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1402 lines
47 KiB
1402 lines
47 KiB
/*
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* Copyright (c) 1997, 2013, Oracle and/or its affiliates. All rights reserved.
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* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*/
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package java.awt.geom;
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import java.awt.Shape;
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import java.awt.Rectangle;
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import java.io.Serializable;
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import sun.awt.geom.Curve;
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/**
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* The <code>QuadCurve2D</code> class defines a quadratic parametric curve
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* segment in {@code (x,y)} coordinate space.
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* <p>
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* This class is only the abstract superclass for all objects that
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* store a 2D quadratic curve segment.
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* The actual storage representation of the coordinates is left to
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* the subclass.
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*
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* @author Jim Graham
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* @since 1.2
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*/
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public abstract class QuadCurve2D implements Shape, Cloneable {
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/**
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* A quadratic parametric curve segment specified with
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* {@code float} coordinates.
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*
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* @since 1.2
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*/
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public static class Float extends QuadCurve2D implements Serializable {
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/**
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* The X coordinate of the start point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public float x1;
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/**
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* The Y coordinate of the start point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public float y1;
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/**
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* The X coordinate of the control point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public float ctrlx;
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/**
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* The Y coordinate of the control point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public float ctrly;
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/**
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* The X coordinate of the end point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public float x2;
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/**
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* The Y coordinate of the end point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public float y2;
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/**
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* Constructs and initializes a <code>QuadCurve2D</code> with
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* coordinates (0, 0, 0, 0, 0, 0).
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* @since 1.2
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*/
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public Float() {
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}
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/**
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* Constructs and initializes a <code>QuadCurve2D</code> from the
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* specified {@code float} coordinates.
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*
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* @param x1 the X coordinate of the start point
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* @param y1 the Y coordinate of the start point
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* @param ctrlx the X coordinate of the control point
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* @param ctrly the Y coordinate of the control point
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* @param x2 the X coordinate of the end point
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* @param y2 the Y coordinate of the end point
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* @since 1.2
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*/
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public Float(float x1, float y1,
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float ctrlx, float ctrly,
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float x2, float y2)
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{
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setCurve(x1, y1, ctrlx, ctrly, x2, y2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getX1() {
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return (double) x1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getY1() {
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return (double) y1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getP1() {
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return new Point2D.Float(x1, y1);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlX() {
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return (double) ctrlx;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlY() {
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return (double) ctrly;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getCtrlPt() {
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return new Point2D.Float(ctrlx, ctrly);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getX2() {
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return (double) x2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getY2() {
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return (double) y2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getP2() {
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return new Point2D.Float(x2, y2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public void setCurve(double x1, double y1,
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double ctrlx, double ctrly,
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double x2, double y2)
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{
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this.x1 = (float) x1;
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this.y1 = (float) y1;
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this.ctrlx = (float) ctrlx;
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this.ctrly = (float) ctrly;
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this.x2 = (float) x2;
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this.y2 = (float) y2;
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}
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/**
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* Sets the location of the end points and control point of this curve
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* to the specified {@code float} coordinates.
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*
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* @param x1 the X coordinate of the start point
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* @param y1 the Y coordinate of the start point
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* @param ctrlx the X coordinate of the control point
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* @param ctrly the Y coordinate of the control point
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* @param x2 the X coordinate of the end point
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* @param y2 the Y coordinate of the end point
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* @since 1.2
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*/
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public void setCurve(float x1, float y1,
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float ctrlx, float ctrly,
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float x2, float y2)
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{
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this.x1 = x1;
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this.y1 = y1;
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this.ctrlx = ctrlx;
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this.ctrly = ctrly;
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this.x2 = x2;
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this.y2 = y2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Rectangle2D getBounds2D() {
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float left = Math.min(Math.min(x1, x2), ctrlx);
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float top = Math.min(Math.min(y1, y2), ctrly);
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float right = Math.max(Math.max(x1, x2), ctrlx);
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float bottom = Math.max(Math.max(y1, y2), ctrly);
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return new Rectangle2D.Float(left, top,
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right - left, bottom - top);
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}
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/*
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* JDK 1.6 serialVersionUID
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*/
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private static final long serialVersionUID = -8511188402130719609L;
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}
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/**
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* A quadratic parametric curve segment specified with
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* {@code double} coordinates.
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*
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* @since 1.2
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*/
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public static class Double extends QuadCurve2D implements Serializable {
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/**
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* The X coordinate of the start point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public double x1;
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/**
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* The Y coordinate of the start point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public double y1;
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/**
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* The X coordinate of the control point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public double ctrlx;
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/**
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* The Y coordinate of the control point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public double ctrly;
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/**
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* The X coordinate of the end point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public double x2;
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/**
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* The Y coordinate of the end point of the quadratic curve
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* segment.
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* @since 1.2
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* @serial
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*/
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public double y2;
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/**
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* Constructs and initializes a <code>QuadCurve2D</code> with
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* coordinates (0, 0, 0, 0, 0, 0).
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* @since 1.2
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*/
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public Double() {
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}
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/**
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* Constructs and initializes a <code>QuadCurve2D</code> from the
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* specified {@code double} coordinates.
