Here’s my own solution, based on the idea in ask Dr. Math. I’d be happy to see your feedback. Disclaimer first. This solution is correct for spheres. Earth isn’t a sphere, and the coordinates system (WGS 84) doesn’t assume it’s a sphere. So this is just an approximation, and I can’t really estimate is error. … Read more
Assuming the map is rectangular, you can loop over all border points, and start a flood fill to find the most distant point from the starting point: bestSolution = { start: (0,0), end: (0,0), distance: 0 }; for each point p on the border flood-fill all points in the map to find the most distant … Read more
This paper reviews the known exact distance transform algorithms: “2D Euclidean distance transform algorithms: A comparative survey” https://rfabbri.github.io/stuff/fabbri-EDT-survey-ACMCSurvFeb2008.pdf The fastest exact distance transform is from Meijster: “A General Algorithm for Computing Distance Transforms in Linear Time.” http://fab.cba.mit.edu/classes/S62.12/docs/Meijster_distance.pdf The design of the algorithm is particularly well suited for parallel calculation. This is implemented in my open … Read more
Based on the @trashgod’s comment, this is the simpliest way to calculate distance: double distance = Math.hypot(x1-x2, y1-y2); From documentation of Math.hypot: Returns: sqrt(x²+ y²) without intermediate overflow or underflow.
Ok, for starters, you don’t really need to use the Haversine formula here. For large distances where a less accurate formula produces a larger error, your users don’t care if the match is plus or minus a few miles, and for closer distances, the error is very small. There are easier (to calculate) formulas listed … Read more
One informal but rather intuitive way to think about this is to consider the 2 components of a vector: direction and magnitude. Direction is the “preference”https://stackoverflow.com/”style”https://stackoverflow.com/”sentiment”https://stackoverflow.com/”latent variable” of the vector, while the magnitude is how strong it is towards that direction. When classifying documents we’d like to categorize them by their overall sentiment, so we … Read more
MapQuest RouteMatrix is pretty much the same thing: http://www.mapquestapi.com/directions/
Here is a single formula that avoids all the case logic. (I happen to be working in JS right now, so here’s a JS implementation). Let rect = {max:{x:_, y:_}, min:{x:_, y:_}} and p={x:_, y:_} function distance(rect, p) { var dx = Math.max(rect.min.x – p.x, 0, p.x – rect.max.x); var dy = Math.max(rect.min.y – p.y, … Read more
The GIS term you are describing is linear referencing, and Shapely has these methods. # Length along line that is closest to the point print(line.project(p)) # Now combine with interpolated point on line p2 = line.interpolate(line.project(p)) print(p2) # POINT (5 7) An alternative method is to use nearest_points: from shapely.ops import nearest_points p2 = nearest_points(line, … Read more