patterson.js

import {geoProjection as projection} from "d3-geo";
import {abs, epsilon} from "./math.js";

// Based on Java implementation by Bojan Savric.
// https://github.com/OSUCartography/JMapProjLib/blob/master/src/com/jhlabs/map/proj/PattersonProjection.java

var pattersonK1 = 1.0148,
    pattersonK2 = 0.23185,
    pattersonK3 = -0.14499,
    pattersonK4 = 0.02406,
    pattersonC1 = pattersonK1,
    pattersonC2 = 5 * pattersonK2,
    pattersonC3 = 7 * pattersonK3,
    pattersonC4 = 9 * pattersonK4,
    pattersonYmax = 1.790857183;

export function pattersonRaw(lambda, phi) {
  var phi2 = phi * phi;
  return [
    lambda,
    phi * (pattersonK1 + phi2 * phi2 * (pattersonK2 + phi2 * (pattersonK3 + pattersonK4 * phi2)))
  ];
}

pattersonRaw.invert = function(x, y) {
  if (y > pattersonYmax) y = pattersonYmax;
  else if (y < -pattersonYmax) y = -pattersonYmax;
  var yc = y, delta;

  do { // Newton-Raphson
    var y2 = yc * yc;
    yc -= delta = ((yc * (pattersonK1 + y2 * y2 * (pattersonK2 + y2 * (pattersonK3 + pattersonK4 * y2)))) - y) / (pattersonC1 + y2 * y2 * (pattersonC2 + y2 * (pattersonC3 + pattersonC4 * y2)));
  } while (abs(delta) > epsilon);

  return [x, yc];
};

export default function() {
  return projection(pattersonRaw)
      .scale(139.319);
}