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-rwxr-xr-xMaster/texmf-dist/scripts/luamesh/luamesh-polygon.lua87
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diff --git a/Master/texmf-dist/scripts/luamesh/luamesh-polygon.lua b/Master/texmf-dist/scripts/luamesh/luamesh-polygon.lua
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+-- 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