/**
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* Cesium - https://github.com/CesiumGS/cesium
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*
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* Copyright 2011-2020 Cesium Contributors
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* Columbus View (Pat. Pend.)
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*
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* Portions licensed separately.
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* See https://github.com/CesiumGS/cesium/blob/master/LICENSE.md for full licensing details.
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*/
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define(['exports', './Math-61ede240', './Cartographic-fe4be337', './BoundingSphere-775c5788', './Transforms-a1cf7267'], function (exports, _Math, Cartographic, BoundingSphere, Transforms) { 'use strict';
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var EllipseGeometryLibrary = {};
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var rotAxis = new Cartographic.Cartesian3();
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var tempVec = new Cartographic.Cartesian3();
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var unitQuat = new Transforms.Quaternion();
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var rotMtx = new BoundingSphere.Matrix3();
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function pointOnEllipsoid(theta, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, result) {
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var azimuth = theta + rotation;
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Cartographic.Cartesian3.multiplyByScalar(eastVec, Math.cos(azimuth), rotAxis);
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Cartographic.Cartesian3.multiplyByScalar(northVec, Math.sin(azimuth), tempVec);
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Cartographic.Cartesian3.add(rotAxis, tempVec, rotAxis);
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var cosThetaSquared = Math.cos(theta);
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cosThetaSquared = cosThetaSquared * cosThetaSquared;
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var sinThetaSquared = Math.sin(theta);
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sinThetaSquared = sinThetaSquared * sinThetaSquared;
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var radius = ab / Math.sqrt(bSqr * cosThetaSquared + aSqr * sinThetaSquared);
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var angle = radius / mag;
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// Create the quaternion to rotate the position vector to the boundary of the ellipse.
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Transforms.Quaternion.fromAxisAngle(rotAxis, angle, unitQuat);
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BoundingSphere.Matrix3.fromQuaternion(unitQuat, rotMtx);
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BoundingSphere.Matrix3.multiplyByVector(rotMtx, unitPos, result);
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Cartographic.Cartesian3.normalize(result, result);
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Cartographic.Cartesian3.multiplyByScalar(result, mag, result);
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return result;
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}
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var scratchCartesian1 = new Cartographic.Cartesian3();
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var scratchCartesian2 = new Cartographic.Cartesian3();
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var scratchCartesian3 = new Cartographic.Cartesian3();
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var scratchNormal = new Cartographic.Cartesian3();
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/**
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* Returns the positions raised to the given heights
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* @private
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*/
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EllipseGeometryLibrary.raisePositionsToHeight = function(positions, options, extrude) {
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var ellipsoid = options.ellipsoid;
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var height = options.height;
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var extrudedHeight = options.extrudedHeight;
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var size = (extrude) ? positions.length / 3 * 2 : positions.length / 3;
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var finalPositions = new Float64Array(size * 3);
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var length = positions.length;
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var bottomOffset = (extrude) ? length : 0;
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for (var i = 0; i < length; i += 3) {
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var i1 = i + 1;
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var i2 = i + 2;
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var position = Cartographic.Cartesian3.fromArray(positions, i, scratchCartesian1);
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ellipsoid.scaleToGeodeticSurface(position, position);
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var extrudedPosition = Cartographic.Cartesian3.clone(position, scratchCartesian2);
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var normal = ellipsoid.geodeticSurfaceNormal(position, scratchNormal);
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var scaledNormal = Cartographic.Cartesian3.multiplyByScalar(normal, height, scratchCartesian3);
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Cartographic.Cartesian3.add(position, scaledNormal, position);
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if (extrude) {
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Cartographic.Cartesian3.multiplyByScalar(normal, extrudedHeight, scaledNormal);
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Cartographic.Cartesian3.add(extrudedPosition, scaledNormal, extrudedPosition);
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finalPositions[i + bottomOffset] = extrudedPosition.x;
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finalPositions[i1 + bottomOffset] = extrudedPosition.y;
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finalPositions[i2 + bottomOffset] = extrudedPosition.z;
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}
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finalPositions[i] = position.x;
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finalPositions[i1] = position.y;
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finalPositions[i2] = position.z;
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}
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return finalPositions;
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};
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var unitPosScratch = new Cartographic.Cartesian3();
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var eastVecScratch = new Cartographic.Cartesian3();
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var northVecScratch = new Cartographic.Cartesian3();
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/**
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* Returns an array of positions that make up the ellipse.
