var thirdPi = Math.PI / 3,
    angles = [0, thirdPi, 2 * thirdPi, 3 * thirdPi, 4 * thirdPi, 5 * thirdPi];

function pointX(d) {
  return d[0];
}

function pointY(d) {
  return d[1];
}

function hexbin() {
  var x0 = 0,
      y0 = 0,
      x1 = 1,
      y1 = 1,
      x = pointX,
      y = pointY,
      r,
      dx,
      dy;

  function hexbin(points) {
    var binsById = {}, bins = [], i, n = points.length;

    for (i = 0; i < n; ++i) {
      if (isNaN(px = +x.call(null, point = points[i], i, points))
          || isNaN(py = +y.call(null, point, i, points))) continue;

      var point,
          px,
          py,
          pj = Math.round(py = py / dy),
          pi = Math.round(px = px / dx - (pj & 1) / 2),
          py1 = py - pj;

      if (Math.abs(py1) * 3 > 1) {
        var px1 = px - pi,
            pi2 = pi + (px < pi ? -1 : 1) / 2,
            pj2 = pj + (py < pj ? -1 : 1),
            px2 = px - pi2,
            py2 = py - pj2;
        if (px1 * px1 + py1 * py1 > px2 * px2 + py2 * py2) pi = pi2 + (pj & 1 ? 1 : -1) / 2, pj = pj2;
      }

      var id = pi + "-" + pj, bin = binsById[id];
      if (bin) bin.push(point);
      else {
        bins.push(bin = binsById[id] = [point]);
        bin.x = (pi + (pj & 1) / 2) * dx;
        bin.y = pj * dy;
      }
    }

    return bins;
  }

  function hexagon(radius) {
    var x0 = 0, y0 = 0;
    return angles.map(function(angle) {
      var x1 = Math.sin(angle) * radius,
          y1 = -Math.cos(angle) * radius,
          dx = x1 - x0,
          dy = y1 - y0;
      x0 = x1, y0 = y1;
      return [dx, dy];
    });
  }

  hexbin.hexagon = function(radius) {
    return "m" + hexagon(radius == null ? r : +radius).join("l") + "z";
  };

  hexbin.centers = function() {
    var centers = [],
        j = Math.round(y0 / dy),
        i = Math.round(x0 / dx);
    for (var y = j * dy; y < y1 + r; y += dy, ++j) {
      for (var x = i * dx + (j & 1) * dx / 2; x < x1 + dx / 2; x += dx) {
        centers.push([x, y]);
      }
    }
    return centers;
  };

  hexbin.mesh = function() {
    var fragment = hexagon(r).slice(0, 4).join("l");
    return hexbin.centers().map(function(p) { return "M" + p + "m" + fragment; }).join("");
  };

  hexbin.x = function(_) {
    return arguments.length ? (x = _, hexbin) : x;
  };

  hexbin.y = function(_) {
    return arguments.length ? (y = _, hexbin) : y;
  };

  hexbin.radius = function(_) {
    return arguments.length ? (r = +_, dx = r * 2 * Math.sin(thirdPi), dy = r * 1.5, hexbin) : r;
  };

  hexbin.size = function(_) {
    return arguments.length ? (x0 = y0 = 0, x1 = +_[0], y1 = +_[1], hexbin) : [x1 - x0, y1 - y0];
  };

  hexbin.extent = function(_) {
    return arguments.length ? (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1], hexbin) : [[x0, y0], [x1, y1]];
  };

  return hexbin.radius(1);
}