
  • ctrly1 – the Y coordinate for the first control point of the resulting CubicCurve2D
  • ctrlx2 – the X coordinate for the second control point of the resulting CubicCurve2D
  • ctrly2 – the Y coordinate for the second control point of the resulting CubicCurve2D
  • x2 – the X coordinate for the end point of the resulting CubicCurve2D
  • y2 – the Y coordinate for the end point of the resulting CubicCurve2D
Since:1.2
/**
         * 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
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getX1() {
            return (double) x1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getY1() {
            return (double) y1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getP1() {
            return new Point2D.Float(x1, y1);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlX1() {
            return (double) ctrlx1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlY1() {
            return (double) ctrly1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getCtrlP1() {
            return new Point2D.Float(ctrlx1, ctrly1);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlX2() {
            return (double) ctrlx2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlY2() {
            return (double) ctrly2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getCtrlP2() {
            return new Point2D.Float(ctrlx2, ctrly2);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getX2() {
            return (double) x2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getY2() {
            return (double) y2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getP2() {
            return new Point2D.Float(x2, y2);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@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 float coordinates. 
Params:
  • x1 – the X coordinate used to set the start point of this CubicCurve2D
  • y1 – the Y coordinate used to set the start point of this CubicCurve2D
  • ctrlx1 – the X coordinate used to set the first control point of this CubicCurve2D
  • ctrly1 – the Y coordinate used to set the first control point of this CubicCurve2D
  • ctrlx2 – the X coordinate used to set the second control point of this CubicCurve2D
  • ctrly2 – the Y coordinate used to set the second control point of this CubicCurve2D
  • x2 – the X coordinate used to set the end point of this CubicCurve2D
  • y2 – the Y coordinate used to set the end point of this CubicCurve2D
Since:1.2
/**
         * 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
/**
         * {@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 double coordinates. 
Since:1.2
/**
     * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * 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
/**
         * Constructs and initializes a CubicCurve with coordinates
         * (0, 0, 0, 0, 0, 0, 0, 0).
         * @since 1.2
         */
        public Double() {
        }

        
Constructs and initializes a CubicCurve2D from the specified double coordinates. 
Params:
  • x1 – the X coordinate for the start point of the resulting CubicCurve2D
  • y1 – the Y coordinate for the start point of the resulting CubicCurve2D
  • ctrlx1 – the X coordinate for the first control point of the resulting CubicCurve2D
  • ctrly1 – the Y coordinate for the first control point of the resulting CubicCurve2D
  • ctrlx2 – the X coordinate for the second control point of the resulting CubicCurve2D
  • ctrly2 – the Y coordinate for the second control point of the resulting CubicCurve2D
  • x2 – the X coordinate for the end point of the resulting CubicCurve2D
  • y2 – the Y coordinate for the end point of the resulting CubicCurve2D
Since:1.2
/**
         * 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
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getX1() {
            return x1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getY1() {
            return y1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getP1() {
            return new Point2D.Double(x1, y1);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlX1() {
            return ctrlx1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlY1() {
            return ctrly1;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getCtrlP1() {
            return new Point2D.Double(ctrlx1, ctrly1);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlX2() {
            return ctrlx2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getCtrlY2() {
            return ctrly2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getCtrlP2() {
            return new Point2D.Double(ctrlx2, ctrly2);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getX2() {
            return x2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getY2() {
            return y2;
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@inheritDoc}
         * @since 1.2
         */
        public Point2D getP2() {
            return new Point2D.Double(x2, y2);
        }

        
{@inheritDoc}

Since:1.2
/**
         * {@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
/**
         * {@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 Also:
Since:1.2
/**
     * 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.

Returns:the X coordinate of the start point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the Y coordinate of the start point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:a Point2D that is the start point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the X coordinate of the first control point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the Y coordinate of the first control point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:a Point2D that is the first control point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the X coordinate of the second control point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the Y coordinate of the second control point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:a Point2D that is the second control point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the X coordinate of the end point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:the Y coordinate of the end point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Returns:a Point2D that is the end point of the CubicCurve2D.
Since:1.2
/**
     * 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.

Params:
  • x1 – the X coordinate used to set the start point of this CubicCurve2D
  • y1 – the Y coordinate used to set the start point of this CubicCurve2D
  • ctrlx1 – the X coordinate used to set the first control point of this CubicCurve2D
  • ctrly1 – the Y coordinate used to set the first control point of this CubicCurve2D
  • ctrlx2 – the X coordinate used to set the second control point of this CubicCurve2D
  • ctrly2 – the Y coordinate used to set the second control point of this CubicCurve2D
  • x2 – the X coordinate used to set the end point of this CubicCurve2D
  • y2 – the Y coordinate used to set the end point of this CubicCurve2D
Since:1.2
/**
     * 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.

