414 lines
17 KiB
JavaScript
414 lines
17 KiB
JavaScript
/**
|
|
* Cesium - https://github.com/AnalyticalGraphicsInc/cesium
|
|
*
|
|
* Copyright 2011-2017 Cesium Contributors
|
|
*
|
|
* 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.
|
|
*
|
|
* Columbus View (Pat. Pend.)
|
|
*
|
|
* Portions licensed separately.
|
|
* See https://github.com/AnalyticalGraphicsInc/cesium/blob/master/LICENSE.md for full licensing details.
|
|
*/
|
|
define(['exports', './when-8d13db60', './Check-70bec281', './Math-61ede240', './Cartographic-fe4be337', './Cartesian2-85064f09'], function (exports, when, Check, _Math, Cartographic, Cartesian2) { 'use strict';
|
|
|
|
function setConstants(ellipsoidGeodesic) {
|
|
var uSquared = ellipsoidGeodesic._uSquared;
|
|
var a = ellipsoidGeodesic._ellipsoid.maximumRadius;
|
|
var b = ellipsoidGeodesic._ellipsoid.minimumRadius;
|
|
var f = (a - b) / a;
|
|
|
|
var cosineHeading = Math.cos(ellipsoidGeodesic._startHeading);
|
|
var sineHeading = Math.sin(ellipsoidGeodesic._startHeading);
|
|
|
|
var tanU = (1 - f) * Math.tan(ellipsoidGeodesic._start.latitude);
|
|
|
|
var cosineU = 1.0 / Math.sqrt(1.0 + tanU * tanU);
|
|
var sineU = cosineU * tanU;
|
|
|
|
var sigma = Math.atan2(tanU, cosineHeading);
|
|
|
|
var sineAlpha = cosineU * sineHeading;
|
|
var sineSquaredAlpha = sineAlpha * sineAlpha;
|
|
|
|
var cosineSquaredAlpha = 1.0 - sineSquaredAlpha;
|
|
var cosineAlpha = Math.sqrt(cosineSquaredAlpha);
|
|
|
|
var u2Over4 = uSquared / 4.0;
|
|
var u4Over16 = u2Over4 * u2Over4;
|
|
var u6Over64 = u4Over16 * u2Over4;
|
|
var u8Over256 = u4Over16 * u4Over16;
|
|
|
|
var a0 = (1.0 + u2Over4 - 3.0 * u4Over16 / 4.0 + 5.0 * u6Over64 / 4.0 - 175.0 * u8Over256 / 64.0);
|
|
var a1 = (1.0 - u2Over4 + 15.0 * u4Over16 / 8.0 - 35.0 * u6Over64 / 8.0);
|
|
var a2 = (1.0 - 3.0 * u2Over4 + 35.0 * u4Over16 / 4.0);
|
|
var a3 = (1.0 - 5.0 * u2Over4);
|
|
|
|
var distanceRatio = a0 * sigma - a1 * Math.sin(2.0 * sigma) * u2Over4 / 2.0 - a2 * Math.sin(4.0 * sigma) * u4Over16 / 16.0 -
|
|
a3 * Math.sin(6.0 * sigma) * u6Over64 / 48.0 - Math.sin(8.0 * sigma) * 5.0 * u8Over256 / 512;
|
|
|
|
var constants = ellipsoidGeodesic._constants;
|
|
|
|
constants.a = a;
|
|
constants.b = b;
|
|
constants.f = f;
|
|
constants.cosineHeading = cosineHeading;
|
|
constants.sineHeading = sineHeading;
|
|
constants.tanU = tanU;
|
|
constants.cosineU = cosineU;
|
|
constants.sineU = sineU;
|
|
constants.sigma = sigma;
|
|
constants.sineAlpha = sineAlpha;
|
|
constants.sineSquaredAlpha = sineSquaredAlpha;
|
|
constants.cosineSquaredAlpha = cosineSquaredAlpha;
|
|
constants.cosineAlpha = cosineAlpha;
|
|
