/// <summary>
/// Returns 0 if no intersections occur, 1 if an intersection point is found,
/// and 2 if the segments are colinear and overlap.
/// </summary>
/// <param name="other"></param>
/// <returns></returns>
public int IntersectionCount(Segment other)
{
double x1 = P1.X;
double y1 = P1.Y;
double x2 = P2.X;
double y2 = P2.Y;
double x3 = other.P1.X;
double y3 = other.P1.Y;
double x4 = other.P2.X;
double y4 = other.P2.Y;
double denom = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1);
// if denom is 0, then the two lines are parallel
double na = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3);
double nb = (x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3);
// if denom is 0 AND na and nb are 0, then the lines are coincident and DO intersect
if (Math.Abs(denom) < Epsilon && Math.Abs(na) < Epsilon && Math.Abs(nb) < Epsilon) return 2;
// If denom is 0, but na or nb are not 0, then the lines are parallel and not coincident
if (denom == 0) return 0;
double ua = na / denom;
double ub = nb / denom;
if (ua < 0 || ua > 1) return 0; // not intersecting with segment a
if (ub < 0 || ub > 1) return 0; // not intersecting with segment b
// If we get here, then one intersection exists and it is found on both line segments
return 1;
}
/// <summary>
/// Uses the intersection count to detect if there is an intersection
/// </summary>
/// <param name="other"></param>
/// <returns></returns>
public bool Intersects(Segment other)
{
return (IntersectionCount(other) > 0);
}
/// <summary>
/// For each coordinate in the other part, if it falls in the extent of this polygon, a
/// ray crossing test is used for point in polygon testing. If it is not in the extent,
/// it is skipped.
/// </summary>
/// <param name="polygonShape">The part of the polygon to analyze polygon</param>
/// <param name="otherPart">The other part</param>
/// polygonshape and the shape extent is the same as the part extent.</param>
/// <returns>Boolean, true if any coordinate falls inside the polygon</returns>
private static bool ContainsVertex(ShapeRange polygonShape, PartRange otherPart)
{
// Create an extent for faster checking in most cases
Extent ext = polygonShape.Extent;
foreach (Vertex point in otherPart)
{
// This extent check shortcut should help speed things up for large polygon parts
if (!ext.Intersects(point)) continue;
// Imagine a ray on the horizontal starting from point.X -> infinity. (In practice this can be ext.XMax)
// Count the intersections of segments with that line. If the resulting count is odd, the point is inside.
double x1 = point.X;
double y1 = point.Y;
double x2 = ext.XMax;
Segment ray = new Segment(point.X, point.Y, ext.XMax, point.Y);
int[] numCrosses = new int[polygonShape.NumParts]; // A cross is a complete cross. Coincident doesn't count because it is either 0 or 2 crosses.
int totalCrosses = 0;
int iPart = 0;
foreach (PartRange ring in polygonShape.Parts)
{
foreach (Segment segment in ring.Segments)
{
if(segment.IntersectionCount(ray) != 1) continue;
numCrosses[iPart]++;
totalCrosses++;
}
iPart++;
}
// If we didn't actually have any polygons we cant intersect with anything
if (polygonShape.NumParts < 1) return false;
// For shapes with only one part, we don't need to test part-containment.
if(polygonShape.NumParts == 1 && totalCrosses % 2 == 1) return true;
// Regardless of number of parts or holiness, 1 crossing can only be inside.
if(totalCrosses == 1) return true;
totalCrosses = 0;
for (iPart = 0; iPart < numCrosses.Length; iPart++)
{
int count = numCrosses[iPart];
// If this part does not contain the point, don't bother trying to figure out if the part is a hole or not.
if (count % 2 == 0) continue;
// If this particular part is a hole, subtract the total crosses by 1, otherwise add one.
// This takes time, so we want to do this as few times as possible.
if(polygonShape.Parts[iPart].IsHole())
{
totalCrosses--;
}
else
{
totalCrosses++;
}
}
return totalCrosses > 0;
}
return false;
}