Params:
  • coords – a double array containing coordinates
  • offset – the index of coords from which to begin setting the end points and control points of this curve to the coordinates contained in coords
Since:1.2
/**
     * Sets the location of the end points and control points of this curve
     * to the double coordinates at the specified offset in the specified
     * array.
     * @param coords a double array containing coordinates
     * @param offset the index of {@code coords} from which to begin
     *          setting the end points and control points of this curve
     *          to the coordinates contained in {@code coords}
     * @since 1.2
     */
    public void setCurve(double[] coords, int offset) {
        setCurve(coords[offset + 0], coords[offset + 1],
                 coords[offset + 2], coords[offset + 3],
                 coords[offset + 4], coords[offset + 5],
                 coords[offset + 6], coords[offset + 7]);
    }

    
Sets the location of the end points and control points of this curve to the specified Point2D coordinates. 
Params:
  • p1 – the first specified Point2D used to set the start point of this curve
  • cp1 – the second specified Point2D used to set the first control point of this curve
  • cp2 – the third specified Point2D used to set the second control point of this curve
  • p2 – the fourth specified Point2D used to set the end point of this curve
Since:1.2
/**
     * Sets the location of the end points and control points of this curve
     * to the specified {@code Point2D} coordinates.
     * @param p1 the first specified {@code Point2D} used to set the
     *          start point of this curve
     * @param cp1 the second specified {@code Point2D} used to set the
     *          first control point of this curve
     * @param cp2 the third specified {@code Point2D} used to set the
     *          second control point of this curve
     * @param p2 the fourth specified {@code Point2D} used to set the
     *          end point of this curve
     * @since 1.2
     */
    public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) {
        setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(),
                 cp2.getX(), cp2.getY(), p2.getX(), p2.getY());
    }

    
Sets the location of the end points and control points of this curve to the coordinates of the Point2D objects at the specified offset in the specified array. 
Params:
  • pts – an array of Point2D objects
  • offset –  the index of pts from which to begin setting the end points and control points of this curve to the points contained in pts
Since:1.2
/**
     * Sets the location of the end points and control points of this curve
     * to the coordinates of the {@code Point2D} objects at the specified
     * offset in the specified array.
     * @param pts an array of {@code Point2D} objects
     * @param offset  the index of {@code pts} from which to begin setting
     *          the end points and control points of this curve to the
     *          points contained in {@code pts}
     * @since 1.2
     */
    public void setCurve(Point2D[] pts, int offset) {
        setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
                 pts[offset + 1].getX(), pts[offset + 1].getY(),
                 pts[offset + 2].getX(), pts[offset + 2].getY(),
                 pts[offset + 3].getX(), pts[offset + 3].getY());
    }

    
Sets the location of the end points and control points of this curve to the same as those in the specified CubicCurve2D. 
Params:
  • c – the specified CubicCurve2D
Since:1.2
/**
     * Sets the location of the end points and control points of this curve
     * to the same as those in the specified {@code CubicCurve2D}.
     * @param c the specified {@code CubicCurve2D}
     * @since 1.2
     */
    public void setCurve(CubicCurve2D c) {
        setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
                 c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
    }

    
Returns the square of the flatness of the cubic curve specified
by the indicated control points. The flatness is the maximum distance
of a control point from the line connecting the end points.

Params:
  • x1 – the X coordinate that specifies the start point of a CubicCurve2D
  • y1 – the Y coordinate that specifies the start point of a CubicCurve2D
  • ctrlx1 – the X coordinate that specifies the first control point of a CubicCurve2D
  • ctrly1 – the Y coordinate that specifies the first control point of a CubicCurve2D
  • ctrlx2 – the X coordinate that specifies the second control point of a CubicCurve2D
  • ctrly2 – the Y coordinate that specifies the second control point of a CubicCurve2D
  • x2 – the X coordinate that specifies the end point of a CubicCurve2D
  • y2 – the Y coordinate that specifies the end point of a CubicCurve2D
Returns:the square of the flatness of the CubicCurve2D represented by the specified coordinates.
Since:1.2
/**
     * 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.

Params:
  • x1 – the X coordinate that specifies the start point of a CubicCurve2D
  • y1 – the Y coordinate that specifies the start point of a CubicCurve2D
  • ctrlx1 – the X coordinate that specifies the first control point of a CubicCurve2D
  • ctrly1 – the Y coordinate that specifies the first control point of a CubicCurve2D
  • ctrlx2 – the X coordinate that specifies the second control point of a CubicCurve2D
  • ctrly2 – the Y coordinate that specifies the second control point of a CubicCurve2D
  • x2 – the X coordinate that specifies the end point of a CubicCurve2D
  • y2 – the Y coordinate that specifies the end point of a CubicCurve2D
Returns:the flatness of the CubicCurve2D represented by the specified coordinates.
Since:1.2
/**
     * 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.