constants.u2Over4 = u2Over4;
|
|
constants.u4Over16 = u4Over16;
|
|
constants.u6Over64 = u6Over64;
|
|
constants.u8Over256 = u8Over256;
|
|
constants.a0 = a0;
|
|
constants.a1 = a1;
|
|
constants.a2 = a2;
|
|
constants.a3 = a3;
|
|
constants.distanceRatio = distanceRatio;
|
|
}
|
|
|
|
function computeC(f, cosineSquaredAlpha) {
|
|
return f * cosineSquaredAlpha * (4.0 + f * (4.0 - 3.0 * cosineSquaredAlpha)) / 16.0;
|
|
}
|
|
|
|
function computeDeltaLambda(f, sineAlpha, cosineSquaredAlpha, sigma, sineSigma, cosineSigma, cosineTwiceSigmaMidpoint) {
|
|
var C = computeC(f, cosineSquaredAlpha);
|
|
|
|
return (1.0 - C) * f * sineAlpha * (sigma + C * sineSigma * (cosineTwiceSigmaMidpoint +
|
|
C * cosineSigma * (2.0 * cosineTwiceSigmaMidpoint * cosineTwiceSigmaMidpoint - 1.0)));
|
|
}
|
|
|
|
function vincentyInverseFormula(ellipsoidGeodesic, major, minor, firstLongitude, firstLatitude, secondLongitude, secondLatitude) {
|
|
var eff = (major - minor) / major;
|
|
var l = secondLongitude - firstLongitude;
|
|
|
|
var u1 = Math.atan((1 - eff) * Math.tan(firstLatitude));
|
|
var u2 = Math.atan((1 - eff) * Math.tan(secondLatitude));
|
|
|
|
var cosineU1 = Math.cos(u1);
|
|
var sineU1 = Math.sin(u1);
|
|
var cosineU2 = Math.cos(u2);
|
|
var sineU2 = Math.sin(u2);
|
|
|
|
var cc = cosineU1 * cosineU2;
|
|
var cs = cosineU1 * sineU2;
|
|
var ss = sineU1 * sineU2;
|
|
var sc = sineU1 * cosineU2;
|
|
|
|
var lambda = l;
|
|
var lambdaDot = _Math.CesiumMath.TWO_PI;
|
|
|
|
var cosineLambda = Math.cos(lambda);
|
|
var sineLambda = Math.sin(lambda);
|
|
|
|
var sigma;
|
|
var cosineSigma;
|
|
var sineSigma;
|
|
var cosineSquaredAlpha;
|
|
var cosineTwiceSigmaMidpoint;
|
|
|
|
do {
|
|
cosineLambda = Math.cos(lambda);
|
|
sineLambda = Math.sin(lambda);
|
|
|
|
var temp = cs - sc * cosineLambda;
|
|
sineSigma = Math.sqrt(cosineU2 * cosineU2 * sineLambda * sineLambda + temp * temp);
|
|
cosineSigma = ss + cc * cosineLambda;
|
|
|
|
sigma = Math.atan2(sineSigma, cosineSigma);
|
|
|
|
var sineAlpha;
|
|
|
|
if (sineSigma === 0.0) {
|
|
sineAlpha = 0.0;
|
|
cosineSquaredAlpha = 1.0;
|
|
} else {
|
|
sineAlpha = cc * sineLambda / sineSigma;
|
|
cosineSquaredAlpha = 1.0 - sineAlpha * sineAlpha;
|
|
}
|
|
|
|
lambdaDot = lambda;
|
|
|
|
cosineTwiceSigmaMidpoint = cosineSigma - 2.0 * ss / cosineSquaredAlpha;
|
|
|
|
if (isNaN(cosineTwiceSigmaMidpoint)) {
|
|
cosineTwiceSigmaMidpoint = 0.0;
|
|
}
|
|
|
|
lambda = l + computeDeltaLambda(eff, sineAlpha, cosineSquaredAlpha,
|
|
sigma, sineSigma, cosineSigma, cosineTwiceSigmaMidpoint);
|
|
} while (Math.abs(lambda - lambdaDot) > _Math.CesiumMath.EPSILON12);
|
|
|
|
