Suppose we have outer points of a polygon in clockwise order. We have to check these points are forming a convex hull or not.
From this diagram it is clear that for each three consecutive points the interior angle is not more than 180°. So if all angles are not more than 180° then the polygon is convex hull.
So, if the input is like points = [(3,4), (4,7),(7,8),(11,6),(12,3),(10,1),(5,2)], then the output will be True.
To solve this, we will follow these steps −
Let us see the following implementation to get better understanding −
import math def get_angle(a, b, c): angle = math.degrees(math.atan2(c-b, c-b) - math.atan2(a-b, a-b)) return angle + 360 if angle < 0 else angle def solve(points): n = len(points) for i in range(len(points)): p1 = points[i-2] p2 = points[i-1] p3 = points[i] if get_angle(p1, p2, p3) > 180: return False return True points = [(3,4), (4,7),(7,8),(11,6),(12,3),(10,1),(5,2)] print(solve(points))