緯度経度と平面直角座標を相互に変換するDart（Flutter）コード

xy.dart

import 'package:latlong2/latlong.dart';
import 'dart:math';

const f = 298.257222;
const r = 6378137.0;
const m0 = 0.9999;
const n1 = 1 / (2 * f - 1);
const alpha = [
  1.0,
  0.0008377318250120707,
  7.608527853531295e-7,
  1.1976455014483125e-9,
  2.429150263945317e-12,
  5.750164393844325e-15
];
const beta = [
  1.0,
  0.0008377321684455561,
  5.905870215034071e-8,
  1.6734826778558678e-10,
  2.1648237340373555e-13,
  3.7940918853103374e-16
];
const a = [
  1.0000007049454083,
  -0.0025188297049783238,
  2.643542951117491e-6,
  -3.4526259108208313e-9,
  4.891830431025234e-12,
  -7.228726058073925e-15
];
const delta = [
  1.0,
  0.003356551486742219,
  6.5719224858971644e-6,
  1.764640439081273e-8,
  5.387753897315289e-11,
  1.764007518903401e-13,
  6.056074067532996e-16
];
const aBar = m0 * r / (1 + n1) * 1.0000007049454083;
const tsnopn = 2.0 * 0.040978291755 / (1.0 + n1);

double rad2deg(double rad) {
  return rad * 180 / pi;
}

double atanh(double x) {
  return log((1 + x) / (1 - x)) / 2;
}

double sinh(double x) {
  return (exp(x) - exp(-x)) / 2;
}

double cosh(double x) {
  return (exp(x) + exp(-x)) / 2;
}

double tanh(double x) {
  return (exp(x) - exp(-x)) / (exp(x) + exp(-x));
}

double sBarCalc(double lat0) {
  double sBar = lat0;
  for (int j = 1; j <= 5; j++) {
    sBar += a[j] * sin(2 * j * lat0);
  }
  sBar *= aBar;
  return sBar;
}

class XY {
  const XY({
    required this.x,
    required this.y,
    required this.source,
    required this.reference,
  });
  final double x;
  final double y;
  final LatLng source;
  final LatLng reference;

  XY zero(LatLng reference) {
    return XY(x: 0, y: 0, source: reference, reference: reference);
  }

  static XY fromLatLng(LatLng source, LatLng reference) {
    final lat = source.latitudeInRad;
    final lng = source.longitudeInRad;
    final lat0 = reference.latitudeInRad;
    final lng0 = reference.longitudeInRad;

    final t = sinh(atanh(sin(lat)) - tsnopn * atanh(tsnopn * sin(lat)));
    final tBar = sqrt(1 + t * t);
    final lngC = cos(lng - lng0);
    final lngS = sin(lng - lng0);
    final xi = atan(t / lngC);
    final eta = atanh(lngS / tBar);
    final sBar = sBarCalc(lat0);
    double x = xi;
    for (int j = 1; j <= 5; j++) {
      x += alpha[j] * sin(2 * j * xi) * cosh(2 * j * eta);
    }
    x = aBar * x - sBar;
    double y = eta;
    for (int j = 1; j <= 5; j++) {
      y += alpha[j] * cos(2 * j * xi) * sinh(2 * j * eta);
    }
    y *= aBar;

    return XY(x: x, y: y, source: source, reference: reference);
  }
  
  static XY fromXY(double x, double y, LatLng reference) {
    final lat0 = reference.latitudeInRad;
    final lng0 = reference.longitudeInRad;

    final sBar = sBarCalc(lat0);
    final xi = (x + sBar) / aBar;
    final eta = y / aBar;
    double xi_ = xi;
    for (int j = 1; j <= 5; j++) {
      xi_ -= beta[j] * sin(2 * j * xi) * cosh(2 * j * eta);
    }
    double eta_ = eta;
    for (int j = 1; j <= 5; j++) {
      eta_ -= beta[j] * cos(2 * j * xi) * sinh(2 * j * eta);
    }
    final chi = asin(sin(xi_) / cosh(eta_));
    double lat = chi;
    for (int j = 1; j <= 6; j++) {
      lat += delta[j] * sin(2 * j * chi);
    }
    final lng = lng0 + atan(sinh(eta_) / cos(xi_));
    return XY(
        x: x,
        y: y,
        source: LatLng(rad2deg(lat), rad2deg(lng)),
        reference: reference);
  }
}