var uSquared = cosineSquaredAlpha * (major * major - minor * minor) / (minor * minor);
|
|
var A = 1.0 + uSquared * (4096.0 + uSquared * (uSquared * (320.0 - 175.0 * uSquared) - 768.0)) / 16384.0;
|
|
var B = uSquared * (256.0 + uSquared * (uSquared * (74.0 - 47.0 * uSquared) - 128.0)) / 1024.0;
|
|
|
|
var cosineSquaredTwiceSigmaMidpoint = cosineTwiceSigmaMidpoint * cosineTwiceSigmaMidpoint;
|
|
var deltaSigma = B * sineSigma * (cosineTwiceSigmaMidpoint + B * (cosineSigma *
|
|
(2.0 * cosineSquaredTwiceSigmaMidpoint - 1.0) - B * cosineTwiceSigmaMidpoint *
|
|
(4.0 * sineSigma * sineSigma - 3.0) * (4.0 * cosineSquaredTwiceSigmaMidpoint - 3.0) / 6.0) / 4.0);
|
|
|
|
var distance = minor * A * (sigma - deltaSigma);
|
|
|
|
var startHeading = Math.atan2(cosineU2 * sineLambda, cs - sc * cosineLambda);
|
|
var endHeading = Math.atan2(cosineU1 * sineLambda, cs * cosineLambda - sc);
|
|
|
|
ellipsoidGeodesic._distance = distance;
|
|
ellipsoidGeodesic._startHeading = startHeading;
|
|
ellipsoidGeodesic._endHeading = endHeading;
|
|
ellipsoidGeodesic._uSquared = uSquared;
|
|
}
|
|
|
|
var scratchCart1 = new Cartographic.Cartesian3();
|
|
var scratchCart2 = new Cartographic.Cartesian3();
|
|
function computeProperties(ellipsoidGeodesic, start, end, ellipsoid) {
|
|
var firstCartesian = Cartographic.Cartesian3.normalize(ellipsoid.cartographicToCartesian(start, scratchCart2), scratchCart1);
|
|
var lastCartesian = Cartographic.Cartesian3.normalize(ellipsoid.cartographicToCartesian(end, scratchCart2), scratchCart2);
|
|
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.typeOf.number.greaterThanOrEquals('value', Math.abs(Math.abs(Cartographic.Cartesian3.angleBetween(firstCartesian, lastCartesian)) - Math.PI), 0.0125);
|
|
//>>includeEnd('debug');
|
|
|
|
vincentyInverseFormula(ellipsoidGeodesic, ellipsoid.maximumRadius, ellipsoid.minimumRadius,
|
|
start.longitude, start.latitude, end.longitude, end.latitude);
|
|
|
|
ellipsoidGeodesic._start = Cartographic.Cartographic.clone(start, ellipsoidGeodesic._start);
|
|
ellipsoidGeodesic._end = Cartographic.Cartographic.clone(end, ellipsoidGeodesic._end);
|
|
ellipsoidGeodesic._start.height = 0;
|
|
ellipsoidGeodesic._end.height = 0;
|
|
|
|
setConstants(ellipsoidGeodesic);
|
|
}
|
|
|
|
/**
|
|
* Initializes a geodesic on the ellipsoid connecting the two provided planetodetic points.
|
|
*
|
|
* @alias EllipsoidGeodesic
|
|
* @constructor
|
|
*
|
|
* @param {Cartographic} [start] The initial planetodetic point on the path.
|
|
* @param {Cartographic} [end] The final planetodetic point on the path.
|
|
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the geodesic lies.
