line2d.java

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/* Line2D.java -- represents a line in 2-D space, plus operations on a line
   Copyright (C) 2000, 2001, 2002 Free Software Foundation

This file is part of GNU Classpath.

GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

GNU Classpath is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with GNU Classpath; see the file COPYING.  If not, write to the
Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA.

Linking this library statically or dynamically with other modules is
making a combined work based on this library.  Thus, the terms and
conditions of the GNU General Public License cover the whole
combination.

As a special exception, the copyright holders of this library give you
permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
modules, and to copy and distribute the resulting executable under
terms of your choice, provided that you also meet, for each linked
independent module, the terms and conditions of the license of that
module.  An independent module is a module which is not derived from
or based on this library.  If you modify this library, you may extend
this exception to your version of the library, but you are not
obligated to do so.  If you do not wish to do so, delete this
exception statement from your version. */

package java.awt.geom;

import java.awt.Rectangle;
import java.awt.Shape;
import java.util.NoSuchElementException;

/**
 * Represents a directed line bewteen two points in (x,y) Cartesian space.
 * Remember, on-screen graphics have increasing x from left-to-right, and
 * increasing y from top-to-bottom. The storage is left to subclasses.
 *
 * @author Tom Tromey <[e-mail]>
 * @author Eric Blake <[e-mail]>
 * @since 1.2
 * @status updated to 1.4
 */
public abstract class Line2D implements Shape, Cloneable
{
  /**
   * The default constructor.
   */
  protected Line2D()
  {
  }

  /**
   * Return the x coordinate of the first point.
   *
   * @return the starting x coordinate
   */
  public abstract double getX1();

  /**
   * Return the y coordinate of the first point.
   *
   * @return the starting y coordinate
   */
  public abstract double getY1();

  /**
   * Return the first point.
   *
   * @return the starting point
   */
  public abstract Point2D getP1();

  /**
   * Return the x coordinate of the second point.
   *
   * @return the ending x coordinate
   */
  public abstract double getX2();

  /**
   * Return the y coordinate of the second point.
   *
   * @return the ending y coordinate
   */
  public abstract double getY2();

  /**
   * Return the second point.
   *
   * @return the ending point
   */
  public abstract Point2D getP2();

  /**
   * Set the coordinates of the line to the given coordinates. Loss of
   * precision may occur due to rounding issues.
   *
   * @param x1 the first x coordinate
   * @param y1 the first y coordinate
   * @param x2 the second x coordinate
   * @param y2 the second y coordinate
   */
  public abstract void setLine(double x1, double y1, double x2, double y2);

  /**
   * Set the coordinates to the given points.
   *
   * @param p1 the first point
   * @param p2 the second point
   * @throws NullPointerException if either point is null
   */
  public void setLine(Point2D p1, Point2D p2)
  {
    setLine(p1.getX(), p1.getY(), p2.getX(), p2.getY());
  }

  /**
   * Set the coordinates to those of the given line.
   *
   * @param l the line to copy
   * @throws NullPointerException if l is null
   */
  public void setLine(Line2D l)
  {
    setLine(l.getX1(), l.getY1(), l.getX2(), l.getY2());
  }

  /**
   * Computes the relative rotation direction needed to pivot the line about
   * the first point in order to have the second point colinear with point p.
   * Because of floating point rounding, don't expect this to be a perfect
   * measure of colinearity. The answer is 1 if the line has a shorter rotation
   * in the direction of the positive X axis to the negative Y axis
   * (counter-clockwise in the default Java coordinate system), or -1 if the
   * shortest rotation is in the opposite direction (clockwise). If p
   * is already colinear, the return value is -1 if it lies beyond the first
   * point, 0 if it lies in the segment, or 1 if it lies beyond the second
   * point. If the first and second point are coincident, this returns 0.
   *
   * @param x1 the first x coordinate
   * @param y1 the first y coordinate
   * @param x2 the second x coordinate
   * @param y2 the second y coordinate
   * @param px the reference x coordinate
   * @param py the reference y coordinate
   * @return the relative rotation direction
   */
  public static int relativeCCW(double x1, double y1, double x2, double y2,
                                double px, double py)
  {
    if ((x1 == x2 && y1 == y2)
        || (x1 == px && y1 == py))
      return 0; // Coincident points.
    // Translate to the origin.
    x2 -= x1;
    y2 -= y1;
    px -= x1;
    py -= y1;
    double slope2 = y2 / x2;
    double slopep = py / px;
    if (slope2 == slopep || (x2 == 0 && px == 0))
      return y2 > 0 // Colinear.
        ? (py < 0 ? -1 : py > y2 ? 1 : 0)
        : (py > 0 ? -1 : py < y2 ? 1 : 0);
    if (x2 >= 0 && slope2 >= 0)
      return px >= 0 // Quadrant 1.
        ? (slope2 > slopep ? 1 : -1)
        : (slope2 < slopep ? 1 : -1);
    if (y2 > 0)
      return px < 0 // Quadrant 2.
        ? (slope2 > slopep ? 1 : -1)
        : (slope2 < slopep ? 1 : -1);
    if (slope2 >= 0.0)
      return px >= 0 // Quadrant 3.
        ? (slope2 < slopep ? 1 : -1)
        : (slope2 > slopep ? 1 : -1);
    return px < 0 // Quadrant 4.
      ? (slope2 < slopep ? 1 : -1)
      : (slope2 > slopep ? 1 : -1);
  }

