/* This file is automatically rebuilt by the Cesium build process. */
define(['exports', './Cartesian2-ea36f114', './Check-c23b5bd5', './when-9f8cafad', './Math-cf2f57e0'], function (exports, Cartesian2, Check, when, _Math) { '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 (!isFinite(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 Cartesian2.Cartesian3();
var scratchCart2 = new Cartesian2.Cartesian3();
function computeProperties(ellipsoidGeodesic, start, end, ellipsoid) {
var firstCartesian = Cartesian2.Cartesian3.normalize(
ellipsoid.cartographicToCartesian(start, scratchCart2),
scratchCart1
);
var lastCartesian = Cartesian2.Cartesian3.normalize(
ellipsoid.cartographicToCartesian(end, scratchCart2),
scratchCart2
);
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number.greaterThanOrEquals(
"value",
Math.abs(
Math.abs(Cartesian2.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 = Cartesian2.Cartographic.clone(
start,
ellipsoidGeodesic._start
);
ellipsoidGeodesic._end = Cartesian2.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 Cartesian2.Cartographic();
this._end = new Cartesian2.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 Cartesian2.Cartographic(this._start.longitude + l, latitude, 0.0);
};
exports.EllipsoidGeodesic = EllipsoidGeodesic;
});
