This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. What does spit mean in "spit in my glove" from the memoir by Powers? I know that it can be calculated with the coordinates but is there another general way? Stack Overflow for Teams is a private, secure spot for you and Finding intersections of features in one line layer using QGIS. You just need to walk the polygon's vertices and perform some inclusion tests until you find a suitable triple. It is formed using a collection of lines. Unordered cloud point of polygon contour to polygon, Computing the Convex Hull of two non intersecting polygon in scipy. The polygon has N vertices. The "Tear one ear at a time" algorithm works, provided the triangle you remove does not contain "holes" (other vertices of the polygon). A concave polygon has one interior angle greater than 180°. Using the expression for the determinant above, you can compute A((0, 0), p, q) efficiently as 0.5 * (-p.y*q.x + p.x*q.y). That is, you need to choose the green triangle below, not the red one: However, it is always possible to do so (Can't prove it mathematically right now, but you'l have to trust me). Although the partitions produced by the algorithms may not have minimal cardinality, their easy implementation and their quick CPU times even for polygons with many vertices make them very suitable to be used when optimal decompositions are not required, as for instance, in constrained optimization problems having as feasible set a non-convex polygon (optimization problems are usually easier to solve in convex regions and making use of a branch and bound process or other techniques, it is not necessary to find the optimal solution in all the subsets, so finding convex decomposition with minimal cardinality may be time-wasting). How did the DEC RP06 respond to unscheduled power off? @Jed I'm open to corrections if you spotted an error (I did this back in High School and I wouldn't exactly be surprised if something was sloppy), but after a cursory glance and trying a couple examples, I think the math is fine here. Please mail your requirement at This implies the following simple algorithm: The remaining unique edges form the external contour of your polygon. In fact, there is not finite number of passes that will guarantee a convex polygon in general, so this algorithm seems a bit awkward. your coworkers to find and share information. All Rights Reserved. Let f  be a function of many variables defined on the convex set S. Then  f  is, (non convex) concave on the set S if for all x ∈ S, all x' ∈ S, and all λ ∈ (0,1) we have, f ((1−λ)x + λx') ≥ (1−λ) f (x) + λ f (x'), convex on the set S if for all x ∈ S, all x' ∈ S, and all λ ∈ (0,1) we have. Is a software open source if its source code is published by its copyright owner but cannot be used without a license? Why don't libraries smell like bookstores? A polygon can be defined as a closed plane figure (a two dimensional shape) that consists of three or more line segments. Do you have a set of coordinates for the squares ? Non-overlapping rectangular cell sare placed in a rectangle with width W,heightH ,andlowerleftcornerat(0,0). What was the most critical supporting software for COBOL on IBM mainframes? These quadrilaterals are convex This quadrilateral is non-convex. Convex Non-convex . (Condition should hold true for at least one pair of points.) I still (very slightly) prefer his answer since each increment to the area is the (signed) area of a triangle connecting the 2 segments with the origin (after the /2), which makes it more intuitive to me.