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Program to check points are forming convex hull or not in Python

Suppose we have outer points of a polygon in clockwise order. We have to check these points are forming a convex hull or not.

Program to check points are forming convex hull or not in Python

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 −

  • n := size of points
  • for i in range 0 to size of points, do
    • p1 := points[i-2] when i > 1, otherwise points[n-2]
    • p2 := points[i-2] when i > 0, otherwise points[n-1]
    • p3 := points[i]
    • if angle between points (p1, p2, p3) > 180, then
      • return False
  • return True

Example

Let us see the following implementation to get better understanding −

import math
def get_angle(a, b, c):
   angle = math.degrees(math.atan2(c[1]-b[1], c[0]-b[0]) - math.atan2(a[1]-b[1], a[0]-b[0]))
   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))

Input

[(3,4), (4,7),(7,8),(11,6),(12,3),(10,1),(5,2)]

Output

True