import Cartesian3 from "./Cartesian3.js";
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import Cartographic from "./Cartographic.js";
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import Check from "./Check.js";
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import defaultValue from "./defaultValue.js";
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import defined from "./defined.js";
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import DeveloperError from "./DeveloperError.js";
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import CesiumMath from "./Math.js";
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import scaleToGeodeticSurface from "./scaleToGeodeticSurface.js";
|
|
function initialize(ellipsoid, x, y, z) {
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x = defaultValue(x, 0.0);
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y = defaultValue(y, 0.0);
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z = defaultValue(z, 0.0);
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|
//>>includeStart('debug', pragmas.debug);
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Check.typeOf.number.greaterThanOrEquals("x", x, 0.0);
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Check.typeOf.number.greaterThanOrEquals("y", y, 0.0);
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Check.typeOf.number.greaterThanOrEquals("z", z, 0.0);
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//>>includeEnd('debug');
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ellipsoid._radii = new Cartesian3(x, y, z);
|
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ellipsoid._radiiSquared = new Cartesian3(x * x, y * y, z * z);
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ellipsoid._radiiToTheFourth = new Cartesian3(
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x * x * x * x,
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y * y * y * y,
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z * z * z * z
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);
|
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ellipsoid._oneOverRadii = new Cartesian3(
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x === 0.0 ? 0.0 : 1.0 / x,
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y === 0.0 ? 0.0 : 1.0 / y,
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z === 0.0 ? 0.0 : 1.0 / z
|
);
|
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ellipsoid._oneOverRadiiSquared = new Cartesian3(
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x === 0.0 ? 0.0 : 1.0 / (x * x),
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y === 0.0 ? 0.0 : 1.0 / (y * y),
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z === 0.0 ? 0.0 : 1.0 / (z * z)
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);
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ellipsoid._minimumRadius = Math.min(x, y, z);
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ellipsoid._maximumRadius = Math.max(x, y, z);
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ellipsoid._centerToleranceSquared = CesiumMath.EPSILON1;
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if (ellipsoid._radiiSquared.z !== 0) {
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ellipsoid._squaredXOverSquaredZ =
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ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;
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}
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}
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/**
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* A quadratic surface defined in Cartesian coordinates by the equation
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* <code>(x / a)^2 + (y / b)^2 + (z / c)^2 = 1</code>. Primarily used
|
* by Cesium to represent the shape of planetary bodies.
|
*
|
* Rather than constructing this object directly, one of the provided
|
* constants is normally used.
|
* @alias Ellipsoid
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* @constructor
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*
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* @param {Number} [x=0] The radius in the x direction.
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* @param {Number} [y=0] The radius in the y direction.
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* @param {Number} [z=0] The radius in the z direction.
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*
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* @exception {DeveloperError} All radii components must be greater than or equal to zero.
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*
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* @see Ellipsoid.fromCartesian3
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* @see Ellipsoid.WGS84
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* @see Ellipsoid.UNIT_SPHERE
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*/
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function Ellipsoid(x, y, z) {
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this._radii = undefined;
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this._radiiSquared = undefined;
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this._radiiToTheFourth = undefined;
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this._oneOverRadii = undefined;
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this._oneOverRadiiSquared = undefined;
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this._minimumRadius = undefined;
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this._maximumRadius = undefined;
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this._centerToleranceSquared = undefined;
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this._squaredXOverSquaredZ = undefined;
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initialize(this, x, y, z);
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}
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Object.defineProperties(Ellipsoid.prototype, {
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/**
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* Gets the radii of the ellipsoid.
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* @memberof Ellipsoid.prototype
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* @type {Cartesian3}
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* @readonly
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*/
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radii: {
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get: function () {
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return this._radii;
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},
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},
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/**
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* Gets the squared radii of the ellipsoid.
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* @memberof Ellipsoid.prototype
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* @type {Cartesian3}
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* @readonly
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*/
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radiiSquared: {
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get: function () {
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return this._radiiSquared;
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},
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},
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/**
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* Gets the radii of the ellipsoid raise to the fourth power.
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* @memberof Ellipsoid.prototype
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* @type {Cartesian3}
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* @readonly
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*/
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radiiToTheFourth: {
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get: function () {
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return this._radiiToTheFourth;
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},
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},
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/**
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* Gets one over the radii of the ellipsoid.
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* @memberof Ellipsoid.prototype
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* @type {Cartesian3}
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* @readonly
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*/
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oneOverRadii: {
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get: function () {
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return this._oneOverRadii;
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},
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},
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/**
|
* Gets one over the squared radii of the ellipsoid.