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*
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* @param x1 the X coordinate of the start point
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* @param y1 the Y coordinate of the start point
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* @param ctrlx the X coordinate of the control point
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* @param ctrly the Y coordinate of the control point
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* @param x2 the X coordinate of the end point
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* @param y2 the Y coordinate of the end point
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* @since 1.2
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*/
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public Double(double x1, double y1,
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double ctrlx, double ctrly,
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double x2, double y2)
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{
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setCurve(x1, y1, ctrlx, ctrly, x2, y2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getX1() {
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return x1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getY1() {
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return y1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getP1() {
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return new Point2D.Double(x1, y1);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlX() {
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return ctrlx;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlY() {
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return ctrly;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getCtrlPt() {
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return new Point2D.Double(ctrlx, ctrly);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getX2() {
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return x2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getY2() {
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return y2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getP2() {
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return new Point2D.Double(x2, y2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public void setCurve(double x1, double y1,
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double ctrlx, double ctrly,
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double x2, double y2)
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{
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this.x1 = x1;
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this.y1 = y1;
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this.ctrlx = ctrlx;
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this.ctrly = ctrly;
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this.x2 = x2;
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this.y2 = y2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Rectangle2D getBounds2D() {
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double left = Math.min(Math.min(x1, x2), ctrlx);
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double top = Math.min(Math.min(y1, y2), ctrly);
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double right = Math.max(Math.max(x1, x2), ctrlx);
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double bottom = Math.max(Math.max(y1, y2), ctrly);
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return new Rectangle2D.Double(left, top,
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right - left, bottom - top);
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}
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/*
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* JDK 1.6 serialVersionUID
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*/
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private static final long serialVersionUID = 4217149928428559721L;
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}
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/**
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* This is an abstract class that cannot be instantiated directly.
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* Type-specific implementation subclasses are available for
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* instantiation and provide a number of formats for storing
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* the information necessary to satisfy the various accessor
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* methods below.
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*
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* @see java.awt.geom.QuadCurve2D.Float
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* @see java.awt.geom.QuadCurve2D.Double
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* @since 1.2
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*/
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protected QuadCurve2D() {
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}
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/**
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* Returns the X coordinate of the start point in
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* <code>double</code> in precision.
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* @return the X coordinate of the start point.
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* @since 1.2
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*/
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public abstract double getX1();
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/**
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* Returns the Y coordinate of the start point in
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* <code>double</code> precision.
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* @return the Y coordinate of the start point.
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* @since 1.2
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*/
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public abstract double getY1();
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/**
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* Returns the start point.
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* @return a <code>Point2D</code> that is the start point of this
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* <code>QuadCurve2D</code>.
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* @since 1.2
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*/
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public abstract Point2D getP1();
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/**
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* Returns the X coordinate of the control point in
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* <code>double</code> precision.
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* @return X coordinate the control point
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* @since 1.2
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*/
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public abstract double getCtrlX();
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/**
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* Returns the Y coordinate of the control point in
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* <code>double</code> precision.
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* @return the Y coordinate of the control point.
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* @since 1.2
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*/
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public abstract double getCtrlY();
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/**
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* Returns the control point.
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* @return a <code>Point2D</code> that is the control point of this
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* <code>Point2D</code>.
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* @since 1.2
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*/
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public abstract Point2D getCtrlPt();
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/**
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* Returns the X coordinate of the end point in
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* <code>double</code> precision.
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* @return the x coordinate of the end point.
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* @since 1.2
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*/
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public abstract double getX2();
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/**
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* Returns the Y coordinate of the end point in
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* <code>double</code> precision.
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* @return the Y coordinate of the end point.
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* @since 1.2
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*/
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public abstract double getY2();
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/**
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* Returns the end point.
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* @return a <code>Point</code> object that is the end point
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* of this <code>Point2D</code>.
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* @since 1.2
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*/
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public abstract Point2D getP2();
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|
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/**
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* Sets the location of the end points and control point of this curve
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* to the specified <code>double</code> coordinates.
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*
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* @param x1 the X coordinate of the start point
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* @param y1 the Y coordinate of the start point
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* @param ctrlx the X coordinate of the control point
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* @param ctrly the Y coordinate of the control point
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* @param x2 the X coordinate of the end point
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* @param y2 the Y coordinate of the end point
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* @since 1.2
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*/
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public abstract void setCurve(double x1, double y1,
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double ctrlx, double ctrly,
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double x2, double y2);
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/**
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* Sets the location of the end points and control points of this
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* <code>QuadCurve2D</code> to the <code>double</code> coordinates at
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* the specified offset in the specified array.
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* @param coords the array containing coordinate values
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* @param offset the index into the array from which to start
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* getting the coordinate values and assigning them to this
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* <code>QuadCurve2D</code>
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* @since 1.2
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*/
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public void setCurve(double[] coords, int offset) {
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setCurve(coords[offset + 0], coords[offset + 1],
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coords[offset + 2], coords[offset + 3],
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coords[offset + 4], coords[offset + 5]);
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}
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/**
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* Sets the location of the end points and control point of this
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* <code>QuadCurve2D</code> to the specified <code>Point2D</code>
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* coordinates.
