/// <summary>
/// Computes the (approximate) intersection point between two line segments
/// using homogeneous coordinates.
/// Notice that this algorithm is
/// not numerically stable; i.e. it can produce intersection points which
/// lie outside the envelope of the line segments themselves. In order
/// to increase the precision of the calculation input points should be normalized
/// before passing them to this routine.
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="q1"></param>
/// <param name="q2"></param>
/// <returns></returns>
public static Coordinate Intersection(Coordinate p1, Coordinate p2, Coordinate q1, Coordinate q2)
{
HCoordinate l1 = new HCoordinate(new HCoordinate(p1), new HCoordinate(p2));
HCoordinate l2 = new HCoordinate(new HCoordinate(q1), new HCoordinate(q2));
HCoordinate intHCoord = new HCoordinate(l1, l2);
Coordinate intPt = intHCoord.Coordinate;
return(intPt);
}
/// <summary>
/// This method computes the actual value of the intersection point.
/// To obtain the maximum precision from the intersection calculation,
/// the coordinates are normalized by subtracting the minimum
/// ordinate values (in absolute value). This has the effect of
/// removing common significant digits from the calculation to
/// maintain more bits of precision.
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="q1"></param>
/// <param name="q2"></param>
/// <returns></returns>
private Coordinate Intersection(Coordinate p1, Coordinate p2, Coordinate q1, Coordinate q2)
{
Coordinate n1 = new Coordinate(p1);
Coordinate n2 = new Coordinate(p2);
Coordinate n3 = new Coordinate(q1);
Coordinate n4 = new Coordinate(q2);
Coordinate normPt = new Coordinate();
NormalizeToEnvCentre(n1, n2, n3, n4, normPt);
Coordinate intPt = HCoordinate.Intersection(n1, n2, n3, n4);
intPt.X += normPt.X;
intPt.Y += normPt.Y;
/*
*
* MD - May 4 2005 - This is still a problem. Here is a failure case:
*
* LINESTRING (2089426.5233462777 1180182.3877339689, 2085646.6891757075 1195618.7333999649)
* LINESTRING (1889281.8148903656 1997547.0560044837, 2259977.3672235999 483675.17050843034)
* int point = (2097408.2633752143, 1144595.8008114607)
*/
if (!IsInSegmentEnvelopes(intPt))
{
Trace.WriteLine("Intersection outside segment envelopes: " + intPt);
}
/*
* // disabled until a better solution is found
* if (!IsInSegmentEnvelopes(intPt))
* {
* Trace.WriteLine("first value outside segment envelopes: " + intPt);
*
* IteratedBisectionIntersector ibi = new IteratedBisectionIntersector(p1, p2, q1, q2);
* intPt = ibi.Intersection;
* }
* if (!IsInSegmentEnvelopes(intPt))
* {
* Trace.WriteLine("ERROR - outside segment envelopes: " + intPt);
*
* IteratedBisectionIntersector ibi = new IteratedBisectionIntersector(p1, p2, q1, q2);
* Coordinate testPt = ibi.Intersection;
* }
*/
if (PrecisionModel != null)
{
PrecisionModel.MakePrecise(intPt);
}
return(intPt);
}
/// <summary>
///
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
public HCoordinate(HCoordinate p1, HCoordinate p2)
{
_x = p1._y * p2._w - p2._y * p1._w;
_y = p2._x * p1._w - p1._x * p2._w;
_w = p1._x * p2._y - p2._x * p1._y;
}