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* @memberof Ellipsoid.prototype
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* @type {Cartesian3}
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* @readonly
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*/
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oneOverRadiiSquared: {
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get: function () {
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return this._oneOverRadiiSquared;
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},
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},
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/**
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* Gets the minimum radius of the ellipsoid.
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* @memberof Ellipsoid.prototype
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* @type {Number}
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* @readonly
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*/
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minimumRadius: {
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get: function () {
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return this._minimumRadius;
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},
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},
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/**
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* Gets the maximum radius of the ellipsoid.
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* @memberof Ellipsoid.prototype
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* @type {Number}
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* @readonly
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*/
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maximumRadius: {
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get: function () {
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return this._maximumRadius;
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},
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},
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});
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/**
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* Duplicates an Ellipsoid instance.
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*
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* @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.
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* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
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* instance should be created.
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* @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)
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*/
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Ellipsoid.clone = function (ellipsoid, result) {
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if (!defined(ellipsoid)) {
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return undefined;
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}
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var radii = ellipsoid._radii;
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if (!defined(result)) {
|
return new Ellipsoid(radii.x, radii.y, radii.z);
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}
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Cartesian3.clone(radii, result._radii);
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Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);
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Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);
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Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);
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Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);
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result._minimumRadius = ellipsoid._minimumRadius;
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result._maximumRadius = ellipsoid._maximumRadius;
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result._centerToleranceSquared = ellipsoid._centerToleranceSquared;
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return result;
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};
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/**
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* Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
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*
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* @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.
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* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
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* instance should be created.
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* @returns {Ellipsoid} A new Ellipsoid instance.
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*
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* @exception {DeveloperError} All radii components must be greater than or equal to zero.
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*
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* @see Ellipsoid.WGS84
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* @see Ellipsoid.UNIT_SPHERE
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*/
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Ellipsoid.fromCartesian3 = function (cartesian, result) {
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if (!defined(result)) {
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result = new Ellipsoid();
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}
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if (!defined(cartesian)) {
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return result;
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}
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initialize(result, cartesian.x, cartesian.y, cartesian.z);
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return result;
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};
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/**
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* An Ellipsoid instance initialized to the WGS84 standard.
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*
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* @type {Ellipsoid}
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* @constant
|
*/
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Ellipsoid.WGS84 = Object.freeze(
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new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793)
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);
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/**
|
* An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).
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*
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* @type {Ellipsoid}
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* @constant
|
*/
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Ellipsoid.UNIT_SPHERE = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0));
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/**
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* An Ellipsoid instance initialized to a sphere with the lunar radius.
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*
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* @type {Ellipsoid}
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* @constant
|
*/
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Ellipsoid.MOON = Object.freeze(
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new Ellipsoid(
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CesiumMath.LUNAR_RADIUS,
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CesiumMath.LUNAR_RADIUS,
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CesiumMath.LUNAR_RADIUS
|
)
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);
|
|
/**
|
* Duplicates an Ellipsoid instance.
|
*
|
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
|
* instance should be created.
|
* @returns {Ellipsoid} The cloned Ellipsoid.
|
*/
|
Ellipsoid.prototype.clone = function (result) {
|
return Ellipsoid.clone(this, result);
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};
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/**
|
* The number of elements used to pack the object into an array.
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* @type {Number}
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*/
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Ellipsoid.packedLength = Cartesian3.packedLength;
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/**
|
* Stores the provided instance into the provided array.
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*
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* @param {Ellipsoid} value The value to pack.
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* @param {Number[]} array The array to pack into.
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* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
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*
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* @returns {Number[]} The array that was packed into
|
*/
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Ellipsoid.pack = function (value, array, startingIndex) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.object("value", value);
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Check.defined("array", array);
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//>>includeEnd('debug');
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startingIndex = defaultValue(startingIndex, 0);
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Cartesian3.pack(value._radii, array, startingIndex);
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return array;
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};
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/**
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* Retrieves an instance from a packed array.
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*
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* @param {Number[]} array The packed array.
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* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
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* @param {Ellipsoid} [result] The object into which to store the result.