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* @param p1 the start point
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* @param cp the control point
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* @param p2 the end point
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* @since 1.2
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*/
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public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
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setCurve(p1.getX(), p1.getY(),
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cp.getX(), cp.getY(),
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p2.getX(), p2.getY());
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}
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|
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/**
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* Sets the location of the end points and control points of this
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* <code>QuadCurve2D</code> to the coordinates of the
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* <code>Point2D</code> objects at the specified offset in
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* the specified array.
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* @param pts an array containing <code>Point2D</code> that define
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* coordinate values
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* @param offset the index into <code>pts</code> from which to start
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|
* getting the coordinate values and assigning them to this
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|
* <code>QuadCurve2D</code>
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|
* @since 1.2
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*/
|
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public void setCurve(Point2D[] pts, int offset) {
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setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
|
|
pts[offset + 1].getX(), pts[offset + 1].getY(),
|
|
pts[offset + 2].getX(), pts[offset + 2].getY());
|
|
}
|
|
|
|
/**
|
|
* Sets the location of the end points and control point of this
|
|
* <code>QuadCurve2D</code> to the same as those in the specified
|
|
* <code>QuadCurve2D</code>.
|
|
* @param c the specified <code>QuadCurve2D</code>
|
|
* @since 1.2
|
|
*/
|
|
public void setCurve(QuadCurve2D c) {
|
|
setCurve(c.getX1(), c.getY1(),
|
|
c.getCtrlX(), c.getCtrlY(),
|
|
c.getX2(), c.getY2());
|
|
}
|
|
|
|
/**
|
|
* Returns the square of the flatness, or maximum distance of a
|
|
* control point from the line connecting the end points, of the
|
|
* quadratic curve specified by the indicated control points.
|
|
*
|
|
* @param x1 the X coordinate of the start point
|
|
* @param y1 the Y coordinate of the start point
|
|
* @param ctrlx the X coordinate of the control point
|
|
* @param ctrly the Y coordinate of the control point
|
|
* @param x2 the X coordinate of the end point
|
|
* @param y2 the Y coordinate of the end point
|
|
* @return the square of the flatness of the quadratic curve
|
|
* defined by the specified coordinates.
|
|
* @since 1.2
|
|
*/
|
|
public static double getFlatnessSq(double x1, double y1,
|
|
double ctrlx, double ctrly,
|
|
double x2, double y2) {
|
|
return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
|
|
}
|
|
|
|
/**
|
|
* Returns the flatness, or maximum distance of a
|
|
* control point from the line connecting the end points, of the
|
|
* quadratic curve specified by the indicated control points.
|
|
*
|
|
* @param x1 the X coordinate of the start point
|
|
* @param y1 the Y coordinate of the start point
|
|
* @param ctrlx the X coordinate of the control point
|
|
* @param ctrly the Y coordinate of the control point
|
|
* @param x2 the X coordinate of the end point
|
|
* @param y2 the Y coordinate of the end point
|
|
* @return the flatness of the quadratic curve defined by the
|
|
* specified coordinates.
|
|
* @since 1.2
|
|
*/
|
|
public static double getFlatness(double x1, double y1,
|
|
double ctrlx, double ctrly,
|
|
double x2, double y2) {
|
|
return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
|
|
}
|
|
|
|
/**
|
|
* Returns the square of the flatness, or maximum distance of a
|
|
* control point from the line connecting the end points, of the
|
|
* quadratic curve specified by the control points stored in the
|
|
* indicated array at the indicated index.
|
|
* @param coords an array containing coordinate values
|
|
* @param offset the index into <code>coords</code> from which to
|
|
* to start getting the values from the array
|
|
* @return the flatness of the quadratic curve that is defined by the
|
|
* values in the specified array at the specified index.
|
|
* @since 1.2
|
|
*/
|
|
public static double getFlatnessSq(double coords[], int offset) {
|
|
return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
|
|
coords[offset + 4], coords[offset + 5],
|
|
coords[offset + 2], coords[offset + 3]);
|
|
}
|
|
|
|
/**
|
|
* Returns the flatness, or maximum distance of a
|
|
* control point from the line connecting the end points, of the
|
|
* quadratic curve specified by the control points stored in the
|
|
* indicated array at the indicated index.
|
|
* @param coords an array containing coordinate values
|
|
* @param offset the index into <code>coords</code> from which to
|
|
* start getting the coordinate values
|
|
* @return the flatness of a quadratic curve defined by the
|
|
* specified array at the specified offset.
|
|
* @since 1.2
|
|
*/
|
|
public static double getFlatness(double coords[], int offset) {
|
|
return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
|
|
coords[offset + 4], coords[offset + 5],
|
|
coords[offset + 2], coords[offset + 3]);
|
|
}
|
|
|
|
/**
|
|
* Returns the square of the flatness, or maximum distance of a
|
|
* control point from the line connecting the end points, of this
|
|
* <code>QuadCurve2D</code>.
