quadcurve2d.java

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   *
   * <p>The left end point and the right start point will always be
   * identical. Memory-concious programmers thus may want to pass the
   * same array for both <code>left</code> and <code>right</code>, and
   * set <code>rightOff</code> to <code>leftOff + 4</code>.
   *
   * @param src an array containing the coordinates of the curve to be
   * subdivided.  The <i>x</i> coordinate of the start point is
   * located at <code>src[srcOff]</code>, its <i>y</i> at
   * <code>src[srcOff + 1]</code>.  The <i>x</i> coordinate of the
   * control point is located at <code>src[srcOff + 2]</code>, its
   * <i>y</i> at <code>src[srcOff + 3]</code>.  The <i>x</i>
   * coordinate of the end point is located at <code>src[srcOff +
   * 4]</code>, its <i>y</i> at <code>src[srcOff + 5]</code>.
   *
   * @param srcOff an offset into <code>src</code>, specifying
   * the index of the start point&#x2019;s <i>x</i> coordinate.
   *
   * @param left an array that will receive the coordinates of the
   * left half of <code>src</code>. It is acceptable to pass
   * <code>src</code>. A caller who is not interested in the left half
   * can pass <code>null</code>.
   *
   * @param leftOff an offset into <code>left</code>, specifying the
   * index where the start point&#x2019;s <i>x</i> coordinate will be
   * stored.
   *
   * @param right an array that will receive the coordinates of the
   * right half of <code>src</code>. It is acceptable to pass
   * <code>src</code> or <code>left</code>. A caller who is not
   * interested in the right half can pass <code>null</code>.
   *
   * @param rightOff an offset into <code>right</code>, specifying the
   * index where the start point&#x2019;s <i>x</i> coordinate will be
   * stored.
   */
  public static void subdivide(double[] src, int srcOff,
                               double[] left, int leftOff,
                               double[] right, int rightOff)
  {
    double x1, y1, xc, yc, x2, y2;

    x1 = src[srcOff];
    y1 = src[srcOff + 1];
    xc = src[srcOff + 2];
    yc = src[srcOff + 3];
    x2 = src[srcOff + 4];
    y2 = src[srcOff + 5];

    if (left != null)
    {
      left[leftOff] = x1;
      left[leftOff + 1] = y1;
    }

    if (right != null)
    {
      right[rightOff + 4] = x2;
      right[rightOff + 5] = y2;
    }

    x1 = (x1 + xc) / 2;
    x2 = (xc + x2) / 2;
    xc = (x1 + x2) / 2;
    y1 = (y1 + yc) / 2;
    y2 = (y2 + yc) / 2;
    yc = (y1 + y2) / 2;

    if (left != null)
    {
      left[leftOff + 2] = x1;
      left[leftOff + 3] = y1;
      left[leftOff + 4] = xc;
      left[leftOff + 5] = yc;
    }

    if (right != null)
    {
      right[rightOff] = xc;
      right[rightOff + 1] = yc;
      right[rightOff + 2] = x2;
      right[rightOff + 3] = y2;
    }
  }


  /**
   * Finds the non-complex roots of a quadratic equation, placing the
   * results into the same array as the equation coefficients. The
   * following equation is being solved:
   *
   * <blockquote><code>eqn[2]</code> &#xb7; <i>x</i><sup>2</sup>
   * + <code>eqn[1]</code> &#xb7; <i>x</i>
   * + <code>eqn[0]</code>
   * = 0
   * </blockquote>
   *
   * <p>For some background about solving quadratic equations, see the
   * article <a href=
   * "http://planetmath.org/encyclopedia/QuadraticFormula.html"
   * >&#x201c;Quadratic Formula&#x201d;</a> in <a href=
   * "http://planetmath.org/">PlanetMath</a>. For an extensive library
   * of numerical algorithms written in the C programming language,
   * see the <a href="http://www.gnu.org/software/gsl/">GNU Scientific
   * Library</a>.
   *
   * @see #solveQuadratic(double[], double[])
   * @see CubicCurve2D#solveCubic(double[], double[])
   *
   * @param eqn an array with the coefficients of the equation. When
   * this procedure has returned, <code>eqn</code> will contain the
   * non-complex solutions of the equation, in no particular order.
   *
   * @return the number of non-complex solutions. A result of 0
   * indicates that the equation has no non-complex solutions. A
   * result of -1 indicates that the equation is constant (i.e.,
   * always or never zero).
   *
   * @author <a href="mailto:[e-mail]">Brian Gough</a>
   * (original C implementation in the <a href=
   * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
   *
   * @author <a href="mailto:[e-mail]">Sascha Brawer</a>
   * (adaptation to Java)
   */
  public static int solveQuadratic(double[] eqn)
  {
    return solveQuadratic(eqn, eqn);
  }