|
|
*/
|
|
function EllipsoidGeodesic(start, end, ellipsoid) {
|
|
var e = when.defaultValue(ellipsoid, Cartesian2.Ellipsoid.WGS84);
|
|
this._ellipsoid = e;
|
|
this._start = new Cartographic.Cartographic();
|
|
this._end = new Cartographic.Cartographic();
|
|
|
|
this._constants = {};
|
|
this._startHeading = undefined;
|
|
this._endHeading = undefined;
|
|
this._distance = undefined;
|
|
this._uSquared = undefined;
|
|
|
|
if (when.defined(start) && when.defined(end)) {
|
|
computeProperties(this, start, end, e);
|
|
}
|
|
}
|
|
|
|
Object.defineProperties(EllipsoidGeodesic.prototype, {
|
|
/**
|
|
* Gets the ellipsoid.
|
|
* @memberof EllipsoidGeodesic.prototype
|
|
* @type {Ellipsoid}
|
|
* @readonly
|
|
*/
|
|
ellipsoid : {
|
|
get : function() {
|
|
return this._ellipsoid;
|
|
}
|
|
},
|
|
|
|
/**
|
|
* Gets the surface distance between the start and end point
|
|
* @memberof EllipsoidGeodesic.prototype
|
|
* @type {Number}
|
|
* @readonly
|
|
*/
|
|
surfaceDistance : {
|
|
get : function() {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined('distance', this._distance);
|
|
//>>includeEnd('debug');
|
|
|
|
return this._distance;
|
|
}
|
|
},
|
|
|
|
/**
|
|
* Gets the initial planetodetic point on the path.
|
|
* @memberof EllipsoidGeodesic.prototype
|
|
* @type {Cartographic}
|
|
* @readonly
|
|
*/
|
|
start : {
|
|
get : function() {
|
|
return this._start;
|
|
}
|
|
},
|
|
|
|
/**
|
|
* Gets the final planetodetic point on the path.
|
|
* @memberof EllipsoidGeodesic.prototype
|
|
* @type {Cartographic}
|
|
* @readonly
|
|
*/
|
|
end : {
|
|
get : function() {
|
|
return this._end;
|
|
}
|
|
},
|
|
|
|
/**
|
|
* Gets the heading at the initial point.
|
|
* @memberof EllipsoidGeodesic.prototype
|
|
* @type {Number}
|
|
* @readonly
|
|
*/
|
|
startHeading : {
|
|
get : function() {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined('distance', this._distance);
|
|
//>>includeEnd('debug');
|
|
|
|
return this._startHeading;
|
|
}
|
|
},
|
|
|
|
/**
|
|
* Gets the heading at the final point.
|
|
* @memberof EllipsoidGeodesic.prototype
|
|
* @type {Number}
|
|
* @readonly
|
|
*/
|
|
endHeading : {
|
|
get : function() {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined('distance', this._distance);
|
|
//>>includeEnd('debug');
|
|
|
|
return this._endHeading;
|
|
}
|
|
}
|
|
});
|
|
|
|
/**
|
|
* Sets the start and end points of the geodesic
|
|
*
|
|
* @param {Cartographic} start The initial planetodetic point on the path.
|
|
* @param {Cartographic} end The final planetodetic point on the path.
|
|
*/
|
|
EllipsoidGeodesic.prototype.setEndPoints = function(start, end) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined('start', start);
|
|
Check.Check.defined('end', end);
|
|
//>>includeEnd('debug');
|
|
|
|
computeProperties(this, start, end, this._ellipsoid);
|
|
};
|
|
|
|
/**
|
|
* Provides the location of a point at the indicated portion along the geodesic.
|
|
*
|
|
* @param {Number} fraction The portion of the distance between the initial and final points.
|
|
* @param {Cartographic} result The object in which to store the result.
|
|
* @returns {Cartographic} The location of the point along the geodesic.
|
|
*/
|
|
EllipsoidGeodesic.prototype.interpolateUsingFraction = function(fraction, result) {
|
|
return this.interpolateUsingSurfaceDistance(this._distance * fraction, result);
|
|
};
|
|
|
|
/**
|
|
* Provides the location of a point at the indicated distance along the geodesic.
|
|
*
|
|
* @param {Number} distance The distance from the inital point to the point of interest along the geodesic
|
|
* @param {Cartographic} result The object in which to store the result.
|
|
* @returns {Cartographic} The location of the point along the geodesic.