Params:
  • coords – an array containing coordinates
  • offset – the index of coords from which to begin getting the end points and control points of the curve
Returns:the square of the flatness of the CubicCurve2D specified by the coordinates in coords at the specified offset.
Since:1.2
/**
     * Returns the square of the flatness of the cubic curve specified
     * by the control points stored in the indicated array at the
     * indicated index. The flatness is the maximum distance
     * of a control point from the line connecting the end points.
     * @param coords an array containing coordinates
     * @param offset the index of {@code coords} from which to begin
     *          getting the end points and control points of the curve
     * @return the square of the flatness of the {@code CubicCurve2D}
     *          specified by the coordinates in {@code coords} at
     *          the specified offset.
     * @since 1.2
     */
    public static double getFlatnessSq(double coords[], int offset) {
        return getFlatnessSq(coords[offset + 0], coords[offset + 1],
                             coords[offset + 2], coords[offset + 3],
                             coords[offset + 4], coords[offset + 5],
                             coords[offset + 6], coords[offset + 7]);
    }

    
Returns the flatness of the cubic curve specified
by the control points stored in the indicated array at the
indicated index.  The flatness is the maximum distance
of a control point from the line connecting the end points.

Params:
  • coords – an array containing coordinates
  • offset – the index of coords from which to begin getting the end points and control points of the curve
Returns:the flatness of the CubicCurve2D specified by the coordinates in coords at the specified offset.
Since:1.2
/**
     * Returns the flatness of the cubic curve specified
     * by the control points stored in the indicated array at the
     * indicated index.  The flatness is the maximum distance
     * of a control point from the line connecting the end points.
     * @param coords an array containing coordinates
     * @param offset the index of {@code coords} from which to begin
     *          getting the end points and control points of the curve
     * @return the flatness of the {@code CubicCurve2D}
     *          specified by the coordinates in {@code coords} at
     *          the specified offset.
     * @since 1.2
     */
    public static double getFlatness(double coords[], int offset) {
        return getFlatness(coords[offset + 0], coords[offset + 1],
                           coords[offset + 2], coords[offset + 3],
                           coords[offset + 4], coords[offset + 5],
                           coords[offset + 6], coords[offset + 7]);
    }

    
Returns the square of the flatness of this curve.  The flatness is the
maximum distance of a control point from the line connecting the
end points.

Returns:the square of the flatness of this curve.
Since:1.2
/**
     * 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.

Returns:the flatness of this curve.
Since:1.2
/**
     * 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.

Params:
  • left – the cubic curve object for storing for the left or
first half of the subdivided curve
  • right – the cubic curve object for storing for the right or
second half of the subdivided curve
Since:1.2
/**
     * 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 src parameter 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 the src object or null. 
Params:
  • src – the cubic curve to be subdivided
  • left – the cubic curve object for storing the left or
first half of the subdivided curve
  • right – the cubic curve object for storing the right or
second half of the subdivided curve
Since:1.2
/**
     * Subdivides the cubic curve specified by the {@code src} parameter
     * and stores the resulting two subdivided curves into the
     * {@code left} and {@code right} curve parameters.
     * Either or both of the {@code left} and {@code right} objects
     * may be the same as the {@code src} object or {@code null}.
     * @param src the cubic curve to be subdivided
     * @param left the cubic curve object for storing the left or
     * first half of the subdivided curve
     * @param right the cubic curve object for storing the right or
     * second half of the subdivided curve
     * @since 1.2
     */
    public static void subdivide(CubicCurve2D src,
                                 CubicCurve2D left,
                                 CubicCurve2D right) {
        double x1 = src.getX1();
        double y1 = src.getY1();
        double ctrlx1 = src.getCtrlX1();
        double ctrly1 = src.getCtrlY1();
        double ctrlx2 = src.getCtrlX2();
        double ctrly2 = src.getCtrlY2();
        double x2 = src.getX2();
        double y2 = src.getY2();
        double centerx = (ctrlx1 + ctrlx2) / 2.0;
        double centery = (ctrly1 + ctrly2) / 2.0;
        ctrlx1 = (x1 + ctrlx1) / 2.0;
        ctrly1 = (y1 + ctrly1) / 2.0;
        ctrlx2 = (x2 + ctrlx2) / 2.0;
        ctrly2 = (y2 + ctrly2) / 2.0;
        double ctrlx12 = (ctrlx1 + centerx) / 2.0;
        double ctrly12 = (ctrly1 + centery) / 2.0;
        double ctrlx21 = (ctrlx2 + centerx) / 2.0;
        double ctrly21 = (ctrly2 + centery) / 2.0;
        centerx = (ctrlx12 + ctrlx21) / 2.0;
        centery = (ctrly12 + ctrly21) / 2.0;
        if (left != null) {
            left.setCurve(x1, y1, ctrlx1, ctrly1,
                          ctrlx12, ctrly12, centerx, centery);
        }
        if (right != null) {
            right.setCurve(centerx, centery, ctrlx21, ctrly21,
                           ctrlx2, ctrly2, x2, y2);
        }
    }

