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Polygon Area in Python

Learn how to find the area of any simple polygon

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

In [1]:
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Area of a Square

Sort the defined corners of a polygon, calculate the angles between each pair of points and calculate the area contained.

In [2]:
def PolygonSort(corners):
    n = len(corners)
    cx = float(sum(x for x, y in corners)) / n
    cy = float(sum(y for x, y in corners)) / n
    cornersWithAngles = []
    for x, y in corners:
        an = (np.arctan2(y - cy, x - cx) + 2.0 * np.pi) % (2.0 * np.pi)
        cornersWithAngles.append((x, y, an))
    cornersWithAngles.sort(key = lambda tup: tup[2])
    return map(lambda (x, y, an): (x, y), cornersWithAngles)

def PolygonArea(corners):
    n = len(corners)
    area = 0.0
    for i in range(n):
        j = (i + 1) % n
        area += corners[i][0] * corners[j][1]
        area -= corners[j][0] * corners[i][1]
    area = abs(area) / 2.0
    return area

corners = [(0, 0), (1, 1), (0, 1), (1, 0)]
corners_sorted = PolygonSort(corners)
area = PolygonArea(corners_sorted)

x = [corner[0] for corner in corners_sorted]
y = [corner[1] for corner in corners_sorted]

annotation = go.Annotation(
    x=1.5,
    y=1.0,
    text='The area of the polygon is approximately %s' % (area),
    showarrow=False
)

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='markers',
    fill='tonexty',
)

layout = go.Layout(
    annotations=[annotation],
    xaxis=dict(
        range=[-1, 2]
    ),
    yaxis=dict(
        range=[-1, 2]
    )
)

trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)

py.iplot(fig, filename='square-area')
Out[2]:

Area of a Polygon

In [3]:
def PolygonSort(corners):
    n = len(corners)
    cx = float(sum(x for x, y in corners)) / n
    cy = float(sum(y for x, y in corners)) / n
    cornersWithAngles = []
    for x, y in corners:
        an = (np.arctan2(y - cy, x - cx) + 2.0 * np.pi) % (2.0 * np.pi)
        cornersWithAngles.append((x, y, an))
    cornersWithAngles.sort(key = lambda tup: tup[2])
    return map(lambda (x, y, an): (x, y), cornersWithAngles)

def PolygonArea(corners):
    n = len(corners)
    area = 0.0
    for i in range(n):
        j = (i + 1) % n
        area += corners[i][0] * corners[j][1]
        area -= corners[j][0] * corners[i][1]
    area = abs(area) / 2.0
    return area

corners = [(0, 0), (3, 0), (2, 10), (3, 4), (1, 5.5)]
corners_sorted = PolygonSort(corners)
area = PolygonArea(corners_sorted)

x = [corner[0] for corner in corners_sorted]
y = [corner[1] for corner in corners_sorted]

annotation = go.Annotation(
    x=5.5,
    y=8.0,
    text='The area of the polygon is approximately %s' % (area),
    showarrow=False
)

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='markers',
    fill='tozeroy',
)

layout = go.Layout(
    annotations=[annotation],
    xaxis=dict(
        range=[-1, 9]
    ),
    yaxis=dict(
        range=[-1, 12]
    )
)

trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)

py.iplot(fig, filename='polygon-area')
Out[3]:
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