## Perimeter of a polygon, Python Programming

Assignment Help:

Perimeter of a polygon

Now, let's consider the problem of computing the length  of the perimeter of a polygon. The input is a structure of vertices,  encoded as a list of lists of two  values (as like[[1, 2], [3.4, 7.6], [-4.4, 3]]). Here is the ?rst attempt:

def perim(vertices):

result = 0

for i in range(len(vertices)-1):

result = result + math.sqrt((vertices[i][0]-vertices[i+1][0])**2 + \ (vertices[i][1]-vertices[i+1][1])**2)

return result + math.sqrt((vertices[-1][0]-vertices[0][0])**2 + \ (vertices[-1][1]-vertices[0][1])**2)

Again, this works,  but it ain't correct. The basic cause is that someone reading the code doesn't immediately see what  all that  subtraction and  squaring is about.    We caould be fixed that  by de?ning another procedure:

def perim(vertices):

result = 0

for i in range(len(vertices)-1):

result = result + pointDist(vertices[i],vertices[i+1])

return result + pointDist(vertices[-1],vertices[0])

def pointDist(p1,p2):

return math.sqrt(sum([(p1[i] - p2[i])**2 for i in range(len(p1))]))

Now,  we've  de?ned a new  procedure pointDist, which  calculates the  Euclidean distance be­ tween  two positions.    And,  in fact,  we've  written it usually enough to work  on  points  of any dimension (not just two).  Just for fun, here's another example  to calculate the distance, which  some people would use  and others  would not.

def pointDist(p1,p2):

return math.sqrt(sum([(c1 - c2)**2 for (c1, c2) in zip(p1, p2)]))

For this to make sense, you have to understand zip. Here's a program of how it works:

> zip([1, 2, 3],[4, 5, 6])

[(1, 4), (2, 5), (3, 6)]

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