// Derived from Tom Carden's Albers implementation for Protovis.

// http://gist.github.com/476238

// http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html

d3.geo.albers = function() {

  var origin = [-98, 38],

      parallels = [29.5, 45.5],

      scale = 1000,

      translate = [480, 250],

      lng0, // d3_geo_radians * origin[0]

      n,

      C,

      p0;

  function albers(coordinates) {

    var t = n * (d3_geo_radians * coordinates[0] - lng0),

        p = Math.sqrt(C - 2 * n * Math.sin(d3_geo_radians * coordinates[1])) / n;

    return [

      scale * p * Math.sin(t) + translate[0],

      scale * (p * Math.cos(t) - p0) + translate[1]

    ];

  }

  albers.invert = function(coordinates) {

    var x = (coordinates[0] - translate[0]) / scale,

        y = (coordinates[1] - translate[1]) / scale,

        p0y = p0 + y,

        t = Math.atan2(x, p0y),

        p = Math.sqrt(x * x + p0y * p0y);

    return [

      (lng0 + t / n) / d3_geo_radians,

      Math.asin((C - p * p * n * n) / (2 * n)) / d3_geo_radians

    ];

  };

  function reload() {

    var phi1 = d3_geo_radians * parallels[0],

        phi2 = d3_geo_radians * parallels[1],

        lat0 = d3_geo_radians * origin[1],

        s = Math.sin(phi1),

        c = Math.cos(phi1);

    lng0 = d3_geo_radians * origin[0];

    n = .5 * (s + Math.sin(phi2));

    C = c * c + 2 * n * s;

    p0 = Math.sqrt(C - 2 * n * Math.sin(lat0)) / n;

    return albers;

  }

  albers.origin = function(x) {

    if (!arguments.length) return origin;

    origin = [+x[0], +x[1]];

    return reload();

  };

  albers.parallels = function(x) {

    if (!arguments.length) return parallels;

    parallels = [+x[0], +x[1]];

    return reload();

  };

  albers.scale = function(x) {

    if (!arguments.length) return scale;

    scale = +x;

    return albers;

  };

  albers.translate = function(x) {

    if (!arguments.length) return translate;

    translate = [+x[0], +x[1]];

    return albers;

  };

  return reload();

};

// A composite projection for the United States, 960x500. The set of standard

// parallels for each region comes from USGS, which is published here:

// http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html#albers

// TODO allow the composite projection to be rescaled?

d3.geo.albersUsa = function() {

  var lower48 = d3.geo.albers();

  var alaska = d3.geo.albers()

      .origin([-160, 60])

      .parallels([55, 65]);

  var hawaii = d3.geo.albers()

      .origin([-160, 20])

      .parallels([8, 18]);

  var puertoRico = d3.geo.albers()

      .origin([-60, 10])

      .parallels([8, 18]);

  function albersUsa(coordinates) {

    var lon = coordinates[0],

        lat = coordinates[1];

    return (lat > 50 ? alaska

        : lon < -140 ? hawaii

        : lat < 21 ? puertoRico

        : lower48)(coordinates);

  }

  albersUsa.scale = function(x) {

    if (!arguments.length) return lower48.scale();

    lower48.scale(x);

    alaska.scale(x * .6);

    hawaii.scale(x);

    puertoRico.scale(x * 1.5);

    return albersUsa.translate(lower48.translate());

  };

  albersUsa.translate = function(x) {

    if (!arguments.length) return lower48.translate();

    var dz = lower48.scale() / 1000,

        dx = x[0],

        dy = x[1];

    lower48.translate(x);

    alaska.translate([dx - 400 * dz, dy + 170 * dz]);

    hawaii.translate([dx - 190 * dz, dy + 200 * dz]);

    puertoRico.translate([dx + 580 * dz, dy + 430 * dz]);

    return albersUsa;

  };

  return albersUsa.scale(lower48.scale());

};