Winding number algorithm and point on boundary/edge of convex

Question

I need algorithm which can tell, if Point lies inside/outside or on boundary (edge) of convex hull (C/C++).

Convex hull is described as array of Points X,Y, integer, connection are from i to i+1.

Currently Im using winding number algorithm, described here: http://geomalgorithms.com/a03-_inclusion.html It's function "wn_PnPoly()".

Is it possible, and how, to make winding number algorithm detect, if Point lies exactly on boundary (edge) of convex? Is there another algorithm to do that? (Needs to work on ints).

Just read the implementation of the function. You will find a test whether a point is left/on/right the edge. — , Jun 08 '16 at 13:16

score 8 · Answer 1 · answered Jun 08 '16 at 13:17

Found solution:

int wn_PnPoly2(Point P, vector<Point> V, int n)
{
    int    wn = 0;    // the  winding number counter

                      // loop through all edges of the polygon
    for (int i = 0; i<n; i++) {   // edge from V[i] to  V[i+1]
        if (V[i].Y <= P.Y) {          // start y <= P.y
            if (V[i + 1].Y  > P.Y)      // an upward crossing
            {
                int l = isLeft(V[i], V[i + 1], P);
                if (l > 0)  // P left of  edge
                    ++wn;            // have  a valid up intersect
                else if (l == 0) // boundary
                    return 0;
            }
        }
        else {                        // start y > P.y (no test needed)
            if (V[i + 1].Y <= P.Y)     // a downward crossing
            {
                int l = isLeft(V[i], V[i + 1], P);
                if (l < 0)  // P right of  edge
                    --wn;            // have  a valid down intersect
                else if (l == 0)
                    return 0;
            }
        }
    }
    return wn;
}

Is missing the isLeft() function, but it could be found in other sources as well. For example here: http://forums.codeguru.com/showthread.php?497679-To-check-if-a-point-is-inside-a-polygon — st6mm, Apr 23 '17 at 13:52

score -1 · Answer 2 · answered Jun 08 '16 at 13:15

I'm not aware of the Winding number algorithm but to detect whether a point lies on one of the edges, you can just loop through all the edges of the convex hull and do the following check:

If points u, v are consecutive points on the convex hull and p is the point in consideration then whether,

p - u = lambda*(v - u) where lambda is any scalar between 0 and 1.

Winding number algorithm and point on boundary/edge of convex

2 Answers2