|
|
*
|
|
* @exception {DeveloperError} start and end must be set before calling function interpolateUsingSurfaceDistance
|
|
*/
|
|
EllipsoidGeodesic.prototype.interpolateUsingSurfaceDistance = function(distance, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.Check.defined('distance', this._distance);
|
|
//>>includeEnd('debug');
|
|
|
|
var constants = this._constants;
|
|
|
|
var s = constants.distanceRatio + distance / constants.b;
|
|
|
|
var cosine2S = Math.cos(2.0 * s);
|
|
var cosine4S = Math.cos(4.0 * s);
|
|
var cosine6S = Math.cos(6.0 * s);
|
|
var sine2S = Math.sin(2.0 * s);
|
|
var sine4S = Math.sin(4.0 * s);
|
|
var sine6S = Math.sin(6.0 * s);
|
|
var sine8S = Math.sin(8.0 * s);
|
|
|
|
var s2 = s * s;
|
|
var s3 = s * s2;
|
|
|
|
var u8Over256 = constants.u8Over256;
|
|
var u2Over4 = constants.u2Over4;
|
|
var u6Over64 = constants.u6Over64;
|
|
var u4Over16 = constants.u4Over16;
|
|
var sigma = 2.0 * s3 * u8Over256 * cosine2S / 3.0 +
|
|
s * (1.0 - u2Over4 + 7.0 * u4Over16 / 4.0 - 15.0 * u6Over64 / 4.0 + 579.0 * u8Over256 / 64.0 -
|
|
(u4Over16 - 15.0 * u6Over64 / 4.0 + 187.0 * u8Over256 / 16.0) * cosine2S -
|
|
(5.0 * u6Over64 / 4.0 - 115.0 * u8Over256 / 16.0) * cosine4S -
|
|
29.0 * u8Over256 * cosine6S / 16.0) +
|
|
(u2Over4 / 2.0 - u4Over16 + 71.0 * u6Over64 / 32.0 - 85.0 * u8Over256 / 16.0) * sine2S +
|
|
(5.0 * u4Over16 / 16.0 - 5.0 * u6Over64 / 4.0 + 383.0 * u8Over256 / 96.0) * sine4S -
|
|
s2 * ((u6Over64 - 11.0 * u8Over256 / 2.0) * sine2S + 5.0 * u8Over256 * sine4S / 2.0) +
|
|
(29.0 * u6Over64 / 96.0 - 29.0 * u8Over256 / 16.0) * sine6S +
|
|
539.0 * u8Over256 * sine8S / 1536.0;
|
|
|
|
var theta = Math.asin(Math.sin(sigma) * constants.cosineAlpha);
|
|
var latitude = Math.atan(constants.a / constants.b * Math.tan(theta));
|
|
|
|
// Redefine in terms of relative argument of latitude.
|
|
sigma = sigma - constants.sigma;
|
|
|
|
var cosineTwiceSigmaMidpoint = Math.cos(2.0 * constants.sigma + sigma);
|
|
|
|
var sineSigma = Math.sin(sigma);
|
|
var cosineSigma = Math.cos(sigma);
|
|
|
|
var cc = constants.cosineU * cosineSigma;
|
|
var ss = constants.sineU * sineSigma;
|
|
|
|
var lambda = Math.atan2(sineSigma * constants.sineHeading, cc - ss * constants.cosineHeading);
|
|
|
|
var l = lambda - computeDeltaLambda(constants.f, constants.sineAlpha, constants.cosineSquaredAlpha,
|
|
sigma, sineSigma, cosineSigma, cosineTwiceSigmaMidpoint);
|
|
|
|
if (when.defined(result)) {
|
|
result.longitude = this._start.longitude + l;
|
|
result.latitude = latitude;
|
|
result.height = 0.0;
|
|
return result;
|
|
}
|
|
|
|
return new Cartographic.Cartographic(this._start.longitude + l, latitude, 0.0);
|
|
};
|
|
|
|
exports.EllipsoidGeodesic = EllipsoidGeodesic;
|
|
|
|
});
|