/// <summary>
/// Computes whether a ring defined by an array of {@link Coordinate}s is oriented counter-clockwise.
/// <ul><li>The list of points is assumed to have the first and last points equal.
/// <li>This will handle coordinate lists which contain repeated points.</ul>
/// This algorithm is <b>only</b> guaranteed to work with valid rings.
/// If the ring is invalid (e.g. self-crosses or touches), the computed result may not be correct.
/// </summary>
/// <param name="ring"></param>
/// <returns></returns>
public static bool IsCCW(Point2 <double>[] ring)
{
if (ring.Length < 3)
{
return(false);
}
int nPts = ring.Length - 1;
// find highest point
Point2 <double> hiPt = ring[0];
int hiIndex = 0;
for (int i = 1; i < ring.Length; i++)
{
Point2 <double> p = ring[i];
if (p.Y > hiPt.Y)
{
hiPt = p;
hiIndex = i;
}
}
// find distinct point before highest point
int iPrev = hiIndex;
do
{
iPrev = iPrev - 1;
if (iPrev < 0)
{
iPrev = nPts;
}
} while (ring[iPrev].Equals(hiPt) && iPrev != hiIndex);
// find distinct point after highest point
int iNext = hiIndex;
do
{
iNext = (iNext + 1) % nPts;
} while (ring[iNext].Equals(hiPt) && iNext != hiIndex);
Point2 <double> prev = ring[iPrev];
Point2 <double> next = ring[iNext];
// This check catches cases where the ring contains an A-B-A configuration of points.
// This can happen if the ring does not contain 3 distinct points (including the case where the input array has fewer than 4 elements), or it contains coincident line segments.
if (prev.Equals(hiPt) || next.Equals(hiPt) || prev.Equals(next))
{
return(false);
}
int disc = Coordinate2Utils.OrientationIndex(prev.X, prev.Y, hiPt.X, hiPt.Y, next.X, next.Y);
// If disc is exactly 0, lines are collinear. There are two possible cases:
// (1) the lines lie along the x axis in opposite directions (is handled by checking if next is left of prev ==> CCW)
// (2) the lines lie on top of one another (will never happen if the ring is valid, so don't check for it)
bool isCCW = false;
if (disc == 0) //poly is CCW if prev x is right of next x
{
isCCW = (prev.X > next.X);
}
else // if area is positive, points are ordered CCW
{
isCCW = (disc > 0);
}
return(isCCW);
}
public static LineSegment2IntersectionResult <double> ComputeIntersection(Point2 <double> p1, Point2 <double> p2, Point2 <double> q1, Point2 <double> q2)
{
if (p1 == null || p2 == null || q1 == null || q2 == null)
{
return(null);
}
//quick rejection
if (!Coordinate2Utils.EnvelopesIntersect(p1, p2, q1, q2))
{
return(new LineSegment2IntersectionResult <double>());
}
// for each endpoint, compute which side of the other segment it lies
// if both endpoints lie on the same side of the other segment, the segments do not intersect
int Pq1 = Coordinate2Utils.OrientationIndex(p1, p2, q1);
int Pq2 = Coordinate2Utils.OrientationIndex(p1, p2, q2);
if ((Pq1 > 0 && Pq2 > 0) || (Pq1 < 0 && Pq2 < 0))
{
return(new LineSegment2IntersectionResult <double>());
}
int Qp1 = Coordinate2Utils.OrientationIndex(q1, q2, p1);
int Qp2 = Coordinate2Utils.OrientationIndex(q1, q2, p2);
if ((Qp1 > 0 && Qp2 > 0) || (Qp1 < 0 && Qp2 < 0))
{
return(new LineSegment2IntersectionResult <double>());
}
//end quick rejection
if (Pq1 == 0 && Pq2 == 0 && Qp1 == 0 && Qp2 == 0) //collinear intersection
{
bool p1q1p2 = Coordinate2Utils.PointInEnvelope(p1, p2, q1);
bool p1q2p2 = Coordinate2Utils.PointInEnvelope(p1, p2, q2);
bool q1p1q2 = Coordinate2Utils.PointInEnvelope(q1, q2, p1);
bool q1p2q2 = Coordinate2Utils.PointInEnvelope(q1, q2, p2);
if (p1q1p2 && p1q2p2)
{
return(new LineSegment2IntersectionResult <double>(LineIntersectionType.CollinearIntersection, q1, q2));
}
if (q1p1q2 && q1p2q2)
{
return(new LineSegment2IntersectionResult <double>(LineIntersectionType.CollinearIntersection, p1, p2));
}
if (p1q1p2 && q1p1q2)
{
if (q1.Equals(p1) && !p1q2p2 && !q1p2q2)
{
return(new LineSegment2IntersectionResult <double>(q1));
}
return(new LineSegment2IntersectionResult <double>(LineIntersectionType.CollinearIntersection, q1, p1));
}
if (p1q1p2 && q1p2q2)
{
if (q1.Equals(p2) && !p1q2p2 && !q1p1q2)
{
return(new LineSegment2IntersectionResult <double>(q1));
}
return(new LineSegment2IntersectionResult <double>(LineIntersectionType.CollinearIntersection, q1, p2));
}
if (p1q2p2 && q1p1q2)
{
if (q2.Equals(p1) && !p1q1p2 && !q1p2q2)
{
return(new LineSegment2IntersectionResult <double>(q2));
}
return(new LineSegment2IntersectionResult <double>(LineIntersectionType.CollinearIntersection, q2, p1));
}
if (p1q2p2 && q1p2q2)
{
if (q2.Equals(p2) && !p1q1p2 && !q1p1q2)
{
return(new LineSegment2IntersectionResult <double>(q2));
}
return(new LineSegment2IntersectionResult <double>(LineIntersectionType.CollinearIntersection, q2, p2));
}
return(new LineSegment2IntersectionResult <double>());
}//end collinear
// At this point we know that there is a single intersection point (since the lines are not collinear).