|
|
* @return the square of the flatness of this
|
|
* <code>QuadCurve2D</code>.
|
|
* @since 1.2
|
|
*/
|
|
public double getFlatnessSq() {
|
|
return Line2D.ptSegDistSq(getX1(), getY1(),
|
|
getX2(), getY2(),
|
|
getCtrlX(), getCtrlY());
|
|
}
|
|
|
|
/**
|
|
* Returns the flatness, or maximum distance of a
|
|
* control point from the line connecting the end points, of this
|
|
* <code>QuadCurve2D</code>.
|
|
* @return the flatness of this <code>QuadCurve2D</code>.
|
|
* @since 1.2
|
|
*/
|
|
public double getFlatness() {
|
|
return Line2D.ptSegDist(getX1(), getY1(),
|
|
getX2(), getY2(),
|
|
getCtrlX(), getCtrlY());
|
|
}
|
|
|
|
/**
|
|
* Subdivides this <code>QuadCurve2D</code> 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 can be the same as this <code>QuadCurve2D</code> or
|
|
* <code>null</code>.
|
|
* @param left the <code>QuadCurve2D</code> object for storing the
|
|
* left or first half of the subdivided curve
|
|
* @param right the <code>QuadCurve2D</code> object for storing the
|
|
* right or second half of the subdivided curve
|
|
* @since 1.2
|
|
*/
|
|
public void subdivide(QuadCurve2D left, QuadCurve2D right) {
|
|
subdivide(this, left, right);
|
|
}
|
|
|
|
/**
|
|
* Subdivides the quadratic curve specified by the <code>src</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 can be the same as the <code>src</code> object or
|
|
* <code>null</code>.
|
|
* @param src the quadratic curve to be subdivided
|
|
* @param left the <code>QuadCurve2D</code> object for storing the
|
|
* left or first half of the subdivided curve
|
|
* @param right the <code>QuadCurve2D</code> object for storing the
|
|
* right or second half of the subdivided curve
|
|
* @since 1.2
|
|
*/
|
|
public static void subdivide(QuadCurve2D src,
|
|
QuadCurve2D left,
|
|
QuadCurve2D right) {
|
|
double x1 = src.getX1();
|
|
double y1 = src.getY1();
|
|
double ctrlx = src.getCtrlX();
|
|
double ctrly = src.getCtrlY();
|
|
double x2 = src.getX2();
|
|
double y2 = src.getY2();
|
|
double ctrlx1 = (x1 + ctrlx) / 2.0;
|
|
double ctrly1 = (y1 + ctrly) / 2.0;
|
|
double ctrlx2 = (x2 + ctrlx) / 2.0;
|
|
double ctrly2 = (y2 + ctrly) / 2.0;
|
|
ctrlx = (ctrlx1 + ctrlx2) / 2.0;
|
|
ctrly = (ctrly1 + ctrly2) / 2.0;
|
|
if (left != null) {
|
|
left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
|
|
}
|
|
if (right != null) {
|
|
right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Subdivides the quadratic curve specified by the coordinates
|
|
* stored in the <code>src</code> array at indices
|
|
* <code>srcoff</code> through <code>srcoff</code> + 5
|
|
* 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 can be <code>null</code> or a reference to the same array
|
|
* and offset 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 that
|
|
* <code>rightoff</code> equals <code>leftoff</code> + 4 in order
|
|
* to avoid allocating extra storage for this common point.
|
|
* @param src the array holding the coordinates for the source curve
|
|
* @param srcoff the offset into the array of the beginning of the
|
|
* the 6 source coordinates
|
|
* @param left the array for storing the coordinates for the first
|
|
* half of the subdivided curve
|
|
* @param leftoff the offset into the array of the beginning of the
|
|
* the 6 left coordinates
|
|
* @param right the array for storing the coordinates for the second
|
|
* half of the subdivided curve
|
|
* @param rightoff the offset into the array of the beginning of the
|
|
* the 6 right coordinates
|
|
* @since 1.2
|
|
*/
|
|
public static void subdivide(double src[], int srcoff,
|
|
double left[], int leftoff,
|
|
double right[], int rightoff) {
|
|
double x1 = src[srcoff + 0];
|
|
double y1 = src[srcoff + 1];
|
|
double ctrlx = src[srcoff + 2];
|
|
double ctrly = src[srcoff + 3];
|
|
double x2 = src[srcoff + 4];
|
|
double y2 = src[srcoff + 5];
|
|
if (left != null) {
|
|
left[leftoff + 0] = x1;
|
|
left[leftoff + 1] = y1;
|
|
}
|
|
if (right != null) {
|
|
right[rightoff + 4] = x2;
|
|
right[rightoff + 5] = y2;
|
|
}
|
|
x1 = (x1 + ctrlx) / 2.0;
|
|
y1 = (y1 + ctrly) / 2.0;
|
|
x2 = (x2 + ctrlx) / 2.0;
|
|
y2 = (y2 + ctrly) / 2.0;
|
|
ctrlx = (x1 + x2) / 2.0;
|
|
ctrly = (y1 + y2) / 2.0;
|
|
if (left != null) {
|
|
left[leftoff + 2] = x1;
|
|
left[leftoff + 3] = y1;
|
|
left[leftoff + 4] = ctrlx;
|
|
left[leftoff + 5] = ctrly;
|
|
}
|
|
if (right != null) {
|
|
right[rightoff + 0] = ctrlx;
|
|
right[rightoff + 1] = ctrly;
|
|
right[rightoff + 2] = x2;
|
|
right[rightoff + 3] = y2;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Solves the quadratic whose coefficients are in the <code>eqn</code>
|
|
* array and places the non-complex roots back into the same array,
|
|
* returning the number of roots. The quadratic solved is represented
|
|
* by the equation:
|
|
* <pre>
|
|
* eqn = {C, B, A};
|
|
* ax^2 + bx + c = 0
|
|
* </pre>
|
|
* A return value of <code>-1</code> is used to distinguish a constant
|
|
* equation, which might be always 0 or never 0, from an equation that
|
|
* has no zeroes.
