/* * Copyright 2003-2006, 2009, 2017, 2020 United States Government, as represented * by the Administrator of the National Aeronautics and Space Administration. * All rights reserved. * * The NASAWorldWind/WebWorldWind platform is licensed under the Apache License, * Version 2.0 (the "License"); you may not use this file except in compliance * with the License. You may obtain a copy of the License * at http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software distributed * under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR * CONDITIONS OF ANY KIND, either express or implied. See the License for the * specific language governing permissions and limitations under the License. * * NASAWorldWind/WebWorldWind also contains the following 3rd party Open Source * software: * * ES6-Promise – under MIT License * libtess.js – SGI Free Software License B * Proj4 – under MIT License * JSZip – under MIT License * * A complete listing of 3rd Party software notices and licenses included in * WebWorldWind can be found in the WebWorldWind 3rd-party notices and licenses * PDF found in code directory. *//** * @exports ProjectionMercator */define([ '../geom/Angle', '../error/ArgumentError', '../projections/GeographicProjection', '../util/Logger', '../geom/Sector', '../geom/Vec3', '../util/WWMath' ], function (Angle, ArgumentError, GeographicProjection, Logger, Sector, Vec3, WWMath) { "use strict"; /** * Constructs a Mercator geographic projection. * @alias ProjectionMercator * @constructor * @augments GeographicProjection * @classdesc Represents a Mercator geographic projection. */ var ProjectionMercator = function () { GeographicProjection.call(this, "Mercator", true, new Sector(-78, 78, -180, 180)); }; ProjectionMercator.prototype = Object.create(GeographicProjection.prototype); // Documented in base class. ProjectionMercator.prototype.geographicToCartesian = function (globe, latitude, longitude, elevation, offset, result) { if (!globe) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "geographicToCartesian", "missingGlobe")); } if (!result) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "geographicToCartesian", "missingResult")); } if (latitude > this.projectionLimits.maxLatitude) { latitude = this.projectionLimits.maxLatitude; } if (latitude < this.projectionLimits.minLatitude) { latitude = this.projectionLimits.minLatitude; } // See "Map Projections: A Working Manual", page 44 for the source of the below formulas. var ecc = Math.sqrt(globe.eccentricitySquared), sinLat = Math.sin(latitude * Angle.DEGREES_TO_RADIANS), s = ((1 + sinLat) / (1 - sinLat)) * Math.pow((1 - ecc * sinLat) / (1 + ecc * sinLat), ecc); result[0] = globe.equatorialRadius * longitude * Angle.DEGREES_TO_RADIANS + (offset ? offset[0] : 0); result[1] = 0.5 * globe.equatorialRadius * Math.log(s); result[2] = elevation; return result; }; Object.defineProperties(ProjectionMercator.prototype, { /** * A string identifying this projection's current state. Used to compare states during rendering to * determine whether globe-state dependent cached values must be updated. Applications typically do not * interact with this property. * @memberof ProjectionMercator.prototype * @readonly * @type {String} */ stateKey: { get: function () { return "projection mercator "; } } }); // Documented in base class. ProjectionMercator.prototype.geographicToCartesianGrid = function (globe, sector, numLat, numLon, elevations, referencePoint, offset, result) { if (!globe) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "geographicToCartesianGrid", "missingGlobe")); } if (!sector) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "geographicToCartesianGrid", "missingSector")); } if (!elevations || elevations.length < numLat * numLon) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "geographicToCartesianGrid", "The specified elevations array is null, undefined or insufficient length")); } if (!result) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "geographicToCartesianGrid", "missingResult")); } var eqr = globe.equatorialRadius, ecc = Math.sqrt(globe.eccentricitySquared), minLat = sector.minLatitude * Angle.DEGREES_TO_RADIANS, maxLat = sector.maxLatitude * Angle.DEGREES_TO_RADIANS, minLon = sector.minLongitude * Angle.DEGREES_TO_RADIANS, maxLon = sector.maxLongitude * Angle.DEGREES_TO_RADIANS, deltaLat = (maxLat - minLat) / (numLat > 1 ? numLat - 1 : 1), deltaLon = (maxLon - minLon) / (numLon > 1 ? numLon - 1 : 1), minLatLimit = this.projectionLimits.minLatitude * Angle.DEGREES_TO_RADIANS, maxLatLimit = this.projectionLimits.maxLatitude * Angle.DEGREES_TO_RADIANS, refCenter = referencePoint ? referencePoint : new Vec3(0, 0, 0), offsetX = offset ? offset[0] : 0, latIndex, lonIndex, elevIndex = 0, resultIndex = 0, lat, lon, clampedLat, sinLat, s, y; // Iterate over the latitude and longitude coordinates in the specified sector, computing the Cartesian point // corresponding to each latitude and longitude. for (latIndex = 0, lat = minLat; latIndex < numLat; latIndex++, lat += deltaLat) { if (latIndex === numLat - 1) { lat = maxLat; // explicitly set the last lat to the max latitude to ensure alignment } // Latitude is constant for each row. Values that are a function of latitude can be computed once per row. clampedLat = WWMath.clamp(lat, minLatLimit, maxLatLimit); sinLat = Math.sin(clampedLat); s = ((1 + sinLat) / (1 - sinLat)) * Math.pow((1 - ecc * sinLat) / (1 + ecc * sinLat), ecc); y = eqr * Math.log(s) * 0.5 - refCenter[1]; for (lonIndex = 0, lon = minLon; lonIndex < numLon; lonIndex++, lon += deltaLon) { if (lonIndex === numLon - 1) { lon = maxLon; // explicitly set the last lon to the max longitude to ensure alignment } result[resultIndex++] = eqr * lon - refCenter[0] + offsetX; result[resultIndex++] = y; result[resultIndex++] = elevations[elevIndex++] - refCenter[2]; } } return result; }; // Documented in base class. ProjectionMercator.prototype.cartesianToGeographic = function (globe, x, y, z, offset, result) { if (!globe) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "cartesianToGeographic", "missingGlobe")); } if (!result) { throw new ArgumentError(Logger.logMessage(Logger.LEVEL_SEVERE, "ProjectionMercator", "cartesianToGeographic", "missingResult")); } // See "Map Projections: A Working Manual", pages 45 and 19 for the source of the below formulas. var ecc2 = globe.eccentricitySquared, ecc4 = ecc2 * ecc2, ecc6 = ecc4 * ecc2, ecc8 = ecc6 * ecc2, t = Math.pow(Math.E, - y / globe.equatorialRadius), A = Math.PI / 2 - 2 * Math.atan(t), B = ecc2 / 2 + 5 * ecc4 / 24 + ecc6 / 12 + 13 * ecc8 / 360, C = 7 * ecc4 / 48 + 29 * ecc6 / 240 + 811 * ecc8 / 11520, D = 7 * ecc6 / 120 + 81 * ecc8 / 1120, E = 4279 * ecc8 / 161280, Ap = A - C + E, Bp = B - 3 * D, Cp = 2 * C - 8 * E, Dp = 4 * D, Ep = 8 * E, s2p = Math.sin(2 * A), lat = Ap + s2p * (Bp + s2p * (Cp + s2p * (Dp + Ep * s2p))); result.latitude = lat * Angle.RADIANS_TO_DEGREES; result.longitude = ((x - (offset ? offset[0] : 0)) / globe.equatorialRadius) * Angle.RADIANS_TO_DEGREES; result.altitude = z; return result; }; return ProjectionMercator; });