/* This file is automatically rebuilt by the Cesium build process. */
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define(['exports', './Matrix2-0e286ffc', './RuntimeError-4fdc4459', './when-8166c7dd', './ComponentDatatype-9ed50558'], (function (exports, Matrix2, RuntimeError, when, ComponentDatatype) { 'use strict';
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function setConstants(ellipsoidGeodesic) {
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var uSquared = ellipsoidGeodesic._uSquared;
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var a = ellipsoidGeodesic._ellipsoid.maximumRadius;
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var b = ellipsoidGeodesic._ellipsoid.minimumRadius;
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var f = (a - b) / a;
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var cosineHeading = Math.cos(ellipsoidGeodesic._startHeading);
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var sineHeading = Math.sin(ellipsoidGeodesic._startHeading);
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var tanU = (1 - f) * Math.tan(ellipsoidGeodesic._start.latitude);
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var cosineU = 1.0 / Math.sqrt(1.0 + tanU * tanU);
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var sineU = cosineU * tanU;
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var sigma = Math.atan2(tanU, cosineHeading);
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var sineAlpha = cosineU * sineHeading;
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var sineSquaredAlpha = sineAlpha * sineAlpha;
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var cosineSquaredAlpha = 1.0 - sineSquaredAlpha;
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var cosineAlpha = Math.sqrt(cosineSquaredAlpha);
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var u2Over4 = uSquared / 4.0;
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var u4Over16 = u2Over4 * u2Over4;
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var u6Over64 = u4Over16 * u2Over4;
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var u8Over256 = u4Over16 * u4Over16;
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var a0 =
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1.0 +
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u2Over4 -
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(3.0 * u4Over16) / 4.0 +
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(5.0 * u6Over64) / 4.0 -
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(175.0 * u8Over256) / 64.0;
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var a1 = 1.0 - u2Over4 + (15.0 * u4Over16) / 8.0 - (35.0 * u6Over64) / 8.0;
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var a2 = 1.0 - 3.0 * u2Over4 + (35.0 * u4Over16) / 4.0;
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var a3 = 1.0 - 5.0 * u2Over4;
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var distanceRatio =
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a0 * sigma -
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(a1 * Math.sin(2.0 * sigma) * u2Over4) / 2.0 -
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(a2 * Math.sin(4.0 * sigma) * u4Over16) / 16.0 -
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(a3 * Math.sin(6.0 * sigma) * u6Over64) / 48.0 -
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(Math.sin(8.0 * sigma) * 5.0 * u8Over256) / 512;
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var constants = ellipsoidGeodesic._constants;
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constants.a = a;
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constants.b = b;
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constants.f = f;
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constants.cosineHeading = cosineHeading;
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constants.sineHeading = sineHeading;
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constants.tanU = tanU;
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constants.cosineU = cosineU;
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constants.sineU = sineU;
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constants.sigma = sigma;
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constants.sineAlpha = sineAlpha;
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constants.sineSquaredAlpha = sineSquaredAlpha;
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constants.cosineSquaredAlpha = cosineSquaredAlpha;
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constants.cosineAlpha = cosineAlpha;
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constants.u2Over4 = u2Over4;
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constants.u4Over16 = u4Over16;
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constants.u6Over64 = u6Over64;
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constants.u8Over256 = u8Over256;
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constants.a0 = a0;
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constants.a1 = a1;
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constants.a2 = a2;
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constants.a3 = a3;
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constants.distanceRatio = distanceRatio;
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}
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function computeC(f, cosineSquaredAlpha) {
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return (
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(f * cosineSquaredAlpha * (4.0 + f * (4.0 - 3.0 * cosineSquaredAlpha))) /
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16.0
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);
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}
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function computeDeltaLambda(
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f,
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sineAlpha,
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cosineSquaredAlpha,
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sigma,
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sineSigma,
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cosineSigma,
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cosineTwiceSigmaMidpoint
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) {
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var C = computeC(f, cosineSquaredAlpha);
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return (
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(1.0 - C) *
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f *
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sineAlpha *
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(sigma +
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C *
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sineSigma *
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(cosineTwiceSigmaMidpoint +
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C *
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cosineSigma *
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(2.0 * cosineTwiceSigmaMidpoint * cosineTwiceSigmaMidpoint - 1.0)))
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);
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}
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function vincentyInverseFormula(
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ellipsoidGeodesic,
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major,
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minor,
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firstLongitude,
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firstLatitude,
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secondLongitude,
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secondLatitude
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) {
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var eff = (major - minor) / major;
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var l = secondLongitude - firstLongitude;
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var u1 = Math.atan((1 - eff) * Math.tan(firstLatitude));
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var u2 = Math.atan((1 - eff) * Math.tan(secondLatitude));
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var cosineU1 = Math.cos(u1);
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var sineU1 = Math.sin(u1);
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var cosineU2 = Math.cos(u2);
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var sineU2 = Math.sin(u2);
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var cc = cosineU1 * cosineU2;
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var cs = cosineU1 * sineU2;
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var ss = sineU1 * sineU2;
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var sc = sineU1 * cosineU2;
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var lambda = l;
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var lambdaDot = ComponentDatatype.CesiumMath.TWO_PI;