|
|
* @param eqn the array that contains the quadratic coefficients
|
|
* @return the number of roots, or <code>-1</code> if the equation is
|
|
* a constant
|
|
* @since 1.2
|
|
*/
|
|
public static int solveQuadratic(double eqn[]) {
|
|
return solveQuadratic(eqn, eqn);
|
|
}
|
|
|
|
/**
|
|
* Solves the quadratic whose coefficients are in the <code>eqn</code>
|
|
* array and places the non-complex roots into the <code>res</code>
|
|
* array, returning the number of roots.
|
|
* The quadratic solved is represented by the equation:
|
|
* <pre>
|
|
* eqn = {C, B, A};
|
|
* ax^2 + bx + c = 0
|
|
* </pre>
|
|
* A return value of <code>-1</code> is used to distinguish a constant
|
|
* equation, which might be always 0 or never 0, from an equation that
|
|
* has no zeroes.
|
|
* @param eqn the specified array of coefficients to use to solve
|
|
* the quadratic equation
|
|
* @param res the array that contains the non-complex roots
|
|
* resulting from the solution of the quadratic equation
|
|
* @return the number of roots, or <code>-1</code> if the equation is
|
|
* a constant.
|
|
* @since 1.3
|
|
*/
|
|
public static int solveQuadratic(double eqn[], double res[]) {
|
|
double a = eqn[2];
|
|
double b = eqn[1];
|
|
double c = eqn[0];
|
|
int roots = 0;
|
|
if (a == 0.0) {
|
|
// The quadratic parabola has degenerated to a line.
|
|
if (b == 0.0) {
|
|
// The line has degenerated to a constant.
|
|
return -1;
|
|
}
|
|
res[roots++] = -c / b;
|
|
} else {
|
|
// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
|
|
double d = b * b - 4.0 * a * c;
|
|
if (d < 0.0) {
|
|
// If d < 0.0, then there are no roots
|
|
return 0;
|
|
}
|
|
d = Math.sqrt(d);
|
|
// For accuracy, calculate one root using:
|
|
// (-b +/- d) / 2a
|
|
// and the other using:
|
|
// 2c / (-b +/- d)
|
|
// Choose the sign of the +/- so that b+d gets larger in magnitude
|
|
if (b < 0.0) {
|
|
d = -d;
|
|
}
|
|
double q = (b + d) / -2.0;
|
|
// We already tested a for being 0 above
|
|
res[roots++] = q / a;
|
|
if (q != 0.0) {
|
|
res[roots++] = c / q;
|
|
}
|
|
}
|
|
return roots;
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public boolean contains(double x, double y) {
|
|
|
|
double x1 = getX1();
|
|
double y1 = getY1();
|
|
double xc = getCtrlX();
|
|
double yc = getCtrlY();
|
|
double x2 = getX2();
|
|
double y2 = getY2();
|
|
|
|
/*
|
|
* We have a convex shape bounded by quad curve Pc(t)
|
|
* and ine Pl(t).
|
|
*
|
|
* P1 = (x1, y1) - start point of curve
|
|
* P2 = (x2, y2) - end point of curve
|
|
* Pc = (xc, yc) - control point
|
|
*
|
|
* Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 =
|
|
* = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1
|
|
* Pl(t) = P1*(1 - t) + P2*t
|
|
* t = [0:1]
|
|
*
|
|
* P = (x, y) - point of interest
|
|
*
|
|
* Let's look at second derivative of quad curve equation:
|
|
*
|
|
* Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq''
|
|
* It's constant vector.
|
|
*
|
|
* Let's draw a line through P to be parallel to this
|
|
* vector and find the intersection of the quad curve
|
|
* and the line.
|
|
*
|
|
* Pq(t) is point of intersection if system of equations
|
|
* below has the solution.
|
|
*
|
|
* L(s) = P + Pq''*s == Pq(t)
|
|
* Pq''*s + (P - Pq(t)) == 0
|
|
*
|
|
* | xq''*s + (x - xq(t)) == 0
|
|
* | yq''*s + (y - yq(t)) == 0
|
|
*
|
|
* This system has the solution if rank of its matrix equals to 1.
