cubiccurve2d.java

gcc的组建

   * Determines whether any part of a Rectangle2D is inside the area bounded 
   * by the curve and the straight line connecting its end points.
   * @see #intersects(double, double, double, double)
   */
  public boolean intersects(Rectangle2D r)
  {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * Determine whether a rectangle is entirely inside the area that is bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
   * alt="A drawing of the area spanned by the curve" />
   *
   * <p>The above drawing illustrates in which area points are
   * considered &#x201c;inside&#x201d; a CubicCurve2D.
   * @see #contains(double, double)
   */
  public boolean contains(double x, double y, double w, double h)
  {
    if (! getBounds2D().intersects(x, y, w, h))
      return false;

    /* Does any edge intersect? */
    if (getAxisIntersections(x, y, true, w) != 0 /* top */
        || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
        || getAxisIntersections(x + w, y, false, h) != 0 /* right */
        || getAxisIntersections(x, y, false, h) != 0) /* left */
      return false;

    /* No intersections, is any point inside? */
    if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
      return true;

    return false;
  }

  /**
   * Determine whether a Rectangle2D is entirely inside the area that is 
   * bounded by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
   * alt="A drawing of the area spanned by the curve" />
   *
   * <p>The above drawing illustrates in which area points are
   * considered &#x201c;inside&#x201d; a CubicCurve2D.
   * @see #contains(double, double)
   */
  public boolean contains(Rectangle2D r)
  {
    return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * Determines the smallest rectangle that encloses the
   * curve&#x2019;s start, end and control points.
   */
  public Rectangle getBounds()
  {
    return getBounds2D().getBounds();
  }

  public PathIterator getPathIterator(final AffineTransform at)
  {
    return new PathIterator()
      {
	/** Current coordinate. */
	private int current = 0;

	public int getWindingRule()
	{
	  return WIND_NON_ZERO;
	}

	public boolean isDone()
	{
	  return current >= 2;
	}

	public void next()
	{
	  current++;
	}

	public int currentSegment(float[] coords)
	{
	  int result;
	  switch (current)
	    {
	    case 0:
	      coords[0] = (float) getX1();
	      coords[1] = (float) getY1();
	      result = SEG_MOVETO;
	      break;
	    case 1:
	      coords[0] = (float) getCtrlX1();
	      coords[1] = (float) getCtrlY1();
	      coords[2] = (float) getCtrlX2();
	      coords[3] = (float) getCtrlY2();
	      coords[4] = (float) getX2();
	      coords[5] = (float) getY2();
	      result = SEG_CUBICTO;
	      break;
	    default:
	      throw new NoSuchElementException("cubic iterator out of bounds");
	    }
	  if (at != null)
	    at.transform(coords, 0, coords, 0, 3);
	  return result;
	}

	public int currentSegment(double[] coords)
	{
	  int result;
	  switch (current)
	    {
	    case 0:
	      coords[0] = getX1();
	      coords[1] = getY1();
	      result = SEG_MOVETO;
	      break;
	    case 1:
	      coords[0] = getCtrlX1();
	      coords[1] = getCtrlY1();
	      coords[2] = getCtrlX2();
	      coords[3] = getCtrlY2();
	      coords[4] = getX2();
	      coords[5] = getY2();
	      result = SEG_CUBICTO;
	      break;
	    default:
	      throw new NoSuchElementException("cubic iterator out of bounds");
	    }
	  if (at != null)
	    at.transform(coords, 0, coords, 0, 3);
	  return result;
	}
      };
  }

  public PathIterator getPathIterator(AffineTransform at, double flatness)
  {
    return new FlatteningPathIterator(getPathIterator(at), flatness);
  }

  /**
   * Create a new curve with the same contents as this one.
   *
   * @return the clone.
   */
  public Object clone()
  {
    try
      {
	return super.clone();
      }
    catch (CloneNotSupportedException e)
      {
	throw (Error) new InternalError().initCause(e); // Impossible
      }
  }

  /**
   * Helper method used by contains() and intersects() methods, that
   * returns the number of curve/line intersections on a given axis
   * extending from a certain point.
   *
   * @param x x coordinate of the origin point
   * @param y y coordinate of the origin point
   * @param useYaxis axis used, if true the positive Y axis is used,
   * false uses the positive X axis.
   *
   * This is an implementation of the line-crossings algorithm,
   * Detailed in an article on Eric Haines' page:
   * http://www.acm.org/tog/editors/erich/ptinpoly/
   *
   * A special-case not adressed in this code is self-intersections
   * of the curve, e.g. if the axis intersects the self-itersection,
   * the degenerate roots of the polynomial will erroneously count as 
   * a single intersection of the curve, and not two.
   */
  private int getAxisIntersections(double x, double y, boolean useYaxis,
                                   double distance)
  {
    int nCrossings = 0;
    double a0;
    double a1;
    double a2;
    double a3;
    double b0;
    double b1;
    double b2;
    double b3;
    double[] r = new double[4];
    int nRoots;

