I have found a very good solution to this from MapBox called Polylabel. The full source is available on their Github too. Essentially it tries to find the visual centre of the polygon as T Austin said. Certain details suggest this may be a practical solution: Unfortunately, calculating [the ideal solution ] is both complex … Read more
After spending a whole day in Rnd and testing some alternatives I have found a solution. Actually I have found two alternatives for the same issue but I would like to suggest the using of Alternative 2 because that is really very easy compared to Alternative 1. Actually I have found Alternative 1 with the … Read more
There is a project on Github with code: https://github.com/substack/point-in-polygon (MIT license): function inside(point, vs) { // ray-casting algorithm based on // https://wrf.ecse.rpi.edu/Research/Short_Notes/pnpoly.html/pnpoly.html var x = point[0], y = point[1]; var inside = false; for (var i = 0, j = vs.length – 1; i < vs.length; j = i++) { var xi = vs[i][0], yi … Read more
Implementation of Shoelace formula could be done in Numpy. Assuming these vertices: import numpy as np x = np.arange(0,1,0.001) y = np.sqrt(1-x**2) We can redefine the function in numpy to find the area: def PolyArea(x,y): return 0.5*np.abs(np.dot(x,np.roll(y,1))-np.dot(y,np.roll(x,1))) And getting results: print PolyArea(x,y) # 0.26353377782163534 Avoiding for loop makes this function ~50X faster than PolygonArea: %timeit … Read more
You can make things a lot easier than the Gift-Wrapping Algorithm… that’s a good answer when you have a set of points w/o any particular boundary and need to find the convex hull. In contrast, consider the case where the polygon is not self-intersecting, and it consists of a set of points in a list … Read more
I understand the original poster was looking for a simple solution, but unfortunately there really is no simple solution. Nevertheless, I’ve recently created an open-source freeware clipping library (written in Delphi, C++ and C#) which clips all kinds of polygons (including self-intersecting ones). This library is pretty simple to use: http://sourceforge.net/projects/polyclipping/ .
Some of the suggested methods will fail in the case of a non-convex polygon, such as a crescent. Here’s a simple one that will work with non-convex polygons (it’ll even work with a self-intersecting polygon like a figure-eight, telling you whether it’s mostly clockwise). Sum over the edges, (x2 − x1)(y2 + y1). If the … Read more
I thought I might briefly mention my own polygon clipping and offsetting library – Clipper. While Clipper is primarily designed for polygon clipping operations, it does polygon offsetting too. The library is open source freeware written in Delphi, C++ and C#. It has a very unencumbered Boost license allowing it to be used in both … Read more
How can I determine whether a 2D Point is within a Polygon?
CSS Triangles: A Tragedy in Five Acts As alex said, borders of equal width butt up against each other at 45 degree angles: When you have no top border, it looks like this: Then you give it a width of 0… …and a height of 0… …and finally, you make the two side borders transparent: … Read more