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An Albers Equal Area Conic projection in javascript, for protovis.
/*
An Albers Equal Area Conic projection in javascript, for protovis.
For centering the contiguous states of the USA in a 800x400 div, I used:
var scale = pv.Geo.scale(albers(23, -96, 29.5, 45.5))
.range({ x: -365, y: -375 }, { x: 1200, y: 1200 });
http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html
*/
function albers(lat0, lng0, phi1, phi2) {
if (lat0 == undefined) lat0 = 23.0; // Latitude_Of_Origin
if (lng0 == undefined) lng0 = -96.0; // Central_Meridian
if (phi1 == undefined) phi1 = 29.5; // Standard_Parallel_1
if (phi2 == undefined) phi2 = 45.5; // Standard_Parallel_2
lat0 = pv.radians(lat0);
lng0 = pv.radians(lng0);
phi1 = pv.radians(phi1);
phi2 = pv.radians(phi2);
var n = 0.5 * (Math.sin(phi1) + Math.sin(phi2)),
c = Math.cos(phi1),
C = c*c + 2*n*Math.sin(phi1),
p0 = Math.sqrt(C - 2*n*Math.sin(lat0)) / n;
return {
project: function(latlng) {
var theta = n * (pv.radians(latlng.lng) - lng0),
p = Math.sqrt(C - 2*n*Math.sin(pv.radians(latlng.lat))) / n;
return {
x: p * Math.sin(theta),
y: p0 - p * Math.cos(theta)
};
},
invert: function(xy) {
var theta = Math.atan(xy.x / (p0 - xy.y)),
p = Math.sqrt(xy.x*xy.y + Math.pow(p0 - xy.y, 2));
return {
lng: pv.degrees(lon0 + theta/n),
lat: pv.degrees(Math.asin( (C - p*p*n*n) / (2*n)))
};
}
};
}
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