var epsilon2 = 1e-12;

function cosh(x) {
  return ((x = Math.exp(x)) + 1 / x) / 2;
}

function sinh(x) {
  return ((x = Math.exp(x)) - 1 / x) / 2;
}

function tanh(x) {
  return ((x = Math.exp(2 * x)) - 1) / (x + 1);
}

export default (function zoomRho(rho, rho2, rho4) {

  // p0 = [ux0, uy0, w0]
  // p1 = [ux1, uy1, w1]
  function zoom(p0, p1) {
    var ux0 = p0[0], uy0 = p0[1], w0 = p0[2],
        ux1 = p1[0], uy1 = p1[1], w1 = p1[2],
        dx = ux1 - ux0,
        dy = uy1 - uy0,
        d2 = dx * dx + dy * dy,
        i,
        S;

    // Special case for u0 ≅ u1.
    if (d2 < epsilon2) {
      S = Math.log(w1 / w0) / rho;
      i = function(t) {
        return [
          ux0 + t * dx,
          uy0 + t * dy,
          w0 * Math.exp(rho * t * S)
        ];
      }
    }

    // General case.
    else {
      var d1 = Math.sqrt(d2),
          b0 = (w1 * w1 - w0 * w0 + rho4 * d2) / (2 * w0 * rho2 * d1),
          b1 = (w1 * w1 - w0 * w0 - rho4 * d2) / (2 * w1 * rho2 * d1),
          r0 = Math.log(Math.sqrt(b0 * b0 + 1) - b0),
          r1 = Math.log(Math.sqrt(b1 * b1 + 1) - b1);
      S = (r1 - r0) / rho;
      i = function(t) {
        var s = t * S,
            coshr0 = cosh(r0),
            u = w0 / (rho2 * d1) * (coshr0 * tanh(rho * s + r0) - sinh(r0));
        return [
          ux0 + u * dx,
          uy0 + u * dy,
          w0 * coshr0 / cosh(rho * s + r0)
        ];
      }
    }

    i.duration = S * 1000 * rho / Math.SQRT2;

    return i;
  }

  zoom.rho = function(_) {
    var _1 = Math.max(1e-3, +_), _2 = _1 * _1, _4 = _2 * _2;
    return zoomRho(_1, _2, _4);
  };

  return zoom;
})(Math.SQRT2, 2, 4);