"use strict"; var D2R = Math.PI / 180; var R2D = 180 / Math.PI; var Coord = function (lon, lat) { this.lon = lon; this.lat = lat; this.x = D2R * lon; this.y = D2R * lat; }; Coord.prototype.view = function () { return String(this.lon).slice(0, 4) + "," + String(this.lat).slice(0, 4); }; Coord.prototype.antipode = function () { var anti_lat = -1 * this.lat; var anti_lon = this.lon < 0 ? 180 + this.lon : (180 - this.lon) * -1; return new Coord(anti_lon, anti_lat); }; var LineString = function () { this.coords = []; this.length = 0; }; LineString.prototype.move_to = function (coord) { this.length++; this.coords.push(coord); }; var Arc = function (properties) { this.properties = properties || {}; this.geometries = []; }; Arc.prototype.json = function () { if (this.geometries.length <= 0) { return { geometry: { type: "LineString", coordinates: null }, type: "Feature", properties: this.properties }; } else if (this.geometries.length == 1) { return { geometry: { type: "LineString", coordinates: this.geometries[0].coords }, type: "Feature", properties: this.properties }; } else { var multiline = []; for (var i = 0; i < this.geometries.length; i++) { multiline.push(this.geometries[i].coords); } return { geometry: { type: "MultiLineString", coordinates: multiline }, type: "Feature", properties: this.properties }; } }; // TODO - output proper multilinestring Arc.prototype.wkt = function () { var wkt_string = ""; var wkt = "LINESTRING("; var collect = function (c) { wkt += c[0] + " " + c[1] + ","; }; for (var i = 0; i < this.geometries.length; i++) { if (this.geometries[i].coords.length === 0) { return "LINESTRING(empty)"; } else { var coords = this.geometries[i].coords; coords.forEach(collect); wkt_string += wkt.substring(0, wkt.length - 1) + ")"; } } return wkt_string; }; /* * http://en.wikipedia.org/wiki/Great-circle_distance * */ var GreatCircle = function (start, end, properties) { if (!start || start.x === undefined || start.y === undefined) { throw new Error( "GreatCircle constructor expects two args: start and end objects with x and y properties" ); } if (!end || end.x === undefined || end.y === undefined) { throw new Error( "GreatCircle constructor expects two args: start and end objects with x and y properties" ); } this.start = new Coord(start.x, start.y); this.end = new Coord(end.x, end.y); this.properties = properties || {}; var w = this.start.x - this.end.x; var h = this.start.y - this.end.y; var z = Math.pow(Math.sin(h / 2.0), 2) + Math.cos(this.start.y) * Math.cos(this.end.y) * Math.pow(Math.sin(w / 2.0), 2); this.g = 2.0 * Math.asin(Math.sqrt(z)); if (this.g == Math.PI) { throw new Error( "it appears " + start.view() + " and " + end.view() + " are 'antipodal', e.g diametrically opposite, thus there is no single route but rather infinite" ); } else if (isNaN(this.g)) { throw new Error( "could not calculate great circle between " + start + " and " + end ); } }; /* * http://williams.best.vwh.net/avform.htm#Intermediate */ GreatCircle.prototype.interpolate = function (f) { var A = Math.sin((1 - f) * this.g) / Math.sin(this.g); var B = Math.sin(f * this.g) / Math.sin(this.g); var x = A * Math.cos(this.start.y) * Math.cos(this.start.x) + B * Math.cos(this.end.y) * Math.cos(this.end.x); var y = A * Math.cos(this.start.y) * Math.sin(this.start.x) + B * Math.cos(this.end.y) * Math.sin(this.end.x); var z = A * Math.sin(this.start.y) + B * Math.sin(this.end.y); var lat = R2D * Math.atan2(z, Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2))); var lon = R2D * Math.atan2(y, x); return [lon, lat]; }; /* * Generate points along the great circle */ GreatCircle.prototype.Arc = function (npoints, options) { var first_pass = []; if (!npoints || npoints <= 