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Add Arc Distance Weights #168

Closed GoogleCodeExporter closed 9 years ago

GoogleCodeExporter commented 9 years ago 
Currently geoda only supports euclidian distances for weights creation.

Add support Arc (spherical) distances when creating weights from unprojected 
shape files.

Original issue reported on code.google.com by schmi...@gmail.com on 30 Sep 2011 at 12:14

GoogleCodeExporter commented 9 years ago 
Efficient weights creations with spherical coordinates...

Based on Scipy-user listserve post:

"convert all the points in question to 3D cartesian coordinates at the 
beginning, and use the kd-tree as it is.  The distances involved will change, 
but the nearest-neighbors should still be the same points", 
http://mail.scipy.org/pipermail/scipy-user/2009-June/021458.html

If this holds true (which I believe it does), we can convert lat/lng to unit 
sphere XYZ, find k nearest neighbors using a 3D kd-tree, then (if needed) 
calculate the surface distances.

For threshold distances, convert the surface distance in S2 to a straight line 
distance in R3 and use the KDTree ball query.

I have some code with empirically tests arc_dist vs. xyz_dist using brute force 
KNN. Both return the same results.

still need a function to convert surface distance to straight line distance... 
(how to find a point x surface units from a reference point?)

Original comment by schmi...@gmail.com on 30 Sep 2011 at 3:09

GoogleCodeExporter commented 9 years ago 
Function relating arc (surface) distance in S2 to euclidean distance in R3 
(unit sphere)...

Given surface distance, d, in kilometers.
Given circumference of earth, r, in kilometers.

theta = (d*360)/c
e = (2-2*cos(theta))**(0.5)

Where, e is the euclidean distance in R3 in the unit sphere.

Original comment by schmi...@gmail.com on 30 Sep 2011 at 3:41

GoogleCodeExporter commented 9 years ago 
[deleted comment]
GoogleCodeExporter commented 9 years ago 
GeoDa does give you the option to select Arc Distance for threshold distance 
weights, but not for kNN.

For kNN, GeoDa does use kd-trees for kNN.  It uses the "Approximate Nearest 
Neighbor" library code (ANN) with the following license:

ANN Library: Approximate Nearest Neighbor Library
 Release 0.1, 1998, By: Sunil Arya and David Mount
 of University of Maryland
License: can be copied and distributed free of chare as long as:
 (1) not part of a commercial product
 (2) this notice appears in all copies of the software and related
   documentation

Original comment by mmcc...@gmail.com on 30 Sep 2011 at 12:54

GoogleCodeExporter commented 9 years ago 
I added some spherical distance tools to cg in r1002.  Need unit tests and more 
documentation.

Original comment by schmi...@gmail.com on 6 Oct 2011 at 7:09

GoogleCodeExporter commented 9 years ago 
completed in r1009.

Steps to create ArcWeights...
1. Create an instance of ArcKDTree
2. pass it to your desired distance method.

Original comment by schmi...@gmail.com on 12 Oct 2011 at 10:47