    
Subdivides the cubic curve specified by the coordinates stored in the src array at indices srcoff through (srcoff + 7) and stores the resulting two subdivided curves into the two result arrays at the corresponding indices. Either or both of the left and right arrays may be null or a reference to the same array as the 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 left and right and to use offsets, such as rightoff equals (leftoff + 6), in order to avoid allocating extra storage for this common point. 
Params:
  • src – the array holding the coordinates for the source curve
  • srcoff – the offset into the array of the beginning of the
the 6 source coordinates
  • left – the array for storing the coordinates for the first
half of the subdivided curve
  • leftoff – the offset into the array of the beginning of the
the 6 left coordinates
  • right – the array for storing the coordinates for the second
half of the subdivided curve
  • rightoff – the offset into the array of the beginning of the
the 6 right coordinates
Since:1.2
/**
     * Subdivides the cubic curve specified by the coordinates
     * stored in the {@code src} array at indices {@code srcoff}
     * through ({@code srcoff}&nbsp;+&nbsp;7) and stores the
     * resulting two subdivided curves into the two result arrays at the
     * corresponding indices.
     * Either or both of the {@code left} and {@code right}
     * arrays may be {@code null} or a reference to the same array
     * as the {@code src} array.
     * Note that the last point in the first subdivided curve is the
     * same as the first point in the second subdivided curve. Thus,
     * it is possible to pass the same array for {@code left}
     * and {@code right} and to use offsets, such as {@code rightoff}
     * equals ({@code leftoff} + 6), in order
     * to avoid allocating extra storage for this common point.
     * @param src the array holding the coordinates for the source curve
     * @param srcoff the offset into the array of the beginning of the
     * the 6 source coordinates
     * @param left the array for storing the coordinates for the first
     * half of the subdivided curve
     * @param leftoff the offset into the array of the beginning of the
     * the 6 left coordinates
     * @param right the array for storing the coordinates for the second
     * half of the subdivided curve
     * @param rightoff the offset into the array of the beginning of the
     * the 6 right coordinates
     * @since 1.2
     */
    public static void subdivide(double src[], int srcoff,
                                 double left[], int leftoff,
                                 double right[], int rightoff) {
        double x1 = src[srcoff + 0];
        double y1 = src[srcoff + 1];
        double ctrlx1 = src[srcoff + 2];
        double ctrly1 = src[srcoff + 3];
        double ctrlx2 = src[srcoff + 4];
        double ctrly2 = src[srcoff + 5];
        double x2 = src[srcoff + 6];
        double y2 = src[srcoff + 7];
        if (left != null) {
            left[leftoff + 0] = x1;
            left[leftoff + 1] = y1;
        }
        if (right != null) {
            right[rightoff + 6] = x2;
            right[rightoff + 7] = y2;
        }
        x1 = (x1 + ctrlx1) / 2.0;
        y1 = (y1 + ctrly1) / 2.0;
        x2 = (x2 + ctrlx2) / 2.0;
        y2 = (y2 + ctrly2) / 2.0;
        double centerx = (ctrlx1 + ctrlx2) / 2.0;
        double centery = (ctrly1 + ctrly2) / 2.0;
        ctrlx1 = (x1 + centerx) / 2.0;
        ctrly1 = (y1 + centery) / 2.0;
        ctrlx2 = (x2 + centerx) / 2.0;
        ctrly2 = (y2 + centery) / 2.0;
        centerx = (ctrlx1 + ctrlx2) / 2.0;
        centery = (ctrly1 + ctrly2) / 2.0;
        if (left != null) {
            left[leftoff + 2] = x1;
            left[leftoff + 3] = y1;
            left[leftoff + 4] = ctrlx1;
            left[leftoff + 5] = ctrly1;
            left[leftoff + 6] = centerx;
            left[leftoff + 7] = centery;
        }
        if (right != null) {
            right[rightoff + 0] = centerx;
            right[rightoff + 1] = centery;
            right[rightoff + 2] = ctrlx2;
            right[rightoff + 3] = ctrly2;
            right[rightoff + 4] = x2;
            right[rightoff + 5] = y2;
        }
    }

    
Solves the cubic whose coefficients are in the eqn array and places the non-complex roots back into the same array, returning the number of roots. The solved cubic is represented by the equation: 
    eqn = {c, b, a, d}
    dx^3 + ax^2 + bx + c = 0


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.

