line2d.java

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     * methods below.
     *
     * @see java.awt.geom.Line2D.Float
     * @see java.awt.geom.Line2D.Double
     */
    protected Line2D() {
    }

    /**
     * Returns the X coordinate of the start point in double precision.
     * @return the X coordinate of this <code>Line2D</code> object's 
     *	    starting point.
     */
    public abstract double getX1();

    /**
     * Returns the Y coordinate of the start point in double precision.
     * @return the Y coordinate of this <code>Line2D</code> object's 
     *	    starting point. 
     */
    public abstract double getY1();

    /**
     * Returns the starting <code>Point2D</code> of this
     * <code>Line2D</code>.
     * @return the starting <code>Point2D</code> of this
     *		<code>Line2D</code>.
     */
    public abstract Point2D getP1();

    /**
     * Returns the X coordinate of the end point in double precision.
     * @return the X coordinate of this <code>Line2D</code> object's 
     *	    starting point.
     */
    public abstract double getX2();

    /**
     * Returns the Y coordinate of the end point in double precision.
     * @return the Y coordinate of this <code>Line2D</code> object's 
     *      starting point.
     */
    public abstract double getY2();

    /**
     * Returns the end <code>Point2D</code> of this <code>Line2D</code>.
     * @return a <code>Point2D</code> that is the endpoint of this
     * 		<code>Line2D</code>.
     */
    public abstract Point2D getP2();

    /**
     * Sets the location of the endpoints of this <code>Line2D</code> to
     * the specified double coordinates.
     * @param X1,&nbsp;Y1 the first specified coordinate
     * @param X2,&nbsp;Y2 the second specified coordinate
     */
    public abstract void setLine(double X1, double Y1, double X2, double Y2);

    /**
     * Sets the location of the endpoints of this <code>Line2D</code> to
     * the specified <code>Point2D</code> coordinates.
     * @param p1,&nbsp;p2 the specified <code>Point2D</code> objects
     */
    public void setLine(Point2D p1, Point2D p2) {
	setLine(p1.getX(), p1.getY(), p2.getX(), p2.getY());
    }

    /**
     * Sets the location of the endpoints of this <code>Line2D</code> to
     * the same as those endpoints of the specified <code>Line2D</code>.
     * @param l the specified <code>Line2D</code>
     */
    public void setLine(Line2D l) {
	setLine(l.getX1(), l.getY1(), l.getX2(), l.getY2());
    }

    /**
     * Returns an indicator of where the specified point 
     * (PX,&nbsp;PY) lies with respect to the line segment from 
     * (X1,&nbsp;Y1) to (X2,&nbsp;Y2).
     * The return value can be either 1, -1, or 0 and indicates
     * in which direction the specified line must pivot around its
     * first endpoint, (X1,&nbsp;Y1), in order to point at the
     * specified point (PX,&nbsp;PY).
     * <p>A return value of 1 indicates that the line segment must
     * turn in the direction that takes the positive X axis towards
     * the negative Y axis.  In the default coordinate system used by
     * Java 2D, this direction is counterclockwise.  
     * <p>A return value of -1 indicates that the line segment must
     * turn in the direction that takes the positive X axis towards
     * the positive Y axis.  In the default coordinate system, this 
     * direction is clockwise.
     * <p>A return value of 0 indicates that the point lies
     * exactly on the line segment.  Note that an indicator value 
     * of 0 is rare and not useful for determining colinearity 
     * because of floating point rounding issues. 
     * <p>If the point is colinear with the line segment, but 
     * not between the endpoints, then the value will be -1 if the point
     * lies "beyond (X1,&nbsp;Y1)" or 1 if the point lies 
     * "beyond (X2,&nbsp;Y2)".
     * @param X1,&nbsp;Y1 the coordinates of the beginning of the
     *		specified line segment
     * @param X2,&nbsp;Y2 the coordinates of the end of the specified
     *		line segment
     * @param PX,&nbsp;PY the coordinates of the specified point to be
     * 		compared with the specified line segment
     * @return an integer that indicates the position of the third specified
     *			coordinates with respect to the line segment formed
     *			by the first two specified coordinates.
     */
    public static int relativeCCW(double X1, double Y1,
				  double X2, double Y2,
				  double PX, double PY) {
	X2 -= X1;
	Y2 -= Y1;
	PX -= X1;
	PY -= Y1;
	double ccw = PX * Y2 - PY * X2;
	if (ccw == 0.0) {
	    // The point is colinear, classify based on which side of
	    // the segment the point falls on.  We can calculate a
	    // relative value using the projection of PX,PY onto the
	    // segment - a negative value indicates the point projects
	    // outside of the segment in the direction of the particular
	    // endpoint used as the origin for the projection.
	    ccw = PX * X2 + PY * Y2;
	    if (ccw > 0.0) {
		// Reverse the projection to be relative to the original X2,Y2
		// X2 and Y2 are simply negated.
		// PX and PY need to have (X2 - X1) or (Y2 - Y1) subtracted
		//    from them (based on the original values)
		// Since we really want to get a positive answer when the
		//    point is "beyond (X2,Y2)", then we want to calculate
		//    the inverse anyway - thus we leave X2 & Y2 negated.
		PX -= X2;
		PY -= Y2;
		ccw = PX * X2 + PY * Y2;
		if (ccw < 0.0) {
		    ccw = 0.0;
		}
	    }
	}
	return (ccw < 0.0) ? -1 : ((ccw > 0.0) ? 1 : 0);
    }

