satellite.js

// See pages 173 and 175 of Snyder's "Map Projections---A Working Manual" (1987): http://pubs.usgs.gov/pp/1395/report.pdf

function satelliteVerticalR(H, R) {
  var P = 1.0 + H/R;
  function forward(λ, φ) {
    var cosφ = Math.cos(φ),
        k = (P - 1) / (P - cosφ * Math.cos(λ));
    return [
      R * k * cosφ * Math.sin(λ),
      R * k * Math.sin(φ)
    ];
  }

  forward.invert = function(x, y) {
    var ρ2 = x * x + y * y,
        ρ = Math.sqrt(ρ2),
        R2 = Math.pow(R, 2),
        sinc = (P - Math.sqrt(1 - ρ2 * (P + 1) / (R2 * (P - 1)))) / (R * (P - 1) / ρ + ρ / (R * (P - 1)));
    return [
      Math.atan2(x * sinc, ρ * Math.sqrt(1 - sinc * sinc)),
      ρ ? asin(y * sinc / ρ) : 0
    ];
  };

  return forward;
}

// No tilt yet
function satelliteProjectionR() {
  var R = 1.0,
      H = 0.4,
      m = projectionMutator(satelliteVerticalR),
      p = m(H, R);

  p.height = function(_) {
    if (!arguments.length) return H;
    return m(H = +_, R);
  };

  p.radius = function(_) {
    if (!arguments.length) return R;
    return m(P, R = +_);
  };

  return p;
}