  /**
   * Finds the non-complex roots of a quadratic equation. The
   * following equation is being solved:
   *
   * <blockquote><code>eqn[2]</code> &#xb7; <i>x</i><sup>2</sup>
   * + <code>eqn[1]</code> &#xb7; <i>x</i>
   * + <code>eqn[0]</code>
   * = 0
   * </blockquote>
   *
   * <p>For some background about solving quadratic equations, see the
   * article <a href=
   * "http://planetmath.org/encyclopedia/QuadraticFormula.html"
   * >&#x201c;Quadratic Formula&#x201d;</a> in <a href=
   * "http://planetmath.org/">PlanetMath</a>. For an extensive library
   * of numerical algorithms written in the C programming language,
   * see the <a href="http://www.gnu.org/software/gsl/">GNU Scientific
   * Library</a>.
   *
   * @see CubicCurve2D#solveCubic(double[],double[])
   *
   * @param eqn an array with the coefficients of the equation.
   *
   * @param res an array into which the non-complex roots will be
   * stored.  The results may be in an arbitrary order. It is safe to
   * pass the same array object reference for both <code>eqn</code>
   * and <code>res</code>.
   *
   * @return the number of non-complex solutions. A result of 0
   * indicates that the equation has no non-complex solutions. A
   * result of -1 indicates that the equation is constant (i.e.,
   * always or never zero).
   *
   * @author <a href="mailto:[e-mail]">Brian Gough</a>
   * (original C implementation in the <a href=
   * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
   *
   * @author <a href="mailto:[e-mail]">Sascha Brawer</a>
   * (adaptation to Java)
   */
  public static int solveQuadratic(double[] eqn, double[] res)
  {
    // Taken from poly/solve_quadratic.c in the GNU Scientific Library
    // (GSL), cvs revision 1.7 of 2003-07-26. For the original source,
    // see http://www.gnu.org/software/gsl/
    //
    // Brian Gough, the author of that code, has granted the
    // permission to use it in GNU Classpath under the GNU Classpath
    // license, and has assigned the copyright to the Free Software
    // Foundation.
    //
    // The Java implementation is very similar to the GSL code, but
    // not a strict one-to-one copy. For example, GSL would sort the
    // result.

    double a, b, c, disc;

    c = eqn[0];
    b = eqn[1];
    a = eqn[2];

    // Check for linear or constant functions. This is not done by the
    // GNU Scientific Library.  Without this special check, we
    // wouldn't return -1 for constant functions, and 2 instead of 1
    // for linear functions.
    if (a == 0)
    {
      if (b == 0)
        return -1;
      
      res[0] = -c / b;
      return 1;
    }

    disc = b * b - 4 * a * c;

    if (disc < 0)
      return 0;

    if (disc == 0)
    {
      // The GNU Scientific Library returns two identical results here.
      // We just return one.
      res[0] = -0.5 * b / a ;
      return 1;
    }

    // disc > 0
    if (b == 0)
    {
      double r;

      r = Math.abs(0.5 * Math.sqrt(disc) / a);
      res[0] = -r;
      res[1] = r;
    }
    else
    {
      double sgnb, temp;
      
      sgnb = (b > 0 ? 1 : -1);
      temp = -0.5 * (b + sgnb * Math.sqrt(disc));

      // The GNU Scientific Library sorts the result here. We don't.
      res[0] = temp / a;
      res[1] = c / temp;
    }
    return 2;
  }


  /**
   * Determines whether a point lies inside the area that is bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/QuadCurve2D-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;contained&#x201d; in a QuadCurve2D.
   */
  public boolean contains(double x, double y)
  {
    // XXX Implement.
    throw new Error("not implemented");
  }


  /**
   * Determines whether a point lies inside the area that is bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/QuadCurve2D-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;contained&#x201d; in a QuadCurve2D.
   */
  public boolean contains(Point2D p)
  {
    return contains(p.getX(), p.getY());
  }


  public boolean intersects(double x, double y, double w, double h)
  {
    // XXX Implement.
    throw new Error("not implemented");
  }


  public boolean intersects(Rectangle2D r)
  {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }


  public boolean contains(double x, double y, double w, double h)
  {
    // XXX Implement.
    throw new Error("not implemented");
  }


  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 point. As the illustration
   * below shows, the invisible control point may cause the bounds to
   * be much larger than the area that is actually covered by the
   * curve.
   *
   * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180"
   * alt="An illustration of the bounds of a QuadCurve2D" />
   */
  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) getCtrlX();
          coords[1] = (float) getCtrlY();
          coords[2] = (float) getX2();
          coords[3] = (float) getY2();
          result = SEG_QUADTO;
          break;

        default:
          throw new NoSuchElementException("quad iterator out of bounds");
        }
        if (at != null)
          at.transform(coords, 0, coords, 0, 2);
        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] = getCtrlX();
          coords[1] = getCtrlY();
          coords[2] = getX2();
          coords[3] = getY2();
          result = SEG_QUADTO;
          break;

        default:
          throw new NoSuchElementException("quad iterator out of bounds");
        }
        if (at != null)
          at.transform(coords, 0, coords, 0, 2);
        return result;
      }
    };
  }


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


  /**
   * Creates 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
    }
  }


  /**
   * A two-dimensional curve that is parameterized with a quadratic
   * function and stores coordinate values in double-precision
   * floating-point format.
   *
   * @see QuadCurve2D.Float
   *
   * @author Eric Blake ([e-mail])
   * @author Sascha Brawer ([e-mail])
   */
  public static class Double
    extends QuadCurve2D
  {
    /**
     * 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 control point.
     */
    public double ctrlx;


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


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