Get geographical coordinates in a given square

Question

My task is as follows: knowing the center (starting point), for example – [{'lat': -7.7940023, 'lng': 110.3656535}] and knowing the radius 5km I need to get all the points included in this square in 1 km increments. How do I achieve this?

P.S Using the Haversine formula I can check if a point is in a given square according to the radius

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Asked By: Lite

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Answer 1

if you consider a spherical Earth with radius R, the associated angle of a segment with length L (5km in your case) is:

import numpy as np
R = 6378.0 # km
L = 5.0 # km
angle = np.degrees(L/R)

so now, you can easily check if a point is inside your square:

center = {'lat': -7.7940023, 'lng': 110.3656535}
point = {'lat': 'point latitude', 'lng': 'point longitude'} # insert here your values

if (point['lat']-center['lat'] < angle) and (point['lng']-center['lng'] < angle):
    print('Point is inside')
else:
    print('Point is outside')

EDIT: check the one below.

import numpy as np

R = 6378.0  # km
L = 5  # side of the square
center = {'lat': -7.7940023, 'lng': 110.3656535}

square_side = np.linspace(-L/2, L/2, L+1)
angle = np.degrees(square_side/R)
latitude, longitude = np.meshgrid(angle+center['lat'], angle+center['lng'])
points = []
for lat, lng in zip(latitude.flatten(), longitude.flatten()):
    points.append({'lat': lat, 'lng': lng})

Answered By: mauro

Answer 2

This example should illustrate the point:

import pandas as pd 
import numpy as np

#for_map = pd.read_csv('campaign_contributions_for_map.tsv', sep='t')
df_airports = pd.read_csv('C:\airports.csv')
print(df_airports.head(3))

df_cities = pd.read_csv('C:\worldcities.csv')
print(df_cities.head(3))

# join the two dataframes - must be the same length
df = pd.concat([df_cities, df_airports], axis=1)

# cast latitudes and longitudes to numeric
cols = ["lat", "lng", "latitude_deg", "longitude_deg"]
df[cols] = df[cols].apply(pd.to_numeric, errors='coerce', axis=1)

# create a mask where our conditions are met (difference between lat fuze and lat air < 5 and difference between long fuze and long air < 0.1)
mask = ((abs(df["lat"] - df["latitude_deg"]) < .5) & (abs(df["lng"] - df["longitude_deg"]) < .5))

# fill the type column
df.loc[mask, 'Type'] = "Airport"
df.shape

pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', None)
df.head()

# The haversine formula determines the great-circle distance between two points on a sphere given 
# their longitudes and latitudes. Important in navigation, it is a special case of a more general 
# formula in spherical trigonometry, the law of haversines, that relates the sides and angles of 
# spherical triangles. 

lat1 = df['lat']
lon1 = df['lng']
lat2 = df['latitude_deg']
lon2 = df['longitude_deg']

from math import radians, cos, sin, asin, sqrt
def haversine(lat1, lon1, lat2, lon2):
    """
    Calculate the great circle distance between two points 
    on the earth (specified in decimal degrees)
    """
    # convert decimal degrees to radians 
    lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
    # haversine formula 
    dlon = lon2 - lon1 
    dlat = lat2 - lat1 
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * asin(sqrt(a)) 
    # Radius of earth in kilometers is 6371
    km = 6371* c
    return km

# Creating a new column to generate the output by passing lat long information to Haversine Equation
df['distance'] = [haversine(df.lat[i],df.lng[i],df.latitude_deg[i],df.longitude_deg[i]) for i in range(len(df))]
df['distance'] = df['distance'].round(decimals=3)

# Printing the data table 
df.sort_values(by=['distance'], inplace=True)
df.head()

# Let's sort by our newly created field, which identifies airport lat/lonn coordinates within .5 places of 
# a city's lat/long coordinates

# Create a mask where our conditions are met (difference between lat and latitude_deg < 0.1 and 
# difference between lng and longitude_deg < 0.1)
mask = ((abs(df["lat"] - df["latitude_deg"]) < 0.1) & (abs(df["lng"] - df["longitude_deg"]) < 0.1))

# Fill the type column
df.loc[mask, 'Type'] = "Airport"

df.sort_values(by=['Type'], inplace=True)
df.head()

More details here.

https://github.com/ASH-WICUS/Notebooks/blob/master/Haversine%20Distance%20-%20Airport%20or%20Not.ipynb

Answered By: ASH

Get geographical coordinates in a given square

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