// To find orientation of ordered triplet (p, q, r).
// The function returns following values
// 0 --> p, q and r are colinear
// 1 --> Clockwise
// 2 --> Counterclockwise
public static int Orientation(Coordenate p, Coordenate q, Coordenate r)
{
double val = (q.y - p.y) * (r.x - q.x) -
(q.x - p.x) * (r.y - q.y);
if (val == 0)
{
return(0); // colinear
}
return((val > 0) ? 1 : 2); // clock or counterclock wise
}
// Given three colinear points p, q, r,
// the function checks if point q lies
// on line segment 'pr'
public static bool OnSegment(Coordenate p, Coordenate q, Coordenate r)
{
if (q.x <= Math.Max(p.x, r.x) &&
q.x >= Math.Min(p.x, r.x) &&
q.y <= Math.Max(p.y, r.y) &&
q.y >= Math.Min(p.y, r.y))
{
return(true);
}
return(false);
}
// The function that returns true if
// line segment 'p1q1' and 'p2q2' intersect.
static bool DoIntersect(Coordenate p1, Coordenate q1,
Coordenate p2, Coordenate q2)
{
// Find the four orientations needed for
// general and special cases
int o1 = Orientation(p1, q1, p2);
int o2 = Orientation(p1, q1, q2);
int o3 = Orientation(p2, q2, p1);
int o4 = Orientation(p2, q2, q1);
// General case
if (o1 != o2 && o3 != o4)
{
return(true);
}
// Special Cases
// p1, q1 and p2 are colinear and
// p2 lies on segment p1q1
if (o1 == 0 && OnSegment(p1, p2, q1))
{
return(true);
}
// p1, q1 and p2 are colinear and
// q2 lies on segment p1q1
if (o2 == 0 && OnSegment(p1, q2, q1))
{
return(true);
}
// p2, q2 and p1 are colinear and
// p1 lies on segment p2q2
if (o3 == 0 && OnSegment(p2, p1, q2))
{
return(true);
}
// p2, q2 and q1 are colinear and
// q1 lies on segment p2q2
if (o4 == 0 && OnSegment(p2, q1, q2))
{
return(true);
}
// Doesn't fall in any of the above cases
return(false);
}
// Returns true if the point p lies
// inside the polygon[] with n vertices
public static bool IsInside(Coordenate[] polygon, Coordenate p)
{
//Vertices numbers
var n = polygon.Length;
// There must be at least 3 vertices in polygon[]
if (n < 3)
{
return(false);
}
// Create a point for line segment from p to infinite
Coordenate extreme = new Coordenate(INF, p.y);
// Count intersections of the above line
// with sides of polygon
int count = 0, i = 0;
do
{
int next = (i + 1) % n;
// Check if the line segment from 'p' to
// 'extreme' intersects with the line
// segment from 'polygon[i]' to 'polygon[next]'
if (DoIntersect(polygon[i],
polygon[next], p, extreme))
{
// If the point 'p' is colinear with line
// segment 'i-next', then check if it lies
// on segment. If it lies, return true, otherwise false
if (Orientation(polygon[i], p, polygon[next]) == 0)
{
return(OnSegment(polygon[i], p,
polygon[next]));
}
count++;
}
i = next;
} while (i != 0);
// Return true if count is odd, false otherwise
return(count % 2 == 1); // Same as (count%2 == 1)
}