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* @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.
|
*/
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Ellipsoid.unpack = function (array, startingIndex, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.defined("array", array);
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//>>includeEnd('debug');
|
|
startingIndex = defaultValue(startingIndex, 0);
|
|
var radii = Cartesian3.unpack(array, startingIndex);
|
return Ellipsoid.fromCartesian3(radii, result);
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};
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/**
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* Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
|
* @function
|
*
|
* @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
*/
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Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;
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/**
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* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
|
*
|
* @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
*/
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Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function (
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cartographic,
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result
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) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.object("cartographic", cartographic);
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//>>includeEnd('debug');
|
|
var longitude = cartographic.longitude;
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var latitude = cartographic.latitude;
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var cosLatitude = Math.cos(latitude);
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var x = cosLatitude * Math.cos(longitude);
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var y = cosLatitude * Math.sin(longitude);
|
var z = Math.sin(latitude);
|
|
if (!defined(result)) {
|
result = new Cartesian3();
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}
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result.x = x;
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result.y = y;
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result.z = z;
|
return Cartesian3.normalize(result, result);
|
};
|
|
/**
|
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
|
*
|
* @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided, or undefined if a normal cannot be found.
|
*/
|
Ellipsoid.prototype.geodeticSurfaceNormal = function (cartesian, result) {
|
if (
|
Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, CesiumMath.EPSILON14)
|
) {
|
return undefined;
|
}
|
if (!defined(result)) {
|
result = new Cartesian3();
|
}
|
result = Cartesian3.multiplyComponents(
|
cartesian,
|
this._oneOverRadiiSquared,
|
result
|
);
|
return Cartesian3.normalize(result, result);
|
};
|
|
var cartographicToCartesianNormal = new Cartesian3();
|
var cartographicToCartesianK = new Cartesian3();
|
|
/**
|
* Converts the provided cartographic to Cartesian representation.
|
*
|
* @param {Cartographic} cartographic The cartographic position.
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
*
|
* @example
|
* //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
|
* var position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
|
* var cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
|
*/
|
Ellipsoid.prototype.cartographicToCartesian = function (cartographic, result) {
|
//`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.
|
var n = cartographicToCartesianNormal;
|
var k = cartographicToCartesianK;
|
this.geodeticSurfaceNormalCartographic(cartographic, n);
|
Cartesian3.multiplyComponents(this._radiiSquared, n, k);
|
var gamma = Math.sqrt(Cartesian3.dot(n, k));
|
Cartesian3.divideByScalar(k, gamma, k);
|
Cartesian3.multiplyByScalar(n, cartographic.height, n);
|
|
if (!defined(result)) {
|
result = new Cartesian3();
|
}
|
return Cartesian3.add(k, n, result);
|
};
|
|
/**
|
* Converts the provided array of cartographics to an array of Cartesians.
|
*
|
* @param {Cartographic[]} cartographics An array of cartographic positions.
|
* @param {Cartesian3[]} [result] The object onto which to store the result.
|
* @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.
|
*
|
* @example
|
* //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
|
* var positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
|
* new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
|
* new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
|
* var cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);
|
*/
|
Ellipsoid.prototype.cartographicArrayToCartesianArray = function (
|
cartographics,
|
result
|
) {
|
//>>includeStart('debug', pragmas.debug);
|
Check.defined("cartographics", cartographics);
|
//>>includeEnd('debug')
|
|
var length = cartographics.length;
|
if (!defined(result)) {
|
result = new Array(length);
|
} else {
|
result.length = length;
|
}
|
for (var i = 0; i < length; i++) {
|
result[i] = this.cartographicToCartesian(cartographics[i], result[i]);
|
}
|
return result;
|
};
|
|
var cartesianToCartographicN = new Cartesian3();
|
var cartesianToCartographicP = new Cartesian3();
|
var cartesianToCartographicH = new Cartesian3();
|
|
/**
|
* Converts the provided cartesian to cartographic representation.
|
* The cartesian is undefined at the center of the ellipsoid.
|
*
|
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
|
* @param {Cartographic} [result] The object onto which to store the result.
|
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
|
*
|
* @example
|
* //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
|
* var position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
|
* var cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);
|
*/
|
Ellipsoid.prototype.cartesianToCartographic = function (cartesian, result) {
|
//`cartesian is required.` is thrown from scaleToGeodeticSurface
|
var p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);
|
|
if (!defined(p)) {
|
return undefined;
|
}
|
|
var n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);
|
var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
|
|
var longitude = Math.atan2(n.y, n.x);
|
var latitude = Math.asin(n.z);
|
var height =
|
CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
|
|
if (!defined(result)) {
|
return new Cartographic(longitude, latitude, height);
|
}
|
result.longitude = longitude;
|
result.latitude = latitude;
|
result.height = height;
|
return result;
|
};
|
|
/**
|
* Converts the provided array of cartesians to an array of cartographics.
|
*
|
* @param {Cartesian3[]} cartesians An array of Cartesian positions.