    a0 = a3 = 0.0;

    if (useYaxis)
      {
	a0 = getY1() - y;
	a1 = getCtrlY1() - y;
	a2 = getCtrlY2() - y;
	a3 = getY2() - y;
	b0 = getX1() - x;
	b1 = getCtrlX1() - x;
	b2 = getCtrlX2() - x;
	b3 = getX2() - x;
      }
    else
      {
	a0 = getX1() - x;
	a1 = getCtrlX1() - x;
	a2 = getCtrlX2() - x;
	a3 = getX2() - x;
	b0 = getY1() - y;
	b1 = getCtrlY1() - y;
	b2 = getCtrlY2() - y;
	b3 = getY2() - y;
      }

    /* If the axis intersects a start/endpoint, shift it up by some small 
       amount to guarantee the line is 'inside'
       If this is not done, bad behaviour may result for points on that axis.*/
    if (a0 == 0.0 || a3 == 0.0)
      {
	double small = getFlatness() * EPSILON;
	if (a0 == 0.0)
	  a0 -= small;
	if (a3 == 0.0)
	  a3 -= small;
      }

    if (useYaxis)
      {
	if (Line2D.linesIntersect(b0, a0, b3, a3, EPSILON, 0.0, distance, 0.0))
	  nCrossings++;
      }
    else
      {
	if (Line2D.linesIntersect(a0, b0, a3, b3, 0.0, EPSILON, 0.0, distance))
	  nCrossings++;
      }

    r[0] = a0;
    r[1] = 3 * (a1 - a0);
    r[2] = 3 * (a2 + a0 - 2 * a1);
    r[3] = a3 - 3 * a2 + 3 * a1 - a0;

    if ((nRoots = solveCubic(r)) != 0)
      for (int i = 0; i < nRoots; i++)
        {
	  double t = r[i];
	  if (t >= 0.0 && t <= 1.0)
	    {
	      double crossing = -(t * t * t) * (b0 - 3 * b1 + 3 * b2 - b3)
	                        + 3 * t * t * (b0 - 2 * b1 + b2)
	                        + 3 * t * (b1 - b0) + b0;
	      if (crossing > 0.0 && crossing <= distance)
		nCrossings++;
	    }
        }

    return (nCrossings);
  }

  /**
   * A two-dimensional curve that is parameterized with a cubic
   * function and stores coordinate values in double-precision
   * floating-point format.
   *
   * @see CubicCurve2D.Float
   *
   * @author Eric Blake ([e-mail])
   * @author Sascha Brawer ([e-mail])
   */
  public static class Double extends CubicCurve2D
  {
    /**
     * The <i>x</i> coordinate of the curve&#x2019;s start point.
     */
    public double x1;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s start point.
     */
    public double y1;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s first control point.
     */
    public double ctrlx1;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s first control point.
     */
    public double ctrly1;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s second control point.
     */
    public double ctrlx2;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s second control point.
     */
    public double ctrly2;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s end point.
     */
    public double x2;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s end point.
     */
    public double y2;

    /**
     * Constructs a new CubicCurve2D that stores its coordinate values
     * in double-precision floating-point format. All points are
     * initially at position (0, 0).
     */
    public Double()
    {
    }

    /**
     * Constructs a new CubicCurve2D that stores its coordinate values
     * in double-precision floating-point format, specifying the
     * initial position of each point.
     *
     * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
     * alt="A drawing of a CubicCurve2D" />
     *
     * @param x1 the <i>x</i> coordinate of the curve&#x2019;s start
     * point.
     *
     * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
     * point.
     *
     * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s first
     * control point.
     *
     * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s first
     * control point.
     *
     * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s second
     * control point.
     *
     * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s second
     * control point.
     *
     * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
     * point.
     *
     * @param y2 the <i>y</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public Double(double x1, double y1, double cx1, double cy1, double cx2,
                  double cy2, double x2, double y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      ctrlx1 = cx1;
      ctrly1 = cy1;
      ctrlx2 = cx2;
      ctrly2 = cy2;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s start
     * point.
     */
    public double getX1()
    {
      return x1;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s start
     * point.
     */
    public double getY1()
    {
      return y1;
    }

    /**
     * Returns the curve&#x2019;s start point.
     */
    public Point2D getP1()
    {
      return new Point2D.Double(x1, y1);
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s first
     * control point.
     */
    public double getCtrlX1()
    {
      return ctrlx1;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s first
     * control point.
     */
    public double getCtrlY1()
    {
      return ctrly1;
    }

    /**
     * Returns the curve&#x2019;s first control point.
     */
    public Point2D getCtrlP1()
    {
      return new Point2D.Double(ctrlx1, ctrly1);
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s second
     * control point.
     */
    public double getCtrlX2()
    {