Params:
  • eqn – an array containing coefficients for a cubic
Returns:the number of roots, or -1 if the equation is a constant.
Since:1.2
/**
     * Solves the cubic whose coefficients are in the {@code eqn}
     * array and places the non-complex roots back into the same array,
     * returning the number of roots.  The solved cubic is represented
     * by the equation:
     * <pre>
     *     eqn = {c, b, a, d}
     *     dx^3 + ax^2 + bx + c = 0
     * </pre>
     * A return value of -1 is used to distinguish a constant equation
     * that might be always 0 or never 0 from an equation that has no
     * zeroes.
     * @param eqn an array containing coefficients for a cubic
     * @return the number of roots, or -1 if the equation is a constant.
     * @since 1.2
     */
    public static int solveCubic(double eqn[]) {
        return solveCubic(eqn, eqn);
    }

    
Solve the cubic whose coefficients are in the eqn array and place the non-complex roots into the res array, returning the number of roots. The cubic solved is represented by the equation: eqn = {c, b, a, d} dx^3 + ax^2 + bx + c = 0 A return value of -1 is used to distinguish a constant equation, which may be always 0 or never 0, from an equation which has no zeroes. 
Params:
  • eqn – the specified array of coefficients to use to solve
       the cubic equation
  • res – the array that contains the non-complex roots
       resulting from the solution of the cubic equation
Returns:the number of roots, or -1 if the equation is a constant
Since:1.3
/**
     * Solve the cubic whose coefficients are in the {@code eqn}
     * array and place the non-complex roots into the {@code res}
     * array, returning the number of roots.
     * The cubic solved is represented by the equation:
     *     eqn = {c, b, a, d}
     *     dx^3 + ax^2 + bx + c = 0
     * A return value of -1 is used to distinguish a constant equation,
     * which may be always 0 or never 0, from an equation which has no
     * zeroes.
     * @param eqn the specified array of coefficients to use to solve
     *        the cubic equation
     * @param res the array that contains the non-complex roots
     *        resulting from the solution of the cubic equation
     * @return the number of roots, or -1 if the equation is a constant
     * @since 1.3
     */
    public static int solveCubic(double eqn[], double res[]) {
        // From Graphics Gems:
        // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
        final double d = eqn[3];
        if (d == 0) {
            return QuadCurve2D.solveQuadratic(eqn, res);
        }

        /* normal form: x^3 + Ax^2 + Bx + C = 0 */
        final double A = eqn[2] / d;
        final double B = eqn[1] / d;
        final double C = eqn[0] / d;


        //  substitute x = y - A/3 to eliminate quadratic term:
        //     x^3 +Px + Q = 0
        //
        // Since we actually need P/3 and Q/2 for all of the
        // calculations that follow, we will calculate
        // p = P/3
        // q = Q/2
        // instead and use those values for simplicity of the code.
        double sq_A = A * A;
        double p = 1.0/3 * (-1.0/3 * sq_A + B);
        double q = 1.0/2 * (2.0/27 * A * sq_A - 1.0/3 * A * B + C);

        /* use Cardano's formula */

        double cb_p = p * p * p;
        double D = q * q + cb_p;

        final double sub = 1.0/3 * A;

        int num;
        if (D < 0) { /* Casus irreducibilis: three real solutions */
            // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
            double phi = 1.0/3 * Math.acos(-q / Math.sqrt(-cb_p));
            double t = 2 * Math.sqrt(-p);

            if (res == eqn) {
                eqn = Arrays.copyOf(eqn, 4);
            }

            res[ 0 ] =  ( t * Math.cos(phi));
            res[ 1 ] =  (-t * Math.cos(phi + Math.PI / 3));
            res[ 2 ] =  (-t * Math.cos(phi - Math.PI / 3));
            num = 3;

            for (int i = 0; i < num; ++i) {
                res[ i ] -= sub;
            }

        } else {
            // Please see the comment in fixRoots marked 'XXX' before changing
            // any of the code in this case.
            double sqrt_D = Math.sqrt(D);
            double u = Math.cbrt(sqrt_D - q);
            double v = - Math.cbrt(sqrt_D + q);
            double uv = u+v;

            num = 1;

            double err = 1200000000*ulp(abs(uv) + abs(sub));
            if (iszero(D, err) || within(u, v, err)) {
                if (res == eqn) {
                    eqn = Arrays.copyOf(eqn, 4);
                }
                res[1] = -(uv / 2) - sub;
                num = 2;
            }
            // this must be done after the potential Arrays.copyOf
            res[ 0 ] =  uv - sub;
        }

        if (num > 1) { // num == 3 || num == 2
            num = fixRoots(eqn, res, num);
        }
        if (num > 2 && (res[2] == res[1] || res[2] == res[0])) {
            num--;
        }
        if (num > 1 && res[1] == res[0]) {
            res[1] = res[--num]; // Copies res[2] to res[1] if needed
        }
        return num;
    }