  /**
   * Computes the relative rotation direction needed to pivot this line about
   * the first point in order to have the second point colinear with point p.
   * Because of floating point rounding, don't expect this to be a perfect
   * measure of colinearity. The answer is 1 if the line has a shorter rotation
   * in the direction of the positive X axis to the negative Y axis
   * (counter-clockwise in the default Java coordinate system), or -1 if the
   * shortest rotation is in the opposite direction (clockwise). If p
   * is already colinear, the return value is -1 if it lies beyond the first
   * point, 0 if it lies in the segment, or 1 if it lies beyond the second
   * point. If the first and second point are coincident, this returns 0.
   *
   * @param px the reference x coordinate
   * @param py the reference y coordinate
   * @return the relative rotation direction
   * @see #relativeCCW(double, double, double, double, double, double)
   */
  public int relativeCCW(double px, double py)
  {
    return relativeCCW(getX1(), getY1(), getX2(), getY2(), px, py);
  }

  /**
   * Computes the relative rotation direction needed to pivot this line about
   * the first point in order to have the second point colinear with point p.
   * Because of floating point rounding, don't expect this to be a perfect
   * measure of colinearity. The answer is 1 if the line has a shorter rotation
   * in the direction of the positive X axis to the negative Y axis
   * (counter-clockwise in the default Java coordinate system), or -1 if the
   * shortest rotation is in the opposite direction (clockwise). If p
   * is already colinear, the return value is -1 if it lies beyond the first
   * point, 0 if it lies in the segment, or 1 if it lies beyond the second
   * point. If the first and second point are coincident, this returns 0.
   *
   * @param p the reference point
   * @return the relative rotation direction
   * @throws NullPointerException if p is null
   * @see #relativeCCW(double, double, double, double, double, double)
   */
  public int relativeCCW(Point2D p)
  {
    return relativeCCW(getX1(), getY1(), getX2(), getY2(), p.getX(), p.getY());
  }

  /**
   * Test if the line segment (x1,y1)-&gt;(x2,y2) intersects the line segment
   * (x3,y3)-&gt;(x4,y4).
   *
   * @param x1 the first x coordinate of the first segment
   * @param y1 the first y coordinate of the first segment
   * @param x2 the second x coordinate of the first segment
   * @param y2 the second y coordinate of the first segment
   * @param x3 the first x coordinate of the second segment
   * @param y3 the first y coordinate of the second segment
   * @param x4 the second x coordinate of the second segment
   * @param y4 the second y coordinate of the second segment
   * @return true if the segments intersect
   */
  public static boolean linesIntersect(double x1, double y1,
                                       double x2, double y2,
                                       double x3, double y3,
                                       double x4, double y4)
  {
    double beta = (((y1 - y3) * (x4 - x3) + (x1 - x3) * (y4 - y3))
                   / ((y2 - y1) * (x4 - x3) + (x2 - x1) * (y4 - y3)));
    if (beta < 0.0 || beta > 1.0)
      return false;
    double alpha = (x1 + beta * (x2 - x1) - x3) / (x4 - x3);
    return alpha >= 0.0 && alpha <= 1.0;
  }

  /**
   * Test if this line intersects the line given by (x1,y1)-&gt;(x2,y2).
   *
   * @param x1 the first x coordinate of the other segment
   * @param y1 the first y coordinate of the other segment
   * @param x2 the second x coordinate of the other segment
   * @param y2 the second y coordinate of the other segment
   * @return true if the segments intersect
   * @see #linesIntersect(double, double, double, double,
   *                      double, double, double, double)
   */
  public boolean intersectsLine(double x1, double y1, double x2, double y2)
  {
    return linesIntersect(getX1(), getY1(), getX2(), getY2(),
                          x1, y1, x2, y2);
  }

  /**
   * Test if this line intersects the given line.
   *
   * @param l the other segment
   * @return true if the segments intersect
   * @throws NullPointerException if l is null
   * @see #linesIntersect(double, double, double, double,
   *                      double, double, double, double)
   */
  public boolean intersectsLine(Line2D l)
  {
    return linesIntersect(getX1(), getY1(), getX2(), getY2(),
                          l.getX1(), l.getY1(), l.getX2(), l.getY2());
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on the line segment. If the point is on the segment, the
   * result will be 0.
   *
   * @param x1 the first x coordinate of the segment
   * @param y1 the first y coordinate of the segment
   * @param x2 the second x coordinate of the segment
   * @param y2 the second y coordinate of the segment
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the square of the distance from the point to the segment
   * @see #ptSegDist(double, double, double, double, double, double)
   * @see #ptLineDistSq(double, double, double, double, double, double)
   */
  public static double ptSegDistSq(double x1, double y1, double x2, double y2,
                                   double px, double py)
  {
    double pd2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);

    double x, y;
    if (pd2 == 0)
      {
        // Points are coincident.
        x = x1;
        y = y2;
      }
    else
      {
        double u = ((px - x1) * (x2 - x1) + (py - y1) * (y2 - y1)) / pd2;

        if (u < 0)
          {
            // "Off the end"
            x = x1;
            y = y1;
          }
        else if (u > 1.0)
          {
            x = x2;
            y = y2;
          }
        else
          {
            x = x1 + u * (x2 - x1);
            y = y1 + u * (y2 - y1);
          }
      }

    return (x - px) * (x - px) + (y - py) * (y - py);
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * the line segment. If the point is on the segment, the result will be 0.
   *
   * @param x1 the first x coordinate of the segment
   * @param y1 the first y coordinate of the segment
   * @param x2 the second x coordinate of the segment
   * @param y2 the second y coordinate of the segment
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the distance from the point to the segment
   * @see #ptSegDistSq(double, double, double, double, double, double)
   * @see #ptLineDist(double, double, double, double, double, double)
   */
  public static double ptSegDist(double x1, double y1, double x2, double y2,
                                 double px, double py)