5月21日のフジテレビ『新報道2001』の北朝鮮ミサイルの地図の正確なプロットを書いてみた

メルカトル図法ではわからない距離が正確にわかる世界地図。 | Topics-Jp
5月末に炎上した、フジテレビの地図の誤表記のネタです

結局、だれもミラー図法での正しいプロットを書いてなかったので書いてみました

距離は、
黄色 1500km
緑色 2500km
紫色 5000km
赤色 10000km

緯度計算は、Vincenty's Formula を使いました。
(緯度経度と方位角と距離から、目的地の緯度経度が求められる便利な公式)

地図は、
地図投影法 地図図法 | From FLand
にある物をベースに計算しました。

mira
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|。・ω・) 。o ( 面白い形でしょう? )


おまけ
Google Map のメルカトル図法だとこうなります

Vincenty formula - JSFiddle

omake

function drawCircle(point, radius, dir, addtoBounds) {
    var extp = []; // best practice is to use [] rather then new Array(), both do the same thing.   
    if (dir == 1) {
        for (var i = 0; i < 361; i++) {
            //destVincenty function returns a object with lat, lon, and final bearing.     
            var destPoint = destVincenty(point.lat(), point.lng(), i, radius);

            //add new point
            extp.push(new google.maps.LatLng(destPoint.lat, destPoint.lon));
            if (addtoBounds) bounds.extend(extp[extp.length - 1]);
        }
    }
    else {
        for (var i = 361; i > 0; i--) {
            //destVincenty function returns a object with lat, lon, and final bearing.     
            var destPoint = destVincenty(point.lat(), point.lng(), i, radius);

            //add new point
            extp.push(new google.maps.LatLng(destPoint.lat, destPoint.lon));
            if (addtoBounds) bounds.extend(extp[extp.length - 1]);
        }
    }

    return extp;
}

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
/* Vincenty Direct Solution of Geodesics on the Ellipsoid (c) Chris Veness 2005-2012              */
/* http://creativecommons.org/licenses/by/3.0/                                                    */
/* from: Vincenty direct formula - T Vincenty, "Direct and Inverse Solutions of Geodesics on the  */
/*       Ellipsoid with application of nested equations", Survey Review, vol XXII no 176, 1975    */
/*       http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf                                             */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */

/**
 * Calculates destination point given start point lat/long, bearing & distance,
 * using Vincenty inverse formula for ellipsoids
 *
 * @param   {Number} lat1, lon1: first point in decimal degrees
 * @param   {Number} brng: initial bearing in decimal degrees
 * @param   {Number} dist: distance along bearing in metres
 * @returns (LatLon} destination point
 */

function destVincenty(lat1, lon1, brng, dist) {
    var a = 6378137,
        b = 6356752.3142,
        f = 1 / 298.257223563; // WGS-84 ellipsiod
    var s = dist;
    var alpha1 = brng.toRad();
    var sinAlpha1 = Math.sin(alpha1);
    var cosAlpha1 = Math.cos(alpha1);

    var tanU1 = (1 - f) * Math.tan(lat1.toRad());
    var cosU1 = 1 / Math.sqrt((1 + tanU1 * tanU1)),
        sinU1 = tanU1 * cosU1;
    var sigma1 = Math.atan2(tanU1, cosAlpha1);
    var sinAlpha = cosU1 * sinAlpha1;
    var cosSqAlpha = 1 - sinAlpha * sinAlpha;
    var uSq = cosSqAlpha * (a * a - b * b) / (b * b);
    var A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
    var B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));

    var sigma = s / (b * A),
        sigmaP = 2 * Math.PI;
    while (Math.abs(sigma - sigmaP) > 1e-12) {
        var cos2SigmaM = Math.cos(2 * sigma1 + sigma);
        var sinSigma = Math.sin(sigma);
        var cosSigma = Math.cos(sigma);
        var deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));
        sigmaP = sigma;
        sigma = s / (b * A) + deltaSigma;
    }

    var tmp = sinU1 * sinSigma - cosU1 * cosSigma * cosAlpha1;
    var lat2 = Math.atan2(sinU1 * cosSigma + cosU1 * sinSigma * cosAlpha1, (1 - f) * Math.sqrt(sinAlpha * sinAlpha + tmp * tmp));
    var lambda = Math.atan2(sinSigma * sinAlpha1, cosU1 * cosSigma - sinU1 * sinSigma * cosAlpha1);
    var C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
    var L = lambda - (1 - C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
    var lon2 = (lon1.toRad() + L + 3 * Math.PI) % (2 * Math.PI) - Math.PI; // normalise to -180...+180
    var revAz = Math.atan2(sinAlpha, -tmp); // final bearing, if required
    return {
        lat: lat2.toDeg(),
        lon: lon2.toDeg(),
        finalBearing: revAz.toDeg()
    };
}

// ---- extend Number object with methods for converting degrees/radians
Number.prototype.toRad = function() {
    return this * Math.PI / 180;
}

Number.prototype.toDeg = function() {
    return this * 180 / Math.PI;
}

    
//-- script entry --//
var bounds;
var map;
function initialize() {
    var centerPosition = new google.maps.LatLng(39.036694, 125.764559);
    var options = {
        zoom: 6,
        center: centerPosition,
        mapTypeId: google.maps.MapTypeId.ROADMAP
    };
    map = new google.m
aps.Map($('#map_canvas')[0], options);
    bounds = new google.maps.LatLngBounds();

    var coords = drawCircle(centerPosition, 10000000, 0, true);
    var circle = new google.maps.Polyline({
        path: coords,
        map: map,
        strokeColor: "#FF0000",
        strokeOpacity: 1.0,
        strokeWeight: 2
    });
    var coords2 = drawCircle(centerPosition, 5000000, 0, true);
    var circle2 = new google.maps.Polyline({
        path: coords2,
        map: map,
        strokeColor: "#FFFF00",
        strokeOpacity: 1.0,
        strokeWeight: 2
    });
    var coords3 = drawCircle(centerPosition, 2500000, 0, true);
    var circle3 = new google.maps.Polyline({
        path: coords3,
        map: map,
        strokeColor: "#00FF00",
        strokeOpacity: 1.0,
        strokeWeight: 2
    });
    var coords4 = drawCircle(centerPosition, 1500000, 0, true);
    var circle4 = new google.maps.Polyline({
        path: coords4,
        map: map,
        strokeColor: "#7fFF00",
        strokeOpacity: 1.0,
        strokeWeight: 2
    });

    map.fitBounds(bounds);

}
google.maps.event.addDomListener(window, 'load', initialize);

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