    // preconditions: eqn != res && eqn[3] != 0 && num > 1
    // This method tries to improve the accuracy of the roots of eqn (which
    // should be in res). It also might eliminate roots in res if it decideds
    // that they're not real roots. It will not check for roots that the
    // computation of res might have missed, so this method should only be
    // used when the roots in res have been computed using an algorithm
    // that never underestimates the number of roots (such as solveCubic above)
    private static int fixRoots(double[] eqn, double[] res, int num) {
        double[] intervals = {eqn[1], 2*eqn[2], 3*eqn[3]};
        int critCount = QuadCurve2D.solveQuadratic(intervals, intervals);
        if (critCount == 2 && intervals[0] == intervals[1]) {
            critCount--;
        }
        if (critCount == 2 && intervals[0] > intervals[1]) {
            double tmp = intervals[0];
            intervals[0] = intervals[1];
            intervals[1] = tmp;
        }

        // below we use critCount to possibly filter out roots that shouldn't
        // have been computed. We require that eqn[3] != 0, so eqn is a proper
        // cubic, which means that its limits at -/+inf are -/+inf or +/-inf.
        // Therefore, if critCount==2, the curve is shaped like a sideways S,
        // and it could have 1-3 roots. If critCount==0 it is monotonic, and
        // if critCount==1 it is monotonic with a single point where it is
        // flat. In the last 2 cases there can only be 1 root. So in cases
        // where num > 1 but critCount < 2, we eliminate all roots in res
        // except one.

        if (num == 3) {
            double xe = getRootUpperBound(eqn);
            double x0 = -xe;

            Arrays.sort(res, 0, num);
            if (critCount == 2) {
                // this just tries to improve the accuracy of the computed
                // roots using Newton's method.
                res[0] = refineRootWithHint(eqn, x0, intervals[0], res[0]);
                res[1] = refineRootWithHint(eqn, intervals[0], intervals[1], res[1]);
                res[2] = refineRootWithHint(eqn, intervals[1], xe, res[2]);
                return 3;
            } else if (critCount == 1) {
                // we only need fx0 and fxe for the sign of the polynomial
                // at -inf and +inf respectively, so we don't need to do
                // fx0 = solveEqn(eqn, 3, x0); fxe = solveEqn(eqn, 3, xe)
                double fxe = eqn[3];
                double fx0 = -fxe;

                double x1 = intervals[0];
                double fx1 = solveEqn(eqn, 3, x1);

                // if critCount == 1 or critCount == 0, but num == 3 then
                // something has gone wrong. This branch and the one below
                // would ideally never execute, but if they do we can't know
                // which of the computed roots is closest to the real root;
                // therefore, we can't use refineRootWithHint. But even if
                // we did know, being here most likely means that the
                // curve is very flat close to two of the computed roots
                // (or maybe even all three). This might make Newton's method
                // fail altogether, which would be a pain to detect and fix.
                // This is why we use a very stable bisection method.
                if (oppositeSigns(fx0, fx1)) {
                    res[0] = bisectRootWithHint(eqn, x0, x1, res[0]);
                } else if (oppositeSigns(fx1, fxe)) {
                    res[0] = bisectRootWithHint(eqn, x1, xe, res[2]);
                } else /* fx1 must be 0 */ {
                    res[0] = x1;
                }
                // return 1
            } else if (critCount == 0) {
                res[0] = bisectRootWithHint(eqn, x0, xe, res[1]);
                // return 1
            }
        } else if (num == 2 && critCount == 2) {
            // XXX: here we assume that res[0] has better accuracy than res[1].
            // This is true because this method is only used from solveCubic
            // which puts in res[0] the root that it would compute anyway even
            // if num==1. If this method is ever used from any other method, or
            // if the solveCubic implementation changes, this assumption should
            // be reevaluated, and the choice of goodRoot might have to become
            // goodRoot = (abs(eqn'(res[0])) > abs(eqn'(res[1]))) ? res[0] : res[1]
            // where eqn' is the derivative of eqn.
            double goodRoot = res[0];
            double badRoot = res[1];
            double x1 = intervals[0];
            double x2 = intervals[1];
            // If a cubic curve really has 2 roots, one of those roots must be
            // at a critical point. That can't be goodRoot, so we compute x to
            // be the farthest critical point from goodRoot. If there are two
            // roots, x must be the second one, so we evaluate eqn at x, and if
            // it is zero (or close enough) we put x in res[1] (or badRoot, if
            // |solveEqn(eqn, 3, badRoot)| < |solveEqn(eqn, 3, x)| but this
            // shouldn't happen often).
            double x = abs(x1 - goodRoot) > abs(x2 - goodRoot) ? x1 : x2;
            double fx = solveEqn(eqn, 3, x);

