Yes, spheroid distance is one issue; computational complexity is another. I looked into this when I had a problem of computing pairwise distances between 10,000 polygons for an application in conservation biology. The brute force computational complexity, searching for the closest pair of points across all pairs of polygons, would be about O(m^2 * n^2), if there were n polygons with an average of m points, say. In Kristian's case these numbers are not so prohibitive as the number of countries is not so many, and he can cut down on the search space for closest points by eye to some degree. Using the MySQL function "distance" may or may not be an efficient algorithm for the single pair case (haven't looked at it carefully), but it would have to be embedded in some outer algorithm for the many pairs situation. I think that the Okabe and Miller approach with Voronoi methods is the general way to go, but I didn't have time to program it, and couldn't find an available implementation, so I punted and used a series of buffered distances (I also had an exponential inverse distance relation and therefore could set a reasonable maximum buffer size). Denis
On Mon, 15 Dec 2003 White.Denis at epamail.epa.gov wrote:
I am a new member of r-sig-geo and saw your message in the archives. I don't know whether you already had algorithms in mind, or received some responses on this, but two publications with algorithms are: Chin F, Wang CA. 1983. Optimal algorithms for the intersection and the minimum distance problems between planar polygons. IEEE Transactions on Computers, Vol C-32(12):1203-1207. Okabe A, Miller HJ. 1996. Exact computation methods for calculating distances between objects in a cartographic database. Cartography and Geographic Information Systems Vol 23(4):180-195.
Thanks for interesting references. In other email (I think offlist,
but
repeating here to get further response), the idea of using OpenGIS functions on a database was floated:
http://www.mysql.com/doc/en/Functions_that_test_spatial_relationships_between_ge
ometries.html (para 10.5.6 in MSQL Manual 4.1) describes a function: Distance(g1,g2) Returns as a double-precision number the shortest
distance
between any two points in the two geometries. I'm not sure whether this supports latlong. PostGIS also has the same function as an OpenGIS function. http://postgis.refractions.net/ has
the
details: Distance(geometry,geometry) Return the cartesian distance between two geometries in projected units. It also has: distance_spheroid(point, point, spheroid) Returns linear distance
between
two lat/lon points given a particular spheroid. See the explanation of spheroids given for length_spheroid(). Currently only implemented for points. as a non-OpenGIS function. Kristian's question is about nation states,
so
latlong is an issue, I believe. This makes it non-trivial, of course! Any other ideas? Roger
What I would like to do is to try to use an algorithm to determine the shortest distance between points on two states??? outer boundaries, with each state defined either as a polygon or union of polygons.
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-- Roger Bivand Economic Geography Section, Department of Economics, Norwegian School
of
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Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93 e-mail: Roger.Bivand at nhh.no