    /**
     * Returns an indicator of where the specified point 
     * (PX,&nbsp;PY) lies with respect to this line segment.
     * See the method comments of 
     * {@link #relativeCCW(double, double, double, double, double, double)}
     * to interpret the return value.
     * @param PX,&nbsp;PY the coordinates of the specified point
     *			to be compared with the current line segment
     * @return an integer that indicates the position of the specified
     *			coordinates with respect to the current line segment.
     * @see #relativeCCW(double, double, double, double, double, double)
     */
    public int relativeCCW(double PX, double PY) {
	return relativeCCW(getX1(), getY1(), getX2(), getY2(), PX, PY);
    }

    /**
     * Returns an indicator of where the specified <code>Point2D</code>
     * lies with respect to this line segment.
     * See the method comments of
     * {@link #relativeCCW(double, double, double, double, double, double)}
     * to interpret the return value.
     * @param p the specified <code>Point2D</code> to be compared 
     *			with the current line segment
     * @return an integer that indicates the position of the 
     *			<code>Point2D</code> with respect to the current 
     *			line segment.
     * @see #relativeCCW(double, double, double, double, double, double)
     */
    public int relativeCCW(Point2D p) {
	return relativeCCW(getX1(), getY1(), getX2(), getY2(),
			   p.getX(), p.getY());
    }

    /**
     * Tests if the line segment from (X1,&nbsp;Y1) to 
     * (X2,&nbsp;Y2) intersects the line segment from (X3,&nbsp;Y3) 
     * to (X4,&nbsp;Y4).
     * @param X1,&nbsp;Y1 the coordinates of the beginning of the first 
     *			specified line segment
     * @param X2,&nbsp;Y2 the coordinates of the end of the first 
     *			specified line segment
     * @param X3,&nbsp;Y3 the coordinates of the beginning of the second
     *			 specified line segment
     * @param X4,&nbsp;Y4 the coordinates of the end of the second 
     *			specified line segment
     * @return <code>true</code> if the first specified line segment 
     *			and the second specified line segment intersect  
     *			each other; <code>false</code> otherwise.  
     */
    public static boolean linesIntersect(double X1, double Y1,
					 double X2, double Y2,
					 double X3, double Y3,
					 double X4, double Y4) {
	return ((relativeCCW(X1, Y1, X2, Y2, X3, Y3) *
		 relativeCCW(X1, Y1, X2, Y2, X4, Y4) <= 0)
		&& (relativeCCW(X3, Y3, X4, Y4, X1, Y1) *
		    relativeCCW(X3, Y3, X4, Y4, X2, Y2) <= 0));
    }

    /**
     * Tests if the line segment from (X1,&nbsp;Y1) to 
     * (X2,&nbsp;Y2) intersects this line segment.
     * @param X1,&nbsp;Y1 the coordinates of the beginning of the 
     *			specified line segment
     * @param X2,&nbsp;Y2 the coordinates of the end of the specified
     *			line segment			
     * @return <true> if this line segment and the specified line segment
     *			intersect each other; <code>false</code> otherwise.
     */
    public boolean intersectsLine(double X1, double Y1, double X2, double Y2) {
	return linesIntersect(X1, Y1, X2, Y2,
			      getX1(), getY1(), getX2(), getY2());
    }

    /**
     * Tests if the specified line segment intersects this line segment.
     * @param l the specified <code>Line2D</code>
     * @return <code>true</code> if this line segment and the specified line
     *			segment intersect each other; 
     *			<code>false</code> otherwise.
     */
    public boolean intersectsLine(Line2D l) {
	return linesIntersect(l.getX1(), l.getY1(), l.getX2(), l.getY2(),
			      getX1(), getY1(), getX2(), getY2());
    }

