cesium/Source/Core/scaleToGeodeticSurface.js

CesiumJS is a JavaScript library for creating 3D globes and 2D maps in a web browser without a plugin.

import Cartesian3 from './Cartesian3.js';
import defined from './defined.js';
import DeveloperError from './DeveloperError.js';
import CesiumMath from './Math.js';

    var scaleToGeodeticSurfaceIntersection = new Cartesian3();
    var scaleToGeodeticSurfaceGradient = new Cartesian3();

    /**
     * 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} oneOverRadii One over radii of the ellipsoid.
     * @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.
     * @param {Number} centerToleranceSquared Tolerance for closeness to the center.
     * @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.
     *
     * @exports scaleToGeodeticSurface
     *
     * @private
     */
    function scaleToGeodeticSurface(cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        if (!defined(oneOverRadii)) {
            throw new DeveloperError('oneOverRadii is required.');
        }
        if (!defined(oneOverRadiiSquared)) {
            throw new DeveloperError('oneOverRadiiSquared is required.');
        }
        if (!defined(centerToleranceSquared)) {
            throw new DeveloperError('centerToleranceSquared is required.');
        }
        //>>includeEnd('debug');

        var positionX = cartesian.x;
        var positionY = cartesian.y;
        var positionZ = cartesian.z;

        var oneOverRadiiX = oneOverRadii.x;
        var oneOverRadiiY = oneOverRadii.y;
        var oneOverRadiiZ = oneOverRadii.z;

        var x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;
        var y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;
        var z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;

        // Compute the squared ellipsoid norm.
        var squaredNorm = x2 + y2 + z2;
        var ratio = Math.sqrt(1.0 / squaredNorm);

        // As an initial approximation, assume that the radial intersection is the projection point.
        var intersection = Cartesian3.multiplyByScalar(cartesian, ratio, scaleToGeodeticSurfaceIntersection);

        // If the position is near the center, the iteration will not converge.
        if (squaredNorm < centerToleranceSquared) {
            return !isFinite(ratio) ? undefined : Cartesian3.clone(intersection, result);
        }

        var oneOverRadiiSquaredX = oneOverRadiiSquared.x;
        var oneOverRadiiSquaredY = oneOverRadiiSquared.y;
        var oneOverRadiiSquaredZ = oneOverRadiiSquared.z;

        // Use the gradient at the intersection point in place of the true unit normal.
        // The difference in magnitude will be absorbed in the multiplier.
        var gradient = scaleToGeodeticSurfaceGradient;
        gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;
        gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;
        gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;

        // Compute the initial guess at the normal vector multiplier, lambda.
        var lambda = (1.0 - ratio) * Cartesian3.magnitude(cartesian) / (0.5 * Cartesian3.magnitude(gradient));
        var correction = 0.0;

        var func;
        var denominator;
        var xMultiplier;
        var yMultiplier;
        var zMultiplier;
        var xMultiplier2;
        var yMultiplier2;
        var zMultiplier2;
        var xMultiplier3;
        var yMultiplier3;
        var zMultiplier3;

        do {
            lambda -= correction;

            xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);
            yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);
            zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);

            xMultiplier2 = xMultiplier * xMultiplier;
            yMultiplier2 = yMultiplier * yMultiplier;
            zMultiplier2 = zMultiplier * zMultiplier;

            xMultiplier3 = xMultiplier2 * xMultiplier;
            yMultiplier3 = yMultiplier2 * yMultiplier;
            zMultiplier3 = zMultiplier2 * zMultiplier;

            func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;

            // "denominator" here refers to the use of this expression in the velocity and acceleration
            // computations in the sections to follow.
            denominator = x2 * xMultiplier3 * oneOverRadiiSquaredX + y2 * yMultiplier3 * oneOverRadiiSquaredY + z2 * zMultiplier3 * oneOverRadiiSquaredZ;

            var derivative = -2.0 * denominator;

            correction = func / derivative;
        } while (Math.abs(func) > CesiumMath.EPSILON12);

        if (!defined(result)) {
            return new Cartesian3(positionX * xMultiplier, positionY * yMultiplier, positionZ * zMultiplier);
        }
        result.x = positionX * xMultiplier;
        result.y = positionY * yMultiplier;
        result.z = positionZ * zMultiplier;
        return result;
    }
export default scaleToGeodeticSurface;