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* @private
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*/
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EllipseGeometryLibrary.computeEllipsePositions = function(options, addFillPositions, addEdgePositions) {
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var semiMinorAxis = options.semiMinorAxis;
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var semiMajorAxis = options.semiMajorAxis;
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var rotation = options.rotation;
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var center = options.center;
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// Computing the arc-length of the ellipse is too expensive to be practical. Estimating it using the
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// arc length of the sphere is too inaccurate and creates sharp edges when either the semi-major or
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// semi-minor axis is much bigger than the other. Instead, scale the angle delta to make
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// the distance along the ellipse boundary more closely match the granularity.
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var granularity = options.granularity * 8.0;
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var aSqr = semiMinorAxis * semiMinorAxis;
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var bSqr = semiMajorAxis * semiMajorAxis;
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var ab = semiMajorAxis * semiMinorAxis;
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var mag = Cartographic.Cartesian3.magnitude(center);
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var unitPos = Cartographic.Cartesian3.normalize(center, unitPosScratch);
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var eastVec = Cartographic.Cartesian3.cross(Cartographic.Cartesian3.UNIT_Z, center, eastVecScratch);
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eastVec = Cartographic.Cartesian3.normalize(eastVec, eastVec);
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var northVec = Cartographic.Cartesian3.cross(unitPos, eastVec, northVecScratch);
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// The number of points in the first quadrant
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var numPts = 1 + Math.ceil(_Math.CesiumMath.PI_OVER_TWO / granularity);
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var deltaTheta = _Math.CesiumMath.PI_OVER_TWO / (numPts - 1);
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var theta = _Math.CesiumMath.PI_OVER_TWO - numPts * deltaTheta;
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if (theta < 0.0) {
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numPts -= Math.ceil(Math.abs(theta) / deltaTheta);
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}
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// If the number of points were three, the ellipse
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// would be tessellated like below:
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//
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// *---*
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// / | \ | \
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// *---*---*---*
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// / | \ | \ | \ | \
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// / .*---*---*---*. \
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// * ` | \ | \ | \ | `*
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// \`.*---*---*---*.`/
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// \ | \ | \ | \ | /
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// *---*---*---*
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// \ | \ | /
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// *---*
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// The first and last column have one position and fan to connect to the adjacent column.
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// Each other vertical column contains an even number of positions.
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var size = 2 * (numPts * (numPts + 2));
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var positions = (addFillPositions) ? new Array(size * 3) : undefined;
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var positionIndex = 0;
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var position = scratchCartesian1;
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var reflectedPosition = scratchCartesian2;
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var outerPositionsLength = (numPts * 4) * 3;
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var outerRightIndex = outerPositionsLength - 1;
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var outerLeftIndex = 0;
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var outerPositions = (addEdgePositions) ? new Array(outerPositionsLength) : undefined;
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var i;
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var j;
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var numInterior;
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var t;
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var interiorPosition;
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// Compute points in the 'eastern' half of the ellipse
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theta = _Math.CesiumMath.PI_OVER_TWO;
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position = pointOnEllipsoid(theta, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, position);
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if (addFillPositions) {
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positions[positionIndex++] = position.x;
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positions[positionIndex++] = position.y;
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positions[positionIndex++] = position.z;
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}
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if (addEdgePositions) {
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outerPositions[outerRightIndex--] = position.z;
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outerPositions[outerRightIndex--] = position.y;
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outerPositions[outerRightIndex--] = position.x;
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}
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theta = _Math.CesiumMath.PI_OVER_TWO - deltaTheta;
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for (i = 1; i < numPts + 1; ++i) {
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position = pointOnEllipsoid(theta, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, position);
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reflectedPosition = pointOnEllipsoid(Math.PI - theta, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, reflectedPosition);
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if (addFillPositions) {
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positions[positionIndex++] = position.x;
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positions[positionIndex++] = position.y;
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positions[positionIndex++] = position.z;
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numInterior = 2 * i + 2;
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for (j = 1; j < numInterior - 1; ++j) {
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t = j / (numInterior - 1);
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interiorPosition = Cartographic.Cartesian3.lerp(position, reflectedPosition, t, scratchCartesian3);
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positions[positionIndex++] = interiorPosition.x;
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positions[positionIndex++] = interiorPosition.y;
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positions[positionIndex++] = interiorPosition.z;
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}
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positions[positionIndex++] = reflectedPosition.x;
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positions[positionIndex++] = reflectedPosition.y;
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positions[positionIndex++] = reflectedPosition.z;
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}
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if (addEdgePositions) {
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outerPositions[outerRightIndex--] = position.z;
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outerPositions[outerRightIndex--] = position.y;
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outerPositions[outerRightIndex--] = position.x;
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outerPositions[outerLeftIndex++] = reflectedPosition.x;
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outerPositions[outerLeftIndex++] = reflectedPosition.y;
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outerPositions[outerLeftIndex++] = reflectedPosition.z;
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}
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theta = _Math.CesiumMath.PI_OVER_TWO - (i + 1) * deltaTheta;
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}
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// Compute points in the 'western' half of the ellipse
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for (i = numPts; i > 1; --i) {
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theta = _Math.CesiumMath.PI_OVER_TWO - (i - 1) * deltaTheta;
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position = pointOnEllipsoid(-theta, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, position);
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reflectedPosition = pointOnEllipsoid(theta + Math.PI, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, reflectedPosition);
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if (addFillPositions) {
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positions[positionIndex++] = position.x;
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positions[positionIndex++] = position.y;
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positions[positionIndex++] = position.z;
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numInterior = 2 * (i - 1) + 2;
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for (j = 1; j < numInterior - 1; ++j) {
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t = j / (numInterior - 1);
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interiorPosition = Cartographic.Cartesian3.lerp(position, reflectedPosition, t, scratchCartesian3);
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positions[positionIndex++] = interiorPosition.x;
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positions[positionIndex++] = interiorPosition.y;
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positions[positionIndex++] = interiorPosition.z;
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}
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positions[positionIndex++] = reflectedPosition.x;
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positions[positionIndex++] = reflectedPosition.y;
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positions[positionIndex++] = reflectedPosition.z;
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}
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if (addEdgePositions) {
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outerPositions[outerRightIndex--] = position.z;
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outerPositions[outerRightIndex--] = position.y;
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outerPositions[outerRightIndex--] = position.x;
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outerPositions[outerLeftIndex++] = reflectedPosition.x;
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outerPositions[outerLeftIndex++] = reflectedPosition.y;
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outerPositions[outerLeftIndex++] = reflectedPosition.z;
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}
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}
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theta = _Math.CesiumMath.PI_OVER_TWO;
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position = pointOnEllipsoid(-theta, rotation, northVec, eastVec, aSqr, ab, bSqr, mag, unitPos, position);
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var r = {};
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if (addFillPositions) {
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positions[positionIndex++] = position.x;
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positions[positionIndex++] = position.y;
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positions[positionIndex++] = position.z;
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r.positions = positions;
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r.numPts = numPts;
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}
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if (addEdgePositions) {
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outerPositions[outerRightIndex--] = position.z;
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outerPositions[outerRightIndex--] = position.y;
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outerPositions[outerRightIndex--] = position.x;
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r.outerPositions = outerPositions;
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}
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return r;
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};
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exports.EllipseGeometryLibrary = EllipseGeometryLibrary;
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});
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