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var cosineLambda = Math.cos(lambda);
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var sineLambda = Math.sin(lambda);
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var sigma;
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var cosineSigma;
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var sineSigma;
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var cosineSquaredAlpha;
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var cosineTwiceSigmaMidpoint;
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do {
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cosineLambda = Math.cos(lambda);
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sineLambda = Math.sin(lambda);
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var temp = cs - sc * cosineLambda;
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sineSigma = Math.sqrt(
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cosineU2 * cosineU2 * sineLambda * sineLambda + temp * temp
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);
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cosineSigma = ss + cc * cosineLambda;
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sigma = Math.atan2(sineSigma, cosineSigma);
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var sineAlpha;
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if (sineSigma === 0.0) {
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sineAlpha = 0.0;
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cosineSquaredAlpha = 1.0;
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} else {
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sineAlpha = (cc * sineLambda) / sineSigma;
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cosineSquaredAlpha = 1.0 - sineAlpha * sineAlpha;
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}
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lambdaDot = lambda;
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cosineTwiceSigmaMidpoint = cosineSigma - (2.0 * ss) / cosineSquaredAlpha;
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if (!isFinite(cosineTwiceSigmaMidpoint)) {
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cosineTwiceSigmaMidpoint = 0.0;
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}
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lambda =
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l +
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computeDeltaLambda(
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eff,
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sineAlpha,
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cosineSquaredAlpha,
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sigma,
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sineSigma,
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cosineSigma,
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cosineTwiceSigmaMidpoint
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);
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} while (Math.abs(lambda - lambdaDot) > ComponentDatatype.CesiumMath.EPSILON12);
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var uSquared =
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(cosineSquaredAlpha * (major * major - minor * minor)) / (minor * minor);
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var A =
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1.0 +
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(uSquared *
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(4096.0 + uSquared * (uSquared * (320.0 - 175.0 * uSquared) - 768.0))) /
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16384.0;
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var B =
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(uSquared *
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(256.0 + uSquared * (uSquared * (74.0 - 47.0 * uSquared) - 128.0))) /
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1024.0;
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var cosineSquaredTwiceSigmaMidpoint =
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cosineTwiceSigmaMidpoint * cosineTwiceSigmaMidpoint;
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var deltaSigma =
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B *
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sineSigma *
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(cosineTwiceSigmaMidpoint +
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(B *
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(cosineSigma * (2.0 * cosineSquaredTwiceSigmaMidpoint - 1.0) -
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(B *
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cosineTwiceSigmaMidpoint *
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(4.0 * sineSigma * sineSigma - 3.0) *
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(4.0 * cosineSquaredTwiceSigmaMidpoint - 3.0)) /
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6.0)) /
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4.0);
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var distance = minor * A * (sigma - deltaSigma);
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var startHeading = Math.atan2(cosineU2 * sineLambda, cs - sc * cosineLambda);
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var endHeading = Math.atan2(cosineU1 * sineLambda, cs * cosineLambda - sc);
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ellipsoidGeodesic._distance = distance;
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ellipsoidGeodesic._startHeading = startHeading;
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ellipsoidGeodesic._endHeading = endHeading;
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ellipsoidGeodesic._uSquared = uSquared;
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}
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var scratchCart1 = new Matrix2.Cartesian3();
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var scratchCart2 = new Matrix2.Cartesian3();
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function computeProperties(ellipsoidGeodesic, start, end, ellipsoid) {
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var firstCartesian = Matrix2.Cartesian3.normalize(
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ellipsoid.cartographicToCartesian(start, scratchCart2),
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scratchCart1
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);
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var lastCartesian = Matrix2.Cartesian3.normalize(
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ellipsoid.cartographicToCartesian(end, scratchCart2),
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scratchCart2
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);
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//>>includeStart('debug', pragmas.debug);
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RuntimeError.Check.typeOf.number.greaterThanOrEquals(
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"value",
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Math.abs(
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Math.abs(Matrix2.Cartesian3.angleBetween(firstCartesian, lastCartesian)) - Math.PI
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),
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0.0125
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);
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//>>includeEnd('debug');
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vincentyInverseFormula(
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ellipsoidGeodesic,
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ellipsoid.maximumRadius,
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ellipsoid.minimumRadius,
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start.longitude,
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start.latitude,
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end.longitude,
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end.latitude
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);
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ellipsoidGeodesic._start = Matrix2.Cartographic.clone(
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start,
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ellipsoidGeodesic._start
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);
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ellipsoidGeodesic._end = Matrix2.Cartographic.clone(end, ellipsoidGeodesic._end);
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ellipsoidGeodesic._start.height = 0;
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ellipsoidGeodesic._end.height = 0;
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setConstants(ellipsoidGeodesic);
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}
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/**
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* Initializes a geodesic on the ellipsoid connecting the two provided planetodetic points.