// Check if the intersection is an endpoint. If it is, copy the endpoint as the intersection point. Copying the point rather than computing it
// ensures the point has the exact value, which is important for robustness. It is sufficient to simply check for an endpoint which is on
// the other line, since at this point we know that the inputLines must intersect.
if (Pq1 == 0 || Pq2 == 0 || Qp1 == 0 || Qp2 == 0)
{
// Check for two equal endpoints. This is done explicitly rather than by the orientation tests below in order to improve robustness.
if (p1.Equals(q1) || p1.Equals(q2))
{
return(new LineSegment2IntersectionResult <double>(p1));
}
else if (p2.Equals(q1) || p2.Equals(q2))
{
return(new LineSegment2IntersectionResult <double>(p2));
}
// Now check to see if any endpoint lies on the interior of the other segment.
else if (Pq1 == 0)
{
return(new LineSegment2IntersectionResult <double>(q1));
}
else if (Pq2 == 0)
{
return(new LineSegment2IntersectionResult <double>(q2));
}
else if (Qp1 == 0)
{
return(new LineSegment2IntersectionResult <double>(p1));
}
else if (Qp2 == 0)
{
return(new LineSegment2IntersectionResult <double>(p2));
}
} //end exact at endpoint
//intersectWNormalization
Coordinate2 <double> n1 = new Coordinate2 <double>(p1);
Coordinate2 <double> n2 = new Coordinate2 <double>(p2);
Coordinate2 <double> n3 = new Coordinate2 <double>(q1);
Coordinate2 <double> n4 = new Coordinate2 <double>(q2);
Coordinate2 <double> normPt = new Coordinate2 <double>();
Coordinate2Utils.NormalizeToEnvCentre(n1, n2, n3, n4, normPt);
//safeHCoordinateIntersection
Coordinate2 <double> intPt = null;
// unrolled computation
double px = n1.Y - n2.Y;
double py = n2.X - n1.X;
double pw = n1.X * n2.Y - n2.X * n1.Y;
double qx = n3.Y - n4.Y;
double qy = n4.X - n3.X;
double qw = n3.X * n4.Y - n4.X * n3.Y;
double x = py * qw - qy * pw;
double y = qx * pw - px * qw;
double w = px * qy - qx * py;
double xInt = x / w;
double yInt = y / w;
if (double.IsNaN(xInt) || double.IsNaN(yInt) || double.IsInfinity(xInt) || double.IsInfinity(yInt))
{
intPt = MeanNearest(n1, n2, n3, n4);
xInt = intPt.X + normPt.X;
yInt = intPt.Y + normPt.Y;
return(new LineSegment2IntersectionResult <double>(p1.Factory.ConstructPoint(xInt, yInt)));
}
else
{
xInt += normPt.X;
yInt += normPt.Y;
intPt = new Coordinate2 <double>(xInt, yInt);
}
//End safeHCoordinateIntersection
//End intersectWNormalization
if (!(Coordinate2Utils.PointInEnvelope(p1, p2, intPt) || Coordinate2Utils.PointInEnvelope(q1, q2, intPt)))
{
intPt = MeanNearest(p1, p2, q1, q2);
}
return(new LineSegment2IntersectionResult <double>(p1.Factory.ConstructPoint(intPt.X, intPt.Y)));
}