|
* @param {Cartographic[]} [result] The object onto which to store the result.
|
* @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.
|
*
|
* @example
|
* //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
|
* var positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
|
* new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
|
* new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
|
* var cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);
|
*/
|
Ellipsoid.prototype.cartesianArrayToCartographicArray = function (
|
cartesians,
|
result
|
) {
|
//>>includeStart('debug', pragmas.debug);
|
Check.defined("cartesians", cartesians);
|
//>>includeEnd('debug');
|
|
var length = cartesians.length;
|
if (!defined(result)) {
|
result = new Array(length);
|
} else {
|
result.length = length;
|
}
|
for (var i = 0; i < length; ++i) {
|
result[i] = this.cartesianToCartographic(cartesians[i], result[i]);
|
}
|
return result;
|
};
|
|
/**
|
* Scales the provided Cartesian position along the geodetic surface normal
|
* so that it is on the surface of this ellipsoid. If the position is
|
* at the center of the ellipsoid, this function returns undefined.
|
*
|
* @param {Cartesian3} cartesian The Cartesian position to scale.
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
|
*/
|
Ellipsoid.prototype.scaleToGeodeticSurface = function (cartesian, result) {
|
return scaleToGeodeticSurface(
|
cartesian,
|
this._oneOverRadii,
|
this._oneOverRadiiSquared,
|
this._centerToleranceSquared,
|
result
|
);
|
};
|
|
/**
|
* Scales the provided Cartesian position along the geocentric surface normal
|
* so that it is on the surface of this ellipsoid.
|
*
|
* @param {Cartesian3} cartesian The Cartesian position to scale.
|
* @param {Cartesian3} [result] The object onto which to store the result.
|
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
|
*/
|
Ellipsoid.prototype.scaleToGeocentricSurface = function (cartesian, result) {
|
//>>includeStart('debug', pragmas.debug);
|
Check.typeOf.object("cartesian", cartesian);
|
//>>includeEnd('debug');
|
|
if (!defined(result)) {
|
result = new Cartesian3();
|
}
|
|
var positionX = cartesian.x;
|
var positionY = cartesian.y;
|
var positionZ = cartesian.z;
|
var oneOverRadiiSquared = this._oneOverRadiiSquared;
|
|
var beta =
|
1.0 /
|
Math.sqrt(
|
positionX * positionX * oneOverRadiiSquared.x +
|
positionY * positionY * oneOverRadiiSquared.y +
|
positionZ * positionZ * oneOverRadiiSquared.z
|
);
|
|
return Cartesian3.multiplyByScalar(cartesian, beta, result);
|
};
|
|
/**
|
* Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying
|
* its components by the result of {@link Ellipsoid#oneOverRadii}.
|
*
|
* @param {Cartesian3} position The position to transform.
|
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
|
* return a new instance.
|
* @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the
|
* one passed as the result parameter if it is not undefined, or a new instance of it is.
|
*/
|
Ellipsoid.prototype.transformPositionToScaledSpace = function (
|
position,
|
result
|
) {
|
if (!defined(result)) {
|
result = new Cartesian3();
|
}
|
|
return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);
|
};
|
|
/**
|
* Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying
|
* its components by the result of {@link Ellipsoid#radii}.
|
*
|
* @param {Cartesian3} position The position to transform.
|
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
|
* return a new instance.
|
* @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the
|
* one passed as the result parameter if it is not undefined, or a new instance of it is.
|
*/
|
Ellipsoid.prototype.transformPositionFromScaledSpace = function (
|
position,
|
result
|
) {
|
if (!defined(result)) {
|
result = new Cartesian3();
|
}
|
|
return Cartesian3.multiplyComponents(position, this._radii, result);
|
};
|
|
/**
|
* Compares this Ellipsoid against the provided Ellipsoid componentwise and returns
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
*
|
* @param {Ellipsoid} [right] The other Ellipsoid.
|
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
|
*/
|
Ellipsoid.prototype.equals = function (right) {
|
return (
|
this === right ||
|
(defined(right) && Cartesian3.equals(this._radii, right._radii))
|
);
|
};
|
|
/**
|
* Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
|
*
|
* @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.
|
*/
|
Ellipsoid.prototype.toString = function () {
|
return this._radii.toString();
|
};
|
|
/**
|
* Computes a point which is the intersection of the surface normal with the z-axis.
|
*
|
* @param {Cartesian3} position the position. must be on the surface of the ellipsoid.
|
* @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
|
* In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
|
* In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
|
* Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
|
* @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and
|
* return a new instance.