|
|
* That is, determinant of the matrix should be zero.
|
|
*
|
|
* (y - yq(t))*xq'' == (x - xq(t))*yq''
|
|
*
|
|
* Let's solve this equation with 't' variable.
|
|
* Also let kx = x1 - 2*xc + x2
|
|
* ky = y1 - 2*yc + y2
|
|
*
|
|
* t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) /
|
|
* ((xc - x1)*ky - (yc - y1)*kx)
|
|
*
|
|
* Let's do the same for our line Pl(t):
|
|
*
|
|
* t0l = ((x - x1)*ky - (y - y1)*kx) /
|
|
* ((x2 - x1)*ky - (y2 - y1)*kx)
|
|
*
|
|
* It's easy to check that t0q == t0l. This fact means
|
|
* we can compute t0 only one time.
|
|
*
|
|
* In case t0 < 0 or t0 > 1, we have an intersections outside
|
|
* of shape bounds. So, P is definitely out of shape.
|
|
*
|
|
* In case t0 is inside [0:1], we should calculate Pq(t0)
|
|
* and Pl(t0). We have three points for now, and all of them
|
|
* lie on one line. So, we just need to detect, is our point
|
|
* of interest between points of intersections or not.
|
|
*
|
|
* If the denominator in the t0q and t0l equations is
|
|
* zero, then the points must be collinear and so the
|
|
* curve is degenerate and encloses no area. Thus the
|
|
* result is false.
|
|
*/
|
|
double kx = x1 - 2 * xc + x2;
|
|
double ky = y1 - 2 * yc + y2;
|
|
double dx = x - x1;
|
|
double dy = y - y1;
|
|
double dxl = x2 - x1;
|
|
double dyl = y2 - y1;
|
|
|
|
double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx);
|
|
if (t0 < 0 || t0 > 1 || t0 != t0) {
|
|
return false;
|
|
}
|
|
|
|
double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1;
|
|
double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1;
|
|
double xl = dxl * t0 + x1;
|
|
double yl = dyl * t0 + y1;
|
|
|
|
return (x >= xb && x < xl) ||
|
|
(x >= xl && x < xb) ||
|
|
(y >= yb && y < yl) ||
|
|
(y >= yl && y < yb);
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public boolean contains(Point2D p) {
|
|
return contains(p.getX(), p.getY());
|
|
}
|
|
|
|
/**
|
|
* Fill an array with the coefficients of the parametric equation
|
|
* in t, ready for solving against val with solveQuadratic.
|
|
* We currently have:
|
|
* val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
|
|
* = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
|
|
* = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
|
|
* 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
|
|
* 0 = C + Bt + At^2
|
|
* C = C1 - val
|
|
* B = 2*CP - 2*C1
|
|
* A = C1 - 2*CP + C2
|
|
*/
|
|
private static void fillEqn(double eqn[], double val,
|
|
double c1, double cp, double c2) {
|
|
eqn[0] = c1 - val;
|
|
eqn[1] = cp + cp - c1 - c1;
|
|
eqn[2] = c1 - cp - cp + c2;
|
|
return;
|
|
}
|
|
|
|
/**
|
|
* Evaluate the t values in the first num slots of the vals[] array
|
|
* and place the evaluated values back into the same array. Only
|
|
* evaluate t values that are within the range <0, 1>, including
|
|
* the 0 and 1 ends of the range iff the include0 or include1
|
|
* booleans are true. If an "inflection" equation is handed in,
|
|
* then any points which represent a point of inflection for that
|
|
* quadratic equation are also ignored.
|
|
*/
|
|
private static int evalQuadratic(double vals[], int num,
|
|
boolean include0,
|
|
boolean include1,
|
|
double inflect[],
|
|
double c1, double ctrl, double c2) {
|
|
int j = 0;
|
|
for (int i = 0; i < num; i++) {
|
|
double t = vals[i];
|
|
if ((include0 ? t >= 0 : t > 0) &&
|
|
(include1 ? t <= 1 : t < 1) &&
|
|
(inflect == null ||
|
|
inflect[1] + 2*inflect[2]*t != 0))
|
|
{
|
|
double u = 1 - t;
|
|
vals[j++] = c1*u*u + 2*ctrl*t*u + c2*t*t;
|
|
}
|
|
}
|
|
return j;
|
|
}
|
|
|
|
private static final int BELOW = -2;
|
|
private static final int LOWEDGE = -1;
|
|
private static final int INSIDE = 0;
|
|
private static final int HIGHEDGE = 1;
|
|
private static final int ABOVE = 2;
|
|
|
|
/**
|
|
* Determine where coord lies with respect to the range from
|
|
* low to high. It is assumed that low <= high. The return
|
|
* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
|
|
* or ABOVE.
|
|
*/
|
|
private static int getTag(double coord, double low, double high) {
|
|
if (coord <= low) {
|
|
return (coord < low ? BELOW : LOWEDGE);
|
|
}
|
|
if (coord >= high) {
|
|
return (coord > high ? ABOVE : HIGHEDGE);
|
|
}
|
|
return INSIDE;
|
|
}
|
|
|
|
/**
|
|
* Determine if the pttag represents a coordinate that is already
|
|
* in its test range, or is on the border with either of the two
|
|
* opttags representing another coordinate that is "towards the
|
|
* inside" of that test range. In other words, are either of the
|
|
* two "opt" points "drawing the pt inward"?
