2D Open Street Map Data Representation in Meters - gis

Question

I am in the process of converting OSM data into an open source Minecraft port (written in javascript - voxel.js). The javascript rendition is written such that each voxel (arbitrarily defined as a cubic meter) is created as a relation from a single point of origin (x,y,z)(0,0,0).
As an example, if one wanted to create a cubic chunk of voxels, one would simply generate voxels as a relation to the origin (0,0,0) : [(0,0,0),(1,0,0), (0,1,0)...].
My question is this: I've exported OSM data, and the standard XML output (.osm) plots nodes in latitude and longitude. My initial thought is that I can create a map by calculating the distance of each node from an arbitrary point of origin (0,0,0) = (37.77559, -122.41392) using the Haversine formula, convert the distance to meters, find the bearing, and plot it as a relation to (0,0,0).
I've noticed, however, that there are a number of other export formats available: (.osm.pbf, .osm2pgsql, .imposm). I'm assuming they plot nodes in a similar fashion (lat, lng), but some of them have the ability to import directly into a database (e.g. PostgreSQL).
I've heard of people using PG add-ons like PostGIS, but (as this is my first dive into GIS) I'm unfamiliar with their capabilities and whether something like PostGIS would help me in plotting OSM data into a 2D voxel grid.
Are there functions within add-ons like PostGIS that would enable me to dynamically calculate the distance between two Lat/Lng points, and plot them in an x,y fashion?
I guess, fundamentally, my question is: if I create a script that plots OSM data into an x,y grid would I be reinventing the wheel, or is there a more efficient way to do this?

Answer 1

You need to transform from the spherical coordinates (LatLon, using WGS84) to cartesian coordinates, like googles spherical mercator.
In pseudo code
transform(double lat, double lon) {
double wgs84radius = 6378137;
double shift = PI * wgs84radius;
double x = lon * shift / 180;
double y = log(tan((90+lat)*PI/360)/ (PI/180);
return {x,y}
}
This is the simplest way. Keep in mind that Lat/Lon are angles, while x and y are distances from (0/0)

Answer 2

The OSM data is by default in the WGS84 (EPSG:4326) projection which is based on an ellipsoidal Earth and measures latitude and longitude in degrees.
Most map tiles are generated in the EPSG:900913 "Google" spherical mercator projection. This projection is based on a spherical Earth and latitude and longitude are measured in metres from the origin.
It really seems like the 900913 projection will fit quite nicely with your requirements.
Here is some code for converting between the two.
You might like to consider using osm2psql. During the import process all of the OSM map data is converted to the 900913 projection. What you are left with is a database of all the nodes, lines and polygons of the OSM map data in an easy to access Postgres database.
I was initially intimidated by this process but it is really quite straightforward and will give you lots of flexibility when it comes to using the OSM data.