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POArea of a polygon (Recursively using Python)
 

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  1. POArea of a polygon (Recursively using Python)
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    <p>I'm trying a solve an exercise from Exploring Python book. But, I guess I don't understand concept of the recursion. I've written some Recursively function. Therefore I know some of the aspects. But, I don't have enough experience. And I've stopped to study programming about one year.</p> <p>Anyway, let me give you the full question:</p> <blockquote> <p>A polygon can be represented by a list of (x, y) pairs where each pair is a tuple: [ (x1, y1), (x2, y2), (x3, y3) , ... (xn, yn)]. Write a recursive function to compute the area of a polygon. This can be accomplished by “cutting off” a triangle, using the fact that a triangle with corners (x1, y1), (x2, y2), (x3, y3) has area (x1y1 + x2y2 + x3y2 – y1x2 –y2x3 – y3x1) / 2.</p> </blockquote> <p>Despite the fact that, the question already gave the formula, I used another formula. Because, I made some research about area of a polygon. And if you look at <a href="http://mathworld.wolfram.com/PolygonArea.html" rel="nofollow">here</a> the formula is different.</p> <p>And describing my program step by step would be better, in order to explain what I want. OK, I had to declare global scopes, because of recursion:</p> <pre><code>area = 0 x = [0] * 3 y = [0] * 3 </code></pre> <p>And then, I created a recursively function. Zero is always returned by this function as a result. So my real problem is this:</p> <pre><code>def areaofpolygon(polygon, i): global area, x, y # My variables try: # I prefered using try statement from using if-else statements. So it is the easier I guess. x[i], y[i] = polygon[i] # X and Y coordinates from tuple area += (x[i]*y[i+1] - x[i+1]*y[i]) #My formula except IndexError: return area/2 areaofpolygon(polygon, i+1) # Here, this is my weird recursion </code></pre> <p>And my main function:</p> <pre><code> def main(): mypolygon = [(1,2), (2,5), (1,4)] # I declared polygon as tuples # I called my function and started to count from zero, and the result will be prompted. print(areaofpolygon(mypolygon,0)) return 0 if __name__ == '__main__': main() </code></pre> <p>And here is my full code without comments:</p> <pre><code>''' Created on Feb 24, 2012 @author: msarialp ''' area = 0 x = [0] * 3 y = [0] * 3 def areaofpolygon(polygon, i): global area, x, y try: x[i], y[i] = polygon[i] area += (x[i]*y[i+1] - x[i+1]*y[i]) except IndexError: return area/2 areaofpolygon(polygon, i+1) def main(): mypolygon = [(1,2), (2,5), (1,4)] print(areaofpolygon(mypolygon,0)) return 0 if __name__ == '__main__': main() </code></pre> <p><strong>EDIT One</strong></p> <p>After reading your answers, I've understood what was wrong with my code. So I decided to share last version of my program in order to get some other helps. Again, I had to declare global variables. How can I apply ( lop_triangle ) function from senderle</p> <pre><code>area = 0 x = [0] * 3 y = [0] * 3 </code></pre> <p>My function that divides tuple and to get x and y coordinates.</p> <pre><code>def sides_of_polygon(polygon, i): global x, y try: x[i], y[i] = polygon[i] return sides_of_polygon(polygon, i+1) except IndexError: return x, y </code></pre> <p>My function calculate area of polygon( Same as before ) </p> <pre><code>def area_of_polygon(x, y, i): global area try: area += x[i]*y[i+1] - x[i+1]*y[i] return area_of_polygon(x, y, i+1) except IndexError: return area/2.0 </code></pre> <p>My main function...</p> <pre><code>def main(): mypolygon = [(1,2), (2,5), (1,4)] dx, dy = sides_of_polygon(mypolygon, 0) print(area_of_polygon(dx,dy,0)) return 0 if __name__ == '__main__': main() </code></pre> <p>Please help me to improve my code without giving full solution.</p> <p><strong>EDIT Two</strong></p> <p>After making discussion with senderle, I understood where is the problem and senderle's solution is better than mine so I suggest that you should use it. Anyway, He helped me to make my code correct.And I had to change my formula again.</p> <pre><code>area += x[i]*y[(i+1) % 3] - x[(i+1) % 3]*y[i] </code></pre> <p>He also added for longer polygons 3 must be len(vertices). Thanks everyone for their time.</p>
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    1. COQuick note: `def areaofpolygon(polygon, i=0):` may clarify a little.
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    2. COQuestion: would the formula for a four sided polygon be `(x1y1 + x2y2 + x3y3 + x4y3 – y1x2 –y2x3 – y3x4 - y4x1) / 2`?
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    3. COAccording the question, yes it is. But, In my opinion the real one is different. It must be, (x1*y2 + x2*y3 + x3*y4 - x2*y1 - x3*y2 - x4*y3) / 2
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