    /**
     * Returns the square of the distance from a point to a line segment.
     * The distance measured is the distance between the specified
     * point and the closest point between the specified endpoints.  
     * If the specified point intersects the line segment in between the
     * endpoints, this method returns 0.0.     
     * @param X1,&nbsp;Y1 the coordinates of the beginning of the 
     *			specified line segment
     * @param X2,&nbsp;Y2 the coordinates of the end of the specified 
     *		line segment
     * @param PX,&nbsp;PY the coordinates of the specified point being
     *		measured against the specified line segment
     * @return a double value that is the square of the distance from the
     *			specified point to the specified line segment.
     * @see #ptLineDistSq(double, double, double, double, double, double)
     */
    public static double ptSegDistSq(double X1, double Y1,
				     double X2, double Y2,
				     double PX, double PY) {
	// Adjust vectors relative to X1,Y1
	// X2,Y2 becomes relative vector from X1,Y1 to end of segment
	X2 -= X1;
	Y2 -= Y1;
	// PX,PY becomes relative vector from X1,Y1 to test point
	PX -= X1;
	PY -= Y1;
	double dotprod = PX * X2 + PY * Y2;
	double projlenSq;
	if (dotprod <= 0.0) {
	    // PX,PY is on the side of X1,Y1 away from X2,Y2
	    // distance to segment is length of PX,PY vector
	    // "length of its (clipped) projection" is now 0.0
	    projlenSq = 0.0;
	} else {
	    // switch to backwards vectors relative to X2,Y2
	    // X2,Y2 are already the negative of X1,Y1=>X2,Y2
	    // to get PX,PY to be the negative of PX,PY=>X2,Y2
	    // the dot product of two negated vectors is the same
	    // as the dot product of the two normal vectors
	    PX = X2 - PX;
	    PY = Y2 - PY;
	    dotprod = PX * X2 + PY * Y2;
	    if (dotprod <= 0.0) {
		// PX,PY is on the side of X2,Y2 away from X1,Y1
		// distance to segment is length of (backwards) PX,PY vector
		// "length of its (clipped) projection" is now 0.0
		projlenSq = 0.0;
	    } else {
		// PX,PY is between X1,Y1 and X2,Y2
		// dotprod is the length of the PX,PY vector
		// projected on the X2,Y2=>X1,Y1 vector times the
		// length of the X2,Y2=>X1,Y1 vector
		projlenSq = dotprod * dotprod / (X2 * X2 + Y2 * Y2);
	    }
	}
	// Distance to line is now the length of the relative point
	// vector minus the length of its projection onto the line
	// (which is zero if the projection falls outside the range
	//  of the line segment).
	double lenSq = PX * PX + PY * PY - projlenSq;
	if (lenSq < 0) {
	    lenSq = 0;
	}
	return lenSq;
    }

    /**
     * Returns the distance from a point to a line segment.
     * The distance measured is the distance between the specified
     * point and the closest point between the specified endpoints.  
     * If the specified point intersects the line segment in between the
     * endpoints, this method returns 0.0.
     * @param X1,&nbsp;Y1 the coordinates of the beginning of the
     *		specified line segment
     * @param X2,&nbsp;Y2 the coordinates of the end of the specified line
     * 		segment
     * @param PX,&nbsp;PY the coordinates of the specified point being
     *		measured against the specified line segment
     * @return a double value that is the distance from the specified point
     *				to the specified line segment.
     * @see #ptLineDist(double, double, double, double, double, double)
     */
    public static double ptSegDist(double X1, double Y1,
				   double X2, double Y2,
				   double PX, double PY) {
	return Math.sqrt(ptSegDistSq(X1, Y1, X2, Y2, PX, PY));
    }

    /**
     * Returns the square of the distance from a point to this line segment.
     * The distance measured is the distance between the specified
     * point and the closest point between the current line's endpoints.  
     * If the specified point intersects the line segment in between the
     * endpoints, this method returns 0.0.
     * @param PX,&nbsp;PY the coordinates of the specified point being
     * 		measured against this line segment
     * @return a double value that is the square of the distance from the
     *			specified point to the current line segment.
     * @see #ptLineDistSq(double, double)
     */
    public double ptSegDistSq(double PX, double PY) {
	return ptSegDistSq(getX1(), getY1(), getX2(), getY2(), PX, PY);