public static bool IsEmpty(Point point)
{
return(DoubleHelper.IsNaN(point.X) && DoubleHelper.IsNaN(point.Y));
}
public Segment Intersection(Segment segment)
{
// if either segment is empty, the intersection is also empty
if (IsEmpty || segment.IsEmpty)
{
return(Segment.Empty);
}
// if the segments are equal, just return a new equal segment
if (this == segment)
{
return(new Segment(_p1, _p2, _isP1Excluded, _isP2Excluded));
}
// if either segment is a Point, just see if the point is contained in the other segment
if (IsPoint)
{
return(segment.Contains(_p1) ? new Segment(_p1) : Segment.Empty);
}
if (segment.IsPoint)
{
return(Contains(segment._p1) ? new Segment(segment._p1) : Segment.Empty);
}
// okay, no easy answer, so let's do the math...
Point p1 = _p1;
Vector v1 = _p2 - _p1;
Point p2 = segment._p1;
Vector v2 = segment._p2 - segment._p1;
Vector endpointVector = p2 - p1;
double xProd = Vector.CrossProduct(v1, v2);
// if segments are not parallel, then look for intersection on each segment
if (!DoubleHelper.AreVirtuallyEqual(Slope, segment.Slope))
{
// check for intersection on other segment
double s = (Vector.CrossProduct(endpointVector, v1)) / xProd;
if (s < 0 || s > 1)
{
return(Segment.Empty);
}
// check for intersection on this segment
s = (Vector.CrossProduct(endpointVector, v2)) / xProd;
if (s < 0 || s > 1)
{
return(Segment.Empty);
}
// intersection of segments is a point
return(new Segment(p1 + s * v1));
}
// segments are parallel
xProd = Vector.CrossProduct(endpointVector, v1);
if (xProd * xProd > 1.0e-06 * v1.LengthSquared * endpointVector.LengthSquared)
{
// segments do not intersect
return(Segment.Empty);
}
// intersection is overlapping segment
Segment result = new Segment();
// to determine the overlapping segment, create reference segments where the endpoints are *not* excluded
Segment refThis = new Segment(_p1, _p2);
Segment refSegment = new Segment(segment._p1, segment._p2);
// check whether this segment is contained in the other segment
bool includeThisP1 = refSegment.Contains(refThis._p1);
bool includeThisP2 = refSegment.Contains(refThis._p2);
if (includeThisP1 && includeThisP2)
{
result._p1 = _p1;
result._p2 = _p2;
result._isP1Excluded = _isP1Excluded || !segment.Contains(_p1);
result._isP2Excluded = _isP2Excluded || !segment.Contains(_p2);
return(result);
}
// check whether the other segment is contained in this segment
bool includeSegmentP1 = refThis.Contains(refSegment._p1);
bool includeSegmentP2 = refThis.Contains(refSegment._p2);
if (includeSegmentP1 && includeSegmentP2)
{
result._p1 = segment._p1;
result._p2 = segment._p2;
result._isP1Excluded = segment._isP1Excluded || !Contains(segment._p1);
result._isP2Excluded = segment._isP2Excluded || !Contains(segment._p2);
return(result);
}
// the intersection must include one endpoint from this segment and one endpoint from the other segment
if (includeThisP1)
{
result._p1 = _p1;
result._isP1Excluded = _isP1Excluded || !segment.Contains(_p1);
}
else
{
result._p1 = _p2;
result._isP1Excluded = _isP2Excluded || !segment.Contains(_p2);
}
if (includeSegmentP1)
{
result._p2 = segment._p1;
result._isP2Excluded = segment._isP1Excluded || !Contains(segment._p1);
}
else
{
result._p2 = segment._p2;
result._isP2Excluded = segment._isP2Excluded || !Contains(segment._p2);
}
return(result);
}