How can I quickly estimate the distance between two (latitude, longitude) points?
The answers to Haversine Formula in Python (Bearing and Distance between two GPS points) provide Python implementations that answer your question.
Using the implementation below I performed 100,000 iterations in less than 1 second on an older laptop. I think for your purposes this should be sufficient. However, you should profile anything before you optimize for performance.
from math import radians, cos, sin, asin, sqrtdef haversine(lon1, lat1, lon2, lat2): """ 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 kmTo underestimate haversine(lat1, long1, lat2, long2) * 0.90 or whatever factor you want. I don't see how introducing error to your underestimation is useful.
Since the distance is relatively small, you can use the equirectangular distance approximation. This approximation is faster than using the Haversine formula. So, to get the distance from your reference point (lat1/lon1) to the point your are testing (lat2/lon2), use the formula below. Important Note: you need to convert all lat/lon points to radians:
R = 6371 // radius of the earth in kmx = (lon2 - lon1) * cos( 0.5*(lat2+lat1) )y = lat2 - lat1d = R * sqrt( x*x + y*y )Since 'R' is in km, the distance 'd' will be in km.
Reference: http://www.movable-type.co.uk/scripts/latlong.html
One idea for speed is to transform the long/lat coordinated into 3D (x,y,z) coordinates. After preprocessing the points, use the Euclidean distance between the points as a quickly computed undershoot of the actual distance.