2) { first_pass.push([this.start.lon, this.start.lat]); first_pass.push([this.end.lon, this.end.lat]); } else { var delta = 1.0 / (npoints - 1); for (var i = 0; i < npoints; ++i) { var step = delta * i; var pair = this.interpolate(step); first_pass.push(pair); } } /* partial port of dateline handling from: gdal/ogr/ogrgeometryfactory.cpp TODO - does not handle all wrapping scenarios yet */ var bHasBigDiff = false; var dfMaxSmallDiffLong = 0; // from http://www.gdal.org/ogr2ogr.html // -datelineoffset: // (starting with GDAL 1.10) offset from dateline in degrees (default long. = +/- 10deg, geometries within 170deg to -170deg will be splited) var dfDateLineOffset = options && options.offset ? options.offset : 10; var dfLeftBorderX = 180 - dfDateLineOffset; var dfRightBorderX = -180 + dfDateLineOffset; var dfDiffSpace = 360 - dfDateLineOffset; // https://github.com/OSGeo/gdal/blob/7bfb9c452a59aac958bff0c8386b891edf8154ca/gdal/ogr/ogrgeometryfactory.cpp#L2342 for (var j = 1; j < first_pass.length; ++j) { var dfPrevX = first_pass[j - 1][0]; var dfX = first_pass[j][0]; var dfDiffLong = Math.abs(dfX - dfPrevX); if ( dfDiffLong > dfDiffSpace && ((dfX > dfLeftBorderX && dfPrevX < dfRightBorderX) || (dfPrevX > dfLeftBorderX && dfX < dfRightBorderX)) ) { bHasBigDiff = true; } else if (dfDiffLong > dfMaxSmallDiffLong) { dfMaxSmallDiffLong = dfDiffLong; } } var poMulti = []; if (bHasBigDiff && dfMaxSmallDiffLong < dfDateLineOffset) { var poNewLS = []; poMulti.push(poNewLS); for (var k = 0; k < first_pass.length; ++k) { var dfX0 = parseFloat(first_pass[k][0]); if (k > 0 && Math.abs(dfX0 - first_pass[k - 1][0]) > dfDiffSpace) { var dfX1 = parseFloat(first_pass[k - 1][0]); var dfY1 = parseFloat(first_pass[k - 1][1]); var dfX2 = parseFloat(first_pass[k][0]); var dfY2 = parseFloat(first_pass[k][1]); if ( dfX1 > -180 && dfX1 < dfRightBorderX && dfX2 == 180 && k + 1 < first_pass.length && first_pass[k - 1][0] > -180 && first_pass[k - 1][0] < dfRightBorderX ) { poNewLS.push([-180, first_pass[k][1]]); k++; poNewLS.push([first_pass[k][0], first_pass[k][1]]); continue; } else if ( dfX1 > dfLeftBorderX && dfX1 < 180 && dfX2 == -180 && k + 1 < first_pass.length && first_pass[k - 1][0] > dfLeftBorderX && first_pass[k - 1][0] < 180 ) { poNewLS.push([180, first_pass[k][1]]); k++; poNewLS.push([first_pass[k][0], first_pass[k][1]]); continue; } if (dfX1 < dfRightBorderX && dfX2 > dfLeftBorderX) { // swap dfX1, dfX2 var tmpX = dfX1; dfX1 = dfX2; dfX2 = tmpX; // swap dfY1, dfY2 var tmpY = dfY1; dfY1 = dfY2; dfY2 = tmpY; } if (dfX1 > dfLeftBorderX && dfX2 < dfRightBorderX) { dfX2 += 360; } if (dfX1 <= 180 && dfX2 >= 180 && dfX1 < dfX2) { var dfRatio = (180 - dfX1) / (dfX2 - dfX1); var dfY = dfRatio * dfY2 + (1 - dfRatio) * dfY1; poNewLS.push([ first_pass[k - 1][0] > dfLeftBorderX ? 180 : -180, dfY ]); poNewLS = []; poNewLS.push([ first_pass[k - 1][0] > dfLeftBorderX ? -180 : 180, dfY ]); poMulti.push(poNewLS); } else { poNewLS = []; poMulti.push(poNewLS); } poNewLS.push([dfX0, first_pass[k][1]]); } else { poNewLS.push([first_pass[k][0], first_pass[k][1]]); } } } else { // add normally var poNewLS0 = []; poMulti.push(poNewLS0); for (var l = 0; l < first_pass.length; ++l) { poNewLS0.push([first_pass[l][0], first_pass[l][1]]); } } var arc = new Arc(this.properties); for (var m = 0; m < poMulti.length; ++m) { var line = new LineString(); arc.geometries.push(line); var points = poMulti[m]; for (var j0 = 0; j0 < points.length; ++j0) { line.move_to(points[j0]); } } return arc; }; if (typeof module !== "undefined" && typeof module.exports !== "undefined") { // nodejs module.exports.Coord = Coord; module.exports.Arc = Arc; module.exports.GreatCircle = GreatCircle; } else { // browser var arc = {}; arc.Coord = Coord; arc.Arc = Arc; arc.GreatCircle = GreatCircle; }