Suppose we have a list of ordered points represents a simple polygon endpoint on a 2D plane. We have to find the area of this polygon.
So, if the input is like points = [(0, 0), (0,5), (3, 5), (3,0)], then the output will be 15.
To solve this, we will follow these steps −
- Define a function getInfo() . This will take x1, y1, x2, y2
- return x1*y2 - y1*x2
- From the main method, do the following
- N := size of points
- (firstx, firsty) := points[0]
- (prevx, prevy) := (firstx, firsty)
- res := 0
- for i in range 1 to N-1, do
- (nextx, nexty) := points[i]
- res := res + getInfo(prevx, prevy, nextx, nexty)
- prevx := nextx
- prevy := nexty
- res := res + getInfo(prevx, prevy, firstx, firsty)
- return |res| / 2.0
Example
Let us see the following implementation to get better understanding −
def getInfo(x1, y1, x2, y2): return x1*y2 - y1*x2 def solve(points): N = len(points) firstx, firsty = points[0] prevx, prevy = firstx, firsty res = 0 for i in range(1, N): nextx, nexty = points[i] res = res + getInfo(prevx,prevy,nextx,nexty) prevx = nextx prevy = nexty res = res + getInfo(prevx,prevy,firstx,firsty) return abs(res)/2.0 points = [(0, 0), (0,5), (3, 5), (3,0)] print(solve(points))
Input
[(0, 0), (0,5), (3, 5), (3,0)]
Output
15.0