|
|
*/
|
|
private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
|
|
switch (pttag) {
|
|
case BELOW:
|
|
case ABOVE:
|
|
default:
|
|
return false;
|
|
case LOWEDGE:
|
|
return (opt1tag >= INSIDE || opt2tag >= INSIDE);
|
|
case INSIDE:
|
|
return true;
|
|
case HIGHEDGE:
|
|
return (opt1tag <= INSIDE || opt2tag <= INSIDE);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public boolean intersects(double x, double y, double w, double h) {
|
|
// Trivially reject non-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 ctrlx = getCtrlX();
|
|
double ctrly = getCtrlY();
|
|
int ctrlxtag = getTag(ctrlx, x, x+w);
|
|
int ctrlytag = getTag(ctrly, y, y+h);
|
|
|
|
// Trivially reject if all points are entirely to one side of
|
|
// the rectangle.
|
|
if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
|
|
return false; // All points left
|
|
}
|
|
if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
|
|
return false; // All points above
|
|
}
|
|
if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
|
|
return false; // All points right
|
|
}
|
|
if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
|
|
return false; // All points below
|
|
}
|
|
|
|
// Test for endpoints on the edge where either the segment
|
|
// or the curve is headed "inwards" from them
|
|
// Note: These tests are a superset of the fast endpoint tests
|
|
// above and thus repeat those tests, but take more time
|
|
// and cover more cases
|
|
if (inwards(x1tag, x2tag, ctrlxtag) &&
|
|
inwards(y1tag, y2tag, ctrlytag))
|
|
{
|
|
// First endpoint on border with either edge moving inside
|
|
return true;
|
|
}
|
|
if (inwards(x2tag, x1tag, ctrlxtag) &&
|
|
inwards(y2tag, y1tag, ctrlytag))
|
|
{
|
|
// Second endpoint on border with either edge moving inside
|
|
return true;
|
|
}
|
|
|
|
// Trivially accept if endpoints span directly across the rectangle
|
|
boolean xoverlap = (x1tag * x2tag <= 0);
|
|
boolean yoverlap = (y1tag * y2tag <= 0);
|
|
if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
|
|
return true;
|
|
}
|
|
if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
|
|
return true;
|
|
}
|
|
|
|
// We now know that both endpoints are outside the rectangle
|
|
// but the 3 points are not all on one side of the rectangle.
|
|
// Therefore the curve cannot be contained inside the rectangle,
|
|
// but the rectangle might be contained inside the curve, or
|
|
// the curve might intersect the boundary of the rectangle.
|
|
|
|
double[] eqn = new double[3];
|
|
double[] res = new double[3];
|
|
if (!yoverlap) {
|
|
// Both Y coordinates for the closing segment are above or
|
|
// below the rectangle which means that we can only intersect
|
|
// if the curve crosses the top (or bottom) of the rectangle
|
|
// in more than one place and if those crossing locations
|
|
// span the horizontal range of the rectangle.
|
|
fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2);
|
|
return (solveQuadratic(eqn, res) == 2 &&
|
|
evalQuadratic(res, 2, true, true, null,
|
|
x1, ctrlx, x2) == 2 &&
|
|
getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
|
|
}
|
|
|
|
// Y ranges overlap. Now we examine the X ranges
|
|
if (!xoverlap) {
|
|
// Both X coordinates for the closing segment are left of
|
|
// or right of the rectangle which means that we can only
|
|
// intersect if the curve crosses the left (or right) edge
|
|
// of the rectangle in more than one place and if those
|
|
// crossing locations span the vertical range of the rectangle.
|
|
fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2);
|
|
return (solveQuadratic(eqn, res) == 2 &&
|
|
evalQuadratic(res, 2, true, true, null,
|
|
y1, ctrly, y2) == 2 &&
|
|
getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
|
|
}
|
|
|
|
// The X and Y ranges of the endpoints overlap the X and Y
|
|
// ranges of the rectangle, now find out how the endpoint
|
|
// line segment intersects the Y range of the rectangle
|
|
double dx = x2 - x1;
|
|
double dy = y2 - y1;
|
|
double k = y2 * x1 - x2 * y1;
|
|
int c1tag, c2tag;
|
|
if (y1tag == INSIDE) {
|
|
c1tag = x1tag;
|
|
} else {
|
|
c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
|
|
}
|
|
if (y2tag == INSIDE) {
|
|
c2tag = x2tag;
|
|
} else {
|
|
c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
|
|
}
|
|
// If the part of the line segment that intersects the Y range
|
|
// of the rectangle crosses it horizontally - trivially accept
|
|
if (c1tag * c2tag <= 0) {
|
|
return true;
|
|
}
|
|
|
|
// Now we know that both the X and Y ranges intersect and that
|
|
// the endpoint line segment does not directly cross the rectangle.
