A fast algorithm which can determine whether a point is inside an arbitrary polygon, this method can support convex and non-convex polygon. It costs O(n), n refers to the n-sided shape.
Input:
point: tuple(x, y) poly: [x1, y1, x2, y2, ..., xn, yn]
Output:
True: inside False: outside
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When a point is inside the polygon, the sum of the angles between it and the vertices of the polygon is 2π. As shown in Convex(a) and Non-Convex(a).
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While the point is outside the polygon, the sum of the angles is 0. As shown in Convex(b) and Non-Convex(b).
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It should be noted that due to the order, the included angle here has positive and negative. Cross product is employed to deal with this problem.
For example:
Convex:
Non-Convex:
