[GIS] Choosing coordinate system to store geography data for celestial coordinates

coordinate systempostgisspatial-database

I am doing an astronomy project. I want to have the information about our images stored in a spatially enabled database. This, I would think, should be a very easy special case for GIS functions because the sky can be treated as perfectly spherical, and does not require an elliptical treatment like the surface of the earth. Unfortunately, I have not found a way to do this yet and I have been dodging mines with spatial functions that use an elliptical earth. (Pretty much any function that returns meters instead of degrees may be using an elliptical calculation. Luckily, many of the PostGIS functions I've needed appear to have incomplete implementations where the documentation explicitly states that the returned results are for a sphere and not for the ellipsoid. But that may change with future versions, which is a cause for concern.)

Background: I am presently using PostgreSQL with PostGIS and WGS 84 coordinates (SRID=4326). This works fairly well. I am creating a closed POLYGON from the right ascension and declination of the four corners of the image. I have a lot of images (10k or more), covering a large area of the sky. Each images is about 1 degree square. From the set of these images, I am making mosaics from small subsets of 15 to 30 images. Each mosaic is about 1.5 degree square.

Presently, I am storing the geography of the mosaics as a MULTIPOLYGON that consists of all the POLYGONS corresponding to each image that went into the mosaic. [A better solution would be to create a single POLYGON that describes the perimeter of the union of all the individual polygons. I don't know if this can be done in spherical coordinates (i.e., that the geography type). This would also be an interesting answer for me too.] The date line and celestial poles may be included in an image in the dataset so I have been avoiding projecting to planar coordinates to the extent possible.

What coordinate system ought I use for celestial coordinates with PostGIS functions?

I have looked at http://spatialreference.org/ but have not found anything so far. Google has turned up little. I am stumped. Basically, I want to ensure that if a function returns meters as a distance, it is meters along a great circle on a sphere.

I am using PostGIS 1.5.2. I have not yet tried PostGIS 2.0. I am curious if the ST_CoveredBy function works with a POLYGON and a MULTIPOLYGON of type geography. If anybody is running 2.0, could you tell me if you get the same error as this:

mydb=# select ST_CoveredBy(ST_GeographyFromText('MULTIPOLYGON(( (10.37795 -69.57926,8.9498 -69.54875,9.0178 -69.21643,10.4242 -69.24648,10.37795 -69.57926),(10.42436 -69.24618,9.01774 -69.2162,     9.08363 -68.88389,10.46914 -68.91344,10.42436 -69.24618)))'),ST_GeographyFromText('POLYGON((10.46915 -68.91315,9.08371 -68.88364,9.14755 -68.5513,10.5125 -68.58038,10.46915 -68.91315))'));
ERROR:  geography_covers: only POLYGON and POINT types are currently supported
CONTEXT:  SQL function "st_coveredby" statement 1

I have tried PostGIS 2.0. This function still only works on points and polygons, not more general shapes.

Best Answer

Check out pgsphere, it's specifically designed for handling astronomical data.

http://pgsphere.projects.postgresql.org/

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Check geometry_columns table: Does it contain a line for "world" table with SRID = 4326? If not, add/edit it. (The shapefile from thematicmapping.org seems to be in 4326.)

Also, looks like the conversion from geometry to geography is missing:

"the_geom"::geography

[GIS] Getting ST_ClosestPoint for Geography type

Sadly there isn't a geographic version of ST_ClosestPoint, so you will have to write your own function. There are two ways of calculating the nearest point of a great circle: spherical trigonometry, or 3D vector algebra. Luckily for you I have just written such a function for the latter method; I've not attempted the former because my spherical trig is pretty poor.

I've written a PL/Python function that you can add to your database, although you will need to install the Python libraries and PL/Python wrappers, which if you're using Linux should be simply to install the postgresql-python-x.x package (where x.x is the version of PostgreSQL you're using).

This function isn't necessarily the most efficient, it includes no bounds or error checking, and it only uses a sphere, but it certainly works well enough with the data I've tried it with. Feel free to modify accordingly.

First I define my own simple long/lat type:

CREATE TYPE lon_lat AS (lon float, lat float);

The function looks like this:

CREATE OR REPLACE FUNCTION geog_nearest_point(lp1 lon_lat, lp2 lon_lat, p lon_lat) RETURNS lon_lat AS
$$
import math
def sph2cart(lon, lat, r):
    return (r * math.cos(lat) * math.cos(lon),
            r * math.cos(lat) * math.sin(lon),
            r * math.sin(lat))

def cart2sph(x, y, z):
    return (math.atan2(y,x),
            math.atan2(z, math.sqrt(x * x + y * y)),
            math.sqrt(x * x + y * y + z * z))

def cross_prod(v1, v2):
    return (v1[1] * v2[2] - v1[2] * v2[1],
            v1[2] * v2[0] - v1[0] * v2[2],
            v1[0] * v2[1] - v1[1] * v2[0])

lv1 = sph2cart(math.radians(lp1['lon']), math.radians(lp1['lat']), 1.0)
lv2 = sph2cart(math.radians(lp2['lon']), math.radians(lp2['lat']), 1.0)
pv = sph2cart(math.radians(p['lon']), math.radians(p['lat']), 1.0)

f = cross_prod(lv1, lv2)
g = cross_prod(pv, f)
h = cross_prod(f, g)

nearest_point = cart2sph(h[0], h[1], h[2])
return (math.degrees(nearest_point[0]), math.degrees(nearest_point[1]))
$$
LANGUAGE 'plpythonu' IMMUTABLE;

And giving it the data you provided gives me this:

geog_db=# SELECT geog_nearest_point((41, 15)::lon_lat, (40, 5)::lon_lat, (41, 12)::lon_lat);
      geog_nearest_point
-------------------------------
 (40.6960040707,12.0295700818)
(1 row)

It works by finding the point f on the sphere which is normal to the plane that describes the great circle. This point is unique for each great circle.
Next, it uses f and the input point p to define a plane perpendicular to the input great circle, and determines its unique normal point g. The vectors from the centre of the sphere to f and g define a plane that is perpendicular to the previous two planes.
Finding the normal of this third plane gives us the point at which the two great circles intersect.
Finally, this Cartesian coordinate is converted back to latitude and longitude.

If anyone has a spherical trig method, which I think will be slightly more efficient, then I'd love to see it.

Best Answer

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