|
|
//
|
|
// We can almost treat this case like one of the cases above
|
|
// where both endpoints are to one side, except that we will
|
|
// only get one intersection of the curve with the vertical
|
|
// side of the rectangle. This is because the endpoint segment
|
|
// accounts for the other intersection.
|
|
//
|
|
// (Remember there is overlap in both the X and Y ranges which
|
|
// means that the segment must cross at least one vertical edge
|
|
// of the rectangle - in particular, the "near vertical side" -
|
|
// leaving only one intersection for the curve.)
|
|
//
|
|
// Now we calculate the y tags of the two intersections on the
|
|
// "near vertical side" of the rectangle. We will have one with
|
|
// the endpoint segment, and one with the curve. If those two
|
|
// vertical intersections overlap the Y range of the rectangle,
|
|
// we have an intersection. Otherwise, we don't.
|
|
|
|
// c1tag = vertical intersection class of the endpoint segment
|
|
//
|
|
// Choose the y tag of the endpoint that was not on the same
|
|
// side of the rectangle as the subsegment calculated above.
|
|
// Note that we can "steal" the existing Y tag of that endpoint
|
|
// since it will be provably the same as the vertical intersection.
|
|
c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);
|
|
|
|
// c2tag = vertical intersection class of the curve
|
|
//
|
|
// We have to calculate this one the straightforward way.
|
|
// Note that the c2tag can still tell us which vertical edge
|
|
// to test against.
|
|
fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2);
|
|
int num = solveQuadratic(eqn, res);
|
|
|
|
// Note: We should be able to assert(num == 2); since the
|
|
// X range "crosses" (not touches) the vertical boundary,
|
|
// but we pass num to evalQuadratic for completeness.
|
|
evalQuadratic(res, num, true, true, null, y1, ctrly, y2);
|
|
|
|
// Note: We can assert(num evals == 1); since one of the
|
|
// 2 crossings will be out of the [0,1] range.
|
|
c2tag = getTag(res[0], y, y+h);
|
|
|
|
// Finally, we have an intersection if the two crossings
|
|
// overlap the Y range of the rectangle.
|
|
return (c1tag * c2tag <= 0);
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public boolean intersects(Rectangle2D r) {
|
|
return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public boolean contains(double x, double y, double w, double h) {
|
|
if (w <= 0 || h <= 0) {
|
|
return false;
|
|
}
|
|
// Assertion: Quadratic curves closed by connecting their
|
|
// endpoints are always convex.
|
|
return (contains(x, y) &&
|
|
contains(x + w, y) &&
|
|
contains(x + w, y + h) &&
|
|
contains(x, y + h));
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public boolean contains(Rectangle2D r) {
|
|
return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
|
|
}
|
|
|
|
/**
|
|
* {@inheritDoc}
|
|
* @since 1.2
|
|
*/
|
|
public Rectangle getBounds() {
|
|
return getBounds2D().getBounds();
|
|
}
|
|
|
|
/**
|
|
* Returns an iteration object that defines the boundary of the
|
|
* shape of this <code>QuadCurve2D</code>.
|
|
* The iterator for this class is not multi-threaded safe,
|
|
* which means that this <code>QuadCurve2D</code> class does not
|
|
* guarantee that modifications to the geometry of this
|
|
* <code>QuadCurve2D</code> object do not affect any iterations of
|
|
* that geometry that are already in process.
|
|
* @param at an optional {@link AffineTransform} to apply to the
|
|
* shape boundary
|
|
* @return a {@link PathIterator} object that defines the boundary
|
|
* of the shape.
|
|
* @since 1.2
|
|
*/
|
|
public PathIterator getPathIterator(AffineTransform at) {
|
|
return new QuadIterator(this, at);
|
|
}
|
|
|
|
/**
|
|
* Returns an iteration object that defines the boundary of the
|
|
* flattened shape of this <code>QuadCurve2D</code>.
|
|
* The iterator for this class is not multi-threaded safe,
|
|
* which means that this <code>QuadCurve2D</code> class does not
|
|
* guarantee that modifications to the geometry of this
|
|
* <code>QuadCurve2D</code> object do not affect any iterations of
|
|
* that geometry that are already in process.
|
|
* @param at an optional <code>AffineTransform</code> to apply
|
|
* to the boundary of the shape
|
|
* @param flatness the maximum distance that the control points for a
|
|
* subdivided curve can be with respect to a line connecting
|
|
* the end points of this curve before this curve is
|
|
* replaced by a straight line connecting the end points.
|
|
* @return a <code>PathIterator</code> object that defines the
|
|
* flattened boundary of the shape.
|
|
* @since 1.2
|
|
*/
|
|
public PathIterator getPathIterator(AffineTransform at, double flatness) {
|
|
return new FlatteningPathIterator(getPathIterator(at), flatness);
|
|
}
|
|
|
|
/**
|
|
* Creates a new object of the same class and with the same contents
|
|
* as this object.
|
|
*
|
|
* @return a clone of this instance.
|
|
* @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);
|
|
}
|
|
}
|
|
}
|