|
* @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise
|
*
|
* @exception {DeveloperError} position is required.
|
* @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
|
* @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.
|
*/
|
Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function (
|
position,
|
buffer,
|
result
|
) {
|
//>>includeStart('debug', pragmas.debug);
|
Check.typeOf.object("position", position);
|
|
if (
|
!CesiumMath.equalsEpsilon(
|
this._radii.x,
|
this._radii.y,
|
CesiumMath.EPSILON15
|
)
|
) {
|
throw new DeveloperError(
|
"Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)"
|
);
|
}
|
|
Check.typeOf.number.greaterThan("Ellipsoid.radii.z", this._radii.z, 0);
|
//>>includeEnd('debug');
|
|
buffer = defaultValue(buffer, 0.0);
|
|
var squaredXOverSquaredZ = this._squaredXOverSquaredZ;
|
|
if (!defined(result)) {
|
result = new Cartesian3();
|
}
|
|
result.x = 0.0;
|
result.y = 0.0;
|
result.z = position.z * (1 - squaredXOverSquaredZ);
|
|
if (Math.abs(result.z) >= this._radii.z - buffer) {
|
return undefined;
|
}
|
|
return result;
|
};
|
|
var abscissas = [
|
0.14887433898163,
|
0.43339539412925,
|
0.67940956829902,
|
0.86506336668898,
|
0.97390652851717,
|
0.0,
|
];
|
var weights = [
|
0.29552422471475,
|
0.26926671930999,
|
0.21908636251598,
|
0.14945134915058,
|
0.066671344308684,
|
0.0,
|
];
|
|
/**
|
* Compute the 10th order Gauss-Legendre Quadrature of the given definite integral.
|
*
|
* @param {Number} a The lower bound for the integration.
|
* @param {Number} b The upper bound for the integration.
|
* @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate.
|
* @returns {Number} The value of the integral of the given function over the given domain.
|
*
|
* @private
|
*/
|
function gaussLegendreQuadrature(a, b, func) {
|
//>>includeStart('debug', pragmas.debug);
|
Check.typeOf.number("a", a);
|
Check.typeOf.number("b", b);
|
Check.typeOf.func("func", func);
|
//>>includeEnd('debug');
|
|
// The range is half of the normal range since the five weights add to one (ten weights add to two).
|
// The values of the abscissas are multiplied by two to account for this.
|
var xMean = 0.5 * (b + a);
|
var xRange = 0.5 * (b - a);
|
|
var sum = 0.0;
|
for (var i = 0; i < 5; i++) {
|
var dx = xRange * abscissas[i];
|
sum += weights[i] * (func(xMean + dx) + func(xMean - dx));
|
}
|
|
// Scale the sum to the range of x.
|
sum *= xRange;
|
return sum;
|
}
|
|
/**
|
* A real valued scalar function.
|
* @callback Ellipsoid~RealValuedScalarFunction
|
*
|
* @param {Number} x The value used to evaluate the function.
|
* @returns {Number} The value of the function at x.
|
*
|
* @private
|
*/
|
|
/**
|
* Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using
|
* Gauss-Legendre 10th order quadrature.
|
*
|
* @param {Rectangle} rectangle The rectangle used for computing the surface area.
|
* @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid.
|
*/
|
Ellipsoid.prototype.surfaceArea = function (rectangle) {
|
//>>includeStart('debug', pragmas.debug);
|
Check.typeOf.object("rectangle", rectangle);
|
//>>includeEnd('debug');
|
var minLongitude = rectangle.west;
|
var maxLongitude = rectangle.east;
|
var minLatitude = rectangle.south;
|
var maxLatitude = rectangle.north;
|
|
while (maxLongitude < minLongitude) {
|
maxLongitude += CesiumMath.TWO_PI;
|
}
|
|
var radiiSquared = this._radiiSquared;
|
var a2 = radiiSquared.x;
|
var b2 = radiiSquared.y;
|
var c2 = radiiSquared.z;
|
var a2b2 = a2 * b2;
|
return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) {
|
// phi represents the angle measured from the north pole
|
// sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar
|
var sinPhi = Math.cos(lat);
|
var cosPhi = Math.sin(lat);
|
return (
|
Math.cos(lat) *
|
gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) {
|
var cosTheta = Math.cos(lon);
|
var sinTheta = Math.sin(lon);
|
return Math.sqrt(
|
a2b2 * cosPhi * cosPhi +
|
c2 *
|
(b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) *
|
sinPhi *
|
sinPhi
|
);
|
})
|
);
|
});
|
};
|
|
export default Ellipsoid;
|
