-- Given three colinear points p, q, r, the function checks if -- point q lies on line segment 'pr' function onSegment(p,q,r) if(q.x <= math.max(p.x,r.x) and q.x >= math.min(p.x,r.x) and q.y <= math.max(p.y,r.y) and q.y>= math.min(p.y,r.y)) then return true else return false end end -- 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 function orientation(p,q,r) val = (q.y-p.y)*(r.x-q.x)-(q.x-p.x)*(r.y-q.y) if(val == 0) then return 0 end if(val > 0) then return 1 else return 2 end end -- The function that returns true if line segment 'p1q1' -- and 'p2q2' intersect. function doIntersect(p1,q1,p2,q2) -- Find the four orientations needed for general and -- special cases o1 = orientation(p1, q1, p2) o2 = orientation(p1, q1, q2) o3 = orientation(p2, q2, p1) o4 = orientation(p2, q2, q1) -- gerenal case (without limite case) if(o1 ~= o2 and o3 ~= o4) then return true end -- Special case -- p1, q1 and p2 are colinear and p2 lies on segment p1q1 if (o1 == 0 and onSegment(p1, p2, q1)) then return true end -- p1, q1 and p2 are colinear and q2 lies on segment p1q1 if (o2 == 0 and onSegment(p1, q2, q1)) then return true end -- p2, q2 and p1 are colinear and p1 lies on segment p2q2 if (o3 == 0 and onSegment(p2, p1, q2)) then return true end -- p2, q2 and q1 are colinear and q1 lies on segment p2q2 if (o4 == 0 and onSegment(p2, q1, q2)) then return true end return false; -- Doesn't fall in any of the above cases end -- Returns true if the point p lies inside the polygon[] with n vertices function isInside(listPoints,p,h) -- if the point is to close to a point of the polygon for i=1,#listPoints do if(math.sqrt(math.pow(p.x-listPoints[i].x,2) + math.pow(p.y-listPoints[i].y,2))<0.4*h) then return false end end -- There must be at least 3 vertices in polygon[] if (#listPoints <= 3) then return false end -- Create a point for line segment from p to infinite extreme = {x=1e05,y=p.y}; -- Count intersections of the above line with sides of polygon count = 0 for i=1,#listPoints do ip = (i)%(#listPoints)+1 -- Check if the line segment from 'p' to 'extreme' intersects -- with the line segment from 'polygon[i]' to 'polygon[next]' if (doIntersect(listPoints[i], listPoints[ip], p, extreme)) then -- If the point 'p' is colinear with line segment 'i-ip', -- then check if it lies on segment. If it lies, return true, -- otherwise false if (orientation(listPoints[i], p, listPoints[ip]) == 0) then return onSegment(listPoints[i], p, listPoints[ip]) end count = count+1 end end -- Return true if count is odd, false otherwise return (count%2 == 1) end