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*
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* @alias EllipsoidGeodesic
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* @constructor
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*
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* @param {Cartographic} [start] The initial planetodetic point on the path.
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* @param {Cartographic} [end] The final planetodetic point on the path.
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* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the geodesic lies.
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*/
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function EllipsoidGeodesic(start, end, ellipsoid) {
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var e = when.defaultValue(ellipsoid, Matrix2.Ellipsoid.WGS84);
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this._ellipsoid = e;
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this._start = new Matrix2.Cartographic();
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this._end = new Matrix2.Cartographic();
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this._constants = {};
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this._startHeading = undefined;
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this._endHeading = undefined;
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this._distance = undefined;
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this._uSquared = undefined;
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if (when.defined(start) && when.defined(end)) {
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computeProperties(this, start, end, e);
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}
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}
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Object.defineProperties(EllipsoidGeodesic.prototype, {
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/**
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* Gets the ellipsoid.
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* @memberof EllipsoidGeodesic.prototype
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* @type {Ellipsoid}
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* @readonly
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*/
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ellipsoid: {
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get: function () {
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return this._ellipsoid;
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},
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},
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/**
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* Gets the surface distance between the start and end point
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* @memberof EllipsoidGeodesic.prototype
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* @type {Number}
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* @readonly
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*/
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surfaceDistance: {
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get: function () {
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//>>includeStart('debug', pragmas.debug);
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RuntimeError.Check.defined("distance", this._distance);
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//>>includeEnd('debug');
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return this._distance;
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},
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},
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/**
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* Gets the initial planetodetic point on the path.
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* @memberof EllipsoidGeodesic.prototype
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* @type {Cartographic}
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* @readonly
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*/
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start: {
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get: function () {
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return this._start;
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},
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},
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/**
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* Gets the final planetodetic point on the path.
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* @memberof EllipsoidGeodesic.prototype
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* @type {Cartographic}
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* @readonly
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*/
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end: {
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get: function () {
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return this._end;
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},
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},
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/**
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* Gets the heading at the initial point.
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* @memberof EllipsoidGeodesic.prototype
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* @type {Number}
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* @readonly
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*/
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startHeading: {
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get: function () {
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//>>includeStart('debug', pragmas.debug);
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RuntimeError.Check.defined("distance", this._distance);
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//>>includeEnd('debug');
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return this._startHeading;
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},
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},
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/**
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* Gets the heading at the final point.
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* @memberof EllipsoidGeodesic.prototype
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* @type {Number}
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* @readonly
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*/
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endHeading: {
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get: function () {
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//>>includeStart('debug', pragmas.debug);
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RuntimeError.Check.defined("distance", this._distance);
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//>>includeEnd('debug');
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return this._endHeading;
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},
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},
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});
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/**
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* Sets the start and end points of the geodesic
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*
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* @param {Cartographic} start The initial planetodetic point on the path.
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* @param {Cartographic} end The final planetodetic point on the path.
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*/
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EllipsoidGeodesic.prototype.setEndPoints = function (start, end) {
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//>>includeStart('debug', pragmas.debug);
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RuntimeError.Check.defined("start", start);
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RuntimeError.Check.defined("end", end);
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//>>includeEnd('debug');
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computeProperties(this, start, end, this._ellipsoid);
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};
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/**
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* Provides the location of a point at the indicated portion along the geodesic.
