// imports
var atan    = Math.atan,
    sqrt1_2 = Math.sqrt(1/2),
    π = Math.PI,
    degrees = 180 / π,
    θ = atan(sqrt1_2) * degrees;

var d3Geo = d3,
    polyhedral = d3.geoPolyhedral;

var width = 900,
    height = 400,
    rotate = [30, 0, 0];


var vertices = [
[0, θ], [90, θ], [180, θ], [-90, θ],
[0, -θ], [90, -θ], [180, -θ], [-90, -θ]
];

var polyhedron = [
  [0, 3, 2, 1], // N
  [0, 1, 5, 4],
  [1, 2, 6, 5],
  [2, 3, 7, 6],
  [3, 0, 4, 7],
  [4, 5, 6, 7] // S
  ].map(function(face) {
    return face.map(function(i) {
      return vertices[i];
    });
  });


var furuti1 = function(faceProjection) {
  faceProjection = faceProjection || function(face) {
    var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face});
    return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]);
  };

  var faces = polyhedron.map(function(face) {
    var polygon = face.slice();
    polygon.push(polygon[0]);
    return {
      face: face,
      contains: function(lambda, phi) {
        return d3Geo.geoContains({ type: "Polygon", coordinates: [ polygon ] },
          [lambda * degrees, phi * degrees]);
      },
      project: faceProjection(face)
    };
  });

  // Connect each face to a parent face.
  [-1, 4, 5, 2, 0, 1].forEach(function (d, i) {
    var node = faces[d];
    node && (node.children || (node.children = [])).push(faces[i]);
  });

  // Polyhedral projection
  var proj = polyhedral(faces[0], function(lambda, phi) {
      for (var i = 0; i < faces.length; i++) {
        if (faces[i].contains(lambda, phi)) return faces[i];
      }
    },
    π/2   // rotation of the root face in the projected (pixel) space
  )
  .rotate(rotate)
  .clipAngle(1) // no antimeridian clipping on the Sphere
  .fitExtent([[20,20], [width - 20, height - 20]], {type:"Sphere"});

  proj.faces = faces;
  return proj;
}

d3.geoPolyhedralFuruti1 = furuti1;

// map in a cube.
var projection = d3.geoPolyhedralFuruti1();
var path = d3.geoPath().projection(projection);
var graticule = d3.geoGraticule();


var svg = d3.select("#map").append("svg")
  .attr("width", width)
  .attr("height", height);

svg.append("path")
  .datum({type: "Sphere"})
  .attr("class", "background")
  .attr("d", path);

svg.append("path")
  .datum(graticule)
  .attr("class", "graticule")
  .attr("d", path);

svg.append("path")
  .datum({type: "Sphere"})
  .attr("class", "outline")
  .attr("d", path);

d3.json("Mystara_2017.topojson", function(error, mystara) {
  if (error) return console.error(error);
  svg.insert("path", ".graticule")
    .datum(topojson.feature(mystara, mystara.objects.Mystara_2017_unprojected))
    .attr("class", "land")
    .attr("d", path);
  });


d3.select(self.frameElement).style("height", height + "px");