/// <summary>
/// Returns the index of the direction of the point <c>q</c>
/// relative to a vector specified by <c>p1-p2</c>.
/// </summary>
/// <param name="p1">The origin point of the vector.</param>
/// <param name="p2">The final point of the vector.</param>
/// <param name="q">The point to compute the direction to.</param>
/// <returns>
/// 1 if q is counter-clockwise (left) from p1-p2,
/// -1 if q is clockwise (right) from p1-p2,
/// 0 if q is collinear with p1-p2.
/// </returns>
public static int OrientationIndex(PointF p1, PointF p2, PointF q)
{
// travelling along p1->p2, turn counter clockwise to get to q return 1,
// travelling along p1->p2, turn clockwise to get to q return -1,
// p1, p2 and q are colinear return 0.
double dx1 = p2.X - p1.X;
double dy1 = p2.Y - p1.Y;
double dx2 = q.X - p2.X;
double dy2 = q.Y - p2.Y;
return(RobustDeterminant.SignOfDet2x2(dx1, dy1, dx2, dy2));
}
/// <summary>
/// Test whether a point lies inside a ring.
/// The ring may be oriented in either direction.
/// If the point lies on the ring boundary the result of this method is unspecified.
/// This algorithm does not attempt to first check the point against the envelope
/// of the ring.
/// </summary>
/// <param name="p">Point to check for ring inclusion.</param>
/// <param name="ring">Assumed to have first point identical to last point.</param>
/// <returns><c>true</c> if p is inside ring.</returns>
public static bool IsPointInRing(PointF p, PointF[] ring)
{
int i;
int i1; // point index; i1 = i-1
double xInt; // x intersection of segment with ray
var crossings = 0; // number of segment/ray crossings
double x1; // translated coordinates
double y1;
double x2;
double y2;
var nPts = ring.Length;
/*
* For each segment l = (i-1, i), see if it crosses ray from test point in positive x direction.
*/
for (i = 1; i < nPts; i++)
{
i1 = i - 1;
var p1 = ring[i];
var p2 = ring[i1];
x1 = p1.X - p.X;
y1 = p1.Y - p.Y;
x2 = p2.X - p.X;
y2 = p2.Y - p.Y;
if (((y1 > 0) && (y2 <= 0)) || ((y2 > 0) && (y1 <= 0)))
{
/* segment straddles x axis, so compute intersection. */
xInt = RobustDeterminant.SignOfDet2x2(x1, y1, x2, y2) / (y2 - y1);
/* crosses ray if strictly positive intersection. */
if (0.0 < xInt)
{
crossings++;
}
}
}
/* p is inside if number of crossings is odd. */
return((crossings % 2) == 1);
}