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*
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* @param {Number} fraction The portion of the distance between the initial and final points.
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* @param {Cartographic} [result] The object in which to store the result.
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* @returns {Cartographic} The location of the point along the geodesic.
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*/
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EllipsoidGeodesic.prototype.interpolateUsingFraction = function (
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fraction,
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result
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) {
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return this.interpolateUsingSurfaceDistance(
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this._distance * fraction,
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result
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);
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};
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/**
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* Provides the location of a point at the indicated distance along the geodesic.
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*
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* @param {Number} distance The distance from the inital point to the point of interest along the geodesic
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* @param {Cartographic} [result] The object in which to store the result.
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* @returns {Cartographic} The location of the point along the geodesic.
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*
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* @exception {DeveloperError} start and end must be set before calling function interpolateUsingSurfaceDistance
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*/
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EllipsoidGeodesic.prototype.interpolateUsingSurfaceDistance = function (
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distance,
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result
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) {
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//>>includeStart('debug', pragmas.debug);
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RuntimeError.Check.defined("distance", this._distance);
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//>>includeEnd('debug');
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var constants = this._constants;
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var s = constants.distanceRatio + distance / constants.b;
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var cosine2S = Math.cos(2.0 * s);
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var cosine4S = Math.cos(4.0 * s);
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var cosine6S = Math.cos(6.0 * s);
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var sine2S = Math.sin(2.0 * s);
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var sine4S = Math.sin(4.0 * s);
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var sine6S = Math.sin(6.0 * s);
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var sine8S = Math.sin(8.0 * s);
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var s2 = s * s;
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var s3 = s * s2;
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var u8Over256 = constants.u8Over256;
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var u2Over4 = constants.u2Over4;
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var u6Over64 = constants.u6Over64;
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var u4Over16 = constants.u4Over16;
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var sigma =
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(2.0 * s3 * u8Over256 * cosine2S) / 3.0 +
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s *
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(1.0 -
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u2Over4 +
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(7.0 * u4Over16) / 4.0 -
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(15.0 * u6Over64) / 4.0 +
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(579.0 * u8Over256) / 64.0 -
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(u4Over16 - (15.0 * u6Over64) / 4.0 + (187.0 * u8Over256) / 16.0) *
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cosine2S -
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((5.0 * u6Over64) / 4.0 - (115.0 * u8Over256) / 16.0) * cosine4S -
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(29.0 * u8Over256 * cosine6S) / 16.0) +
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(u2Over4 / 2.0 -
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u4Over16 +
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(71.0 * u6Over64) / 32.0 -
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(85.0 * u8Over256) / 16.0) *
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sine2S +
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((5.0 * u4Over16) / 16.0 -
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(5.0 * u6Over64) / 4.0 +
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(383.0 * u8Over256) / 96.0) *
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sine4S -
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s2 *
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((u6Over64 - (11.0 * u8Over256) / 2.0) * sine2S +
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(5.0 * u8Over256 * sine4S) / 2.0) +
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((29.0 * u6Over64) / 96.0 - (29.0 * u8Over256) / 16.0) * sine6S +
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(539.0 * u8Over256 * sine8S) / 1536.0;
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var theta = Math.asin(Math.sin(sigma) * constants.cosineAlpha);
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var latitude = Math.atan((constants.a / constants.b) * Math.tan(theta));
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// Redefine in terms of relative argument of latitude.
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sigma = sigma - constants.sigma;
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var cosineTwiceSigmaMidpoint = Math.cos(2.0 * constants.sigma + sigma);
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var sineSigma = Math.sin(sigma);
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var cosineSigma = Math.cos(sigma);
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var cc = constants.cosineU * cosineSigma;
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var ss = constants.sineU * sineSigma;
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var lambda = Math.atan2(
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sineSigma * constants.sineHeading,
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cc - ss * constants.cosineHeading
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);
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var l =
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lambda -
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computeDeltaLambda(
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constants.f,
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constants.sineAlpha,
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constants.cosineSquaredAlpha,
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sigma,
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sineSigma,
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cosineSigma,
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cosineTwiceSigmaMidpoint
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);
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if (when.defined(result)) {
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result.longitude = this._start.longitude + l;
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result.latitude = latitude;
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result.height = 0.0;
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return result;
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}
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return new Matrix2.Cartographic(this._start.longitude + l, latitude, 0.0);
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};
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exports.EllipsoidGeodesic = EllipsoidGeodesic;
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}));
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