            if (iszero(fx, 10000000*ulp(x))) {
                double badRootVal = solveEqn(eqn, 3, badRoot);
                res[1] = abs(badRootVal) < abs(fx) ? badRoot : x;
                return 2;
            }
        } // else there can only be one root - goodRoot, and it is already in res[0]

        return 1;
    }

    // use newton's method.
    private static double refineRootWithHint(double[] eqn, double min, double max, double t) {
        if (!inInterval(t, min, max)) {
            return t;
        }
        double[] deriv = {eqn[1], 2*eqn[2], 3*eqn[3]};
        double origt = t;
        for (int i = 0; i < 3; i++) {
            double slope = solveEqn(deriv, 2, t);
            double y = solveEqn(eqn, 3, t);
            double delta = - (y / slope);
            double newt = t + delta;

            if (slope == 0 || y == 0 || t == newt) {
                break;
            }

            t = newt;
        }
        if (within(t, origt, 1000*ulp(origt)) && inInterval(t, min, max)) {
            return t;
        }
        return origt;
    }

    private static double bisectRootWithHint(double[] eqn, double x0, double xe, double hint) {
        double delta1 = Math.min(abs(hint - x0) / 64, 0.0625);
        double delta2 = Math.min(abs(hint - xe) / 64, 0.0625);
        double x02 = hint - delta1;
        double xe2 = hint + delta2;
        double fx02 = solveEqn(eqn, 3, x02);
        double fxe2 = solveEqn(eqn, 3, xe2);
        while (oppositeSigns(fx02, fxe2)) {
            if (x02 >= xe2) {
                return x02;
            }
            x0 = x02;
            xe = xe2;
            delta1 /= 64;
            delta2 /= 64;
            x02 = hint - delta1;
            xe2 = hint + delta2;
            fx02 = solveEqn(eqn, 3, x02);
            fxe2 = solveEqn(eqn, 3, xe2);
        }
        if (fx02 == 0) {
            return x02;
        }
        if (fxe2 == 0) {
            return xe2;
        }

        return bisectRoot(eqn, x0, xe);
    }

    private static double bisectRoot(double[] eqn, double x0, double xe) {
        double fx0 = solveEqn(eqn, 3, x0);
        double m = x0 + (xe - x0) / 2;
        while (m != x0 && m != xe) {
            double fm = solveEqn(eqn, 3, m);
            if (fm == 0) {
                return m;
            }
            if (oppositeSigns(fx0, fm)) {
                xe = m;
            } else {
                fx0 = fm;
                x0 = m;
            }
            m = x0 + (xe-x0)/2;
        }
        return m;
    }

    private static boolean inInterval(double t, double min, double max) {
        return min <= t && t <= max;
    }

    private static boolean within(double x, double y, double err) {
        double d = y - x;
        return (d <= err && d >= -err);
    }

    private static boolean iszero(double x, double err) {
        return within(x, 0, err);
    }

    private static boolean oppositeSigns(double x1, double x2) {
        return (x1 < 0 && x2 > 0) || (x1 > 0 && x2 < 0);
    }

    private static double solveEqn(double eqn[], int order, double t) {
        double v = eqn[order];
        while (--order >= 0) {
            v = v * t + eqn[order];
        }
        return v;
    }

    /*
     * Computes M+1 where M is an upper bound for all the roots in of eqn.
     * See: http://en.wikipedia.org/wiki/Sturm%27s_theorem#Applications.
     * The above link doesn't contain a proof, but I [dlila] proved it myself
     * so the result is reliable. The proof isn't difficult, but it's a bit
     * long to include here.
     * Precondition: eqn must represent a cubic polynomial
     */
    private static double getRootUpperBound(double[] eqn) {
        double d = eqn[3];
        double a = eqn[2];
        double b = eqn[1];
        double c = eqn[0];

        double M = 1 + max(max(abs(a), abs(b)), abs(c)) / abs(d);
        M += ulp(M) + 1;
        return M;
    }


    
{@inheritDoc}

Since:1.2
/**
     * {@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
/**
     * {@inheritDoc}
     * @since 1.2
     */
    public boolean contains(Point2D p) {
        return contains(p.getX(), p.getY());
    }

    
{@inheritDoc}

Since:1.2
/**
     * {@inheritDoc}
     * @since 1.2
     */
    public boolean intersects(double x, double y, double w, double h) {
        // Trivially reject non-existant rectangles
        if (w <= 0 || h <= 0) {
            return false;
        }

        int numCrossings = rectCrossings(x, y, w, h);
        // the intended return value is
        // numCrossings != 0 || numCrossings == Curve.RECT_INTERSECTS
        // but if (numCrossings != 0) numCrossings == INTERSECTS won't matter
        // and if !(numCrossings != 0) then numCrossings == 0, so
        // numCrossings != RECT_INTERSECT
        return numCrossings != 0;
    }

    
{@inheritDoc}

Since:1.2
/**
     * {@inheritDoc}
     * @since 1.2
     */
    public boolean intersects(Rectangle2D r) {
        return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    
{@inheritDoc}

Since:1.2
/**
     * {@inheritDoc}
     * @since 1.2
     */
    public boolean contains(double x, double y, double w, double h) {
        if (w <= 0 || h <= 0) {
            return false;
        }

        int numCrossings = rectCrossings(x, y, w, h);
        return !(numCrossings == 0 || numCrossings == Curve.RECT_INTERSECTS);
    }

    private int rectCrossings(double x, double y, double w, double h) {
        int crossings = 0;
        if (!(getX1() == getX2() && getY1() == getY2())) {
            crossings = Curve.rectCrossingsForLine(crossings,
                                                   x, y,
                                                   x+w, y+h,
                                                   getX1(), getY1(),
                                                   getX2(), getY2());
            if (crossings == Curve.RECT_INTERSECTS) {
                return crossings;
            }
        }
        // we call this with the curve's direction reversed, because we wanted
        // to call rectCrossingsForLine first, because it's cheaper.
        return Curve.rectCrossingsForCubic(crossings,
                                           x, y,
                                           x+w, y+h,
                                           getX2(), getY2(),
                                           getCtrlX2(), getCtrlY2(),
                                           getCtrlX1(), getCtrlY1(),
                                           getX1(), getY1(), 0);
    }

    
{@inheritDoc}

Since:1.2
/**
     * {@inheritDoc}
     * @since 1.2
     */
    public boolean contains(Rectangle2D r) {
        return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    
{@inheritDoc}

Since:1.2
/**
     * {@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 CubicCurve2D class does not guarantee that modifications to the geometry of this CubicCurve2D object do not affect any iterations of that geometry that are already in process. 
Params:
  • at – an optional AffineTransform to be applied to the coordinates as they are returned in the iteration, or null if untransformed coordinates are desired
Returns: the PathIterator object that returns the geometry of the outline of this CubicCurve2D, one segment at a time.
Since:1.2
/**
     * Returns an iteration object that defines the boundary of the
     * shape.
     * The iterator for this class is not multi-threaded safe,
     * which means that this {@code CubicCurve2D} class does not
     * guarantee that modifications to the geometry of this
     * {@code CubicCurve2D} object do not affect any iterations of
     * that geometry that are already in process.
     * @param at an optional {@code AffineTransform} to be applied to the
     * coordinates as they are returned in the iteration, or {@code null}
     * if untransformed coordinates are desired
     * @return    the {@code PathIterator} object that returns the
     *          geometry of the outline of this {@code CubicCurve2D}, one
     *          segment at a time.
     * @since 1.2
     */
    public PathIterator getPathIterator(AffineTransform at) {
        return new CubicIterator(this, at);
    }

    
Return an iteration object that defines the boundary of the flattened shape. The iterator for this class is not multi-threaded safe, which means that this CubicCurve2D class does not guarantee that modifications to the geometry of this CubicCurve2D object do not affect any iterations of that geometry that are already in process. 
Params:
  • at – an optional AffineTransform to be applied to the coordinates as they are returned in the iteration, or null if untransformed coordinates are desired
  • 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
Returns: the PathIterator object that returns the geometry of the outline of this CubicCurve2D, one segment at a time.
Since:1.2
/**
     * Return an iteration object that defines the boundary of the
     * flattened shape.
     * The iterator for this class is not multi-threaded safe,
     * which means that this {@code CubicCurve2D} class does not
     * guarantee that modifications to the geometry of this
     * {@code CubicCurve2D} object do not affect any iterations of
     * that geometry that are already in process.
     * @param at an optional {@code AffineTransform} to be applied to the
     * coordinates as they are returned in the iteration, or {@code null}
     * if untransformed coordinates are desired
     * @param flatness the maximum amount that the control points
     * for a given curve can vary from colinear before a subdivided
     * curve is replaced by a straight line connecting the end points
     * @return    the {@code PathIterator} object that returns the
     * geometry of the outline of this {@code CubicCurve2D},
     * one segment at a time.
     * @since 1.2
     */
    public PathIterator getPathIterator(AffineTransform at, double flatness) {
        return new FlatteningPathIterator(getPathIterator(at), flatness);
    }

    
Creates a new object of the same class as this object.

Throws:
See Also:
Returns:    a clone of this instance.
Since:     1.2
/**
     * Creates a new object of the same class as this object.
     *
     * @return     a clone of this instance.
     * @exception  OutOfMemoryError            if there is not enough memory.
     * @see        java.lang.Cloneable
     * @since      1.2
     */
    public Object clone() {
        try {
            return super.clone();
        } catch (CloneNotSupportedException e) {
            // this shouldn't happen, since we are Cloneable
            throw new InternalError(e);
        }
    }
}