import BoundingSphere from './BoundingSphere.js'; import Cartesian3 from './Cartesian3.js'; import defaultValue from './defaultValue.js'; import defined from './defined.js'; import defineProperties from './defineProperties.js'; import DeveloperError from './DeveloperError.js'; import Ellipsoid from './Ellipsoid.js'; import CesiumMath from './Math.js'; import Rectangle from './Rectangle.js'; import Visibility from './Visibility.js'; /** * Creates an Occluder derived from an object's position and radius, as well as the camera position. * The occluder can be used to determine whether or not other objects are visible or hidden behind the * visible horizon defined by the occluder and camera position. * * @alias Occluder * * @param {BoundingSphere} occluderBoundingSphere The bounding sphere surrounding the occluder. * @param {Cartesian3} cameraPosition The coordinate of the viewer/camera. * * @constructor * * @example * // Construct an occluder one unit away from the origin with a radius of one. * var cameraPosition = Cesium.Cartesian3.ZERO; * var occluderBoundingSphere = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -1), 1); * var occluder = new Cesium.Occluder(occluderBoundingSphere, cameraPosition); */ function Occluder(occluderBoundingSphere, cameraPosition) { //>>includeStart('debug', pragmas.debug); if (!defined(occluderBoundingSphere)) { throw new DeveloperError('occluderBoundingSphere is required.'); } if (!defined(cameraPosition)) { throw new DeveloperError('camera position is required.'); } //>>includeEnd('debug'); this._occluderPosition = Cartesian3.clone(occluderBoundingSphere.center); this._occluderRadius = occluderBoundingSphere.radius; this._horizonDistance = 0.0; this._horizonPlaneNormal = undefined; this._horizonPlanePosition = undefined; this._cameraPosition = undefined; // cameraPosition fills in the above values this.cameraPosition = cameraPosition; } var scratchCartesian3 = new Cartesian3(); defineProperties(Occluder.prototype, { /** * The position of the occluder. * @memberof Occluder.prototype * @type {Cartesian3} */ position: { get: function() { return this._occluderPosition; } }, /** * The radius of the occluder. * @memberof Occluder.prototype * @type {Number} */ radius: { get: function() { return this._occluderRadius; } }, /** * The position of the camera. * @memberof Occluder.prototype * @type {Cartesian3} */ cameraPosition: { set: function(cameraPosition) { //>>includeStart('debug', pragmas.debug); if (!defined(cameraPosition)) { throw new DeveloperError('cameraPosition is required.'); } //>>includeEnd('debug'); cameraPosition = Cartesian3.clone(cameraPosition, this._cameraPosition); var cameraToOccluderVec = Cartesian3.subtract(this._occluderPosition, cameraPosition, scratchCartesian3); var invCameraToOccluderDistance = Cartesian3.magnitudeSquared(cameraToOccluderVec); var occluderRadiusSqrd = this._occluderRadius * this._occluderRadius; var horizonDistance; var horizonPlaneNormal; var horizonPlanePosition; if (invCameraToOccluderDistance > occluderRadiusSqrd) { horizonDistance = Math.sqrt(invCameraToOccluderDistance - occluderRadiusSqrd); invCameraToOccluderDistance = 1.0 / Math.sqrt(invCameraToOccluderDistance); horizonPlaneNormal = Cartesian3.multiplyByScalar(cameraToOccluderVec, invCameraToOccluderDistance, scratchCartesian3); var nearPlaneDistance = horizonDistance * horizonDistance * invCameraToOccluderDistance; horizonPlanePosition = Cartesian3.add(cameraPosition, Cartesian3.multiplyByScalar(horizonPlaneNormal, nearPlaneDistance, scratchCartesian3), scratchCartesian3); } else { horizonDistance = Number.MAX_VALