Check Points Forming Concave Polygon in Python

Suppose we have outer points of a polygon in clockwise order. We have to check these points are forming a convex polygon or not. A polygon is said to be concave if any one of its interior angle is greater than 180°.

From this diagram it is clear that for each three consecutive points the interior angle is not more than 180° except CDE.

So, if the input is like points = [(3,4), (4,7),(7,8),(8,4),(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 True
• return False

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 True
   return False

points = [(3,4), (4,7),(7,8),(8,4),(12,3),(10,1),(5,2)]
print(solve(points))

Input

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

Output

True