// @flow
import LngLat from '../lng_lat.js';
import {clamp, degToRad, radToDeg} from '../../util/util.js';
import {MAX_MERCATOR_LATITUDE} from '../mercator_coordinate.js';
import Projection from './projection.js';

import type {ProjectedPoint} from './projection.js';

const maxPhi = degToRad(MAX_MERCATOR_LATITUDE);

export default class NaturalEarth extends Projection {

    project(lng: number, lat: number): ProjectedPoint {
        // based on https://github.com/d3/d3-geo, MIT-licensed
        lat = degToRad(lat);
        lng = degToRad(lng);

        const phi2 = lat * lat;
        const phi4 = phi2 * phi2;
        const x = lng * (0.8707 - 0.131979 * phi2 + phi4 * (-0.013791 + phi4 * (0.003971 * phi2 - 0.001529 * phi4)));
        const y = lat * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4)));

        return {
            x: (x / Math.PI + 0.5) * 0.5,
            y: 1 - (y / Math.PI + 1) * 0.5,
            z: 0
        };
    }

    unproject(x: number, y: number): LngLat {
        // based on https://github.com/d3/d3-geo, MIT-licensed
        x = (2 * x - 0.5) * Math.PI;
        y = (2 * (1 - y) - 1) * Math.PI;
        const epsilon = 1e-6;
        let phi = y;
        let i = 25;
        let delta = 0;
        let phi2 = phi * phi;

        do {
            phi2 = phi * phi;
            const phi4 = phi2 * phi2;
            delta = (phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4))) - y) /
                (1.007226 + phi2 * (0.015085 * 3 + phi4 * (-0.044475 * 7 + 0.028874 * 9 * phi2 - 0.005916 * 11 * phi4)));
            phi = clamp(phi - delta, -maxPhi, maxPhi);
        } while (Math.abs(delta) > epsilon && --i > 0);

        phi2 = phi * phi;
        const lambda = x / (0.8707 + phi2 * (-0.131979 + phi2 * (-0.013791 + phi2 * phi2 * phi2 * (0.003971 - 0.001529 * phi2))));

        const lng = clamp(radToDeg(lambda), -180, 180);
        const lat = radToDeg(phi);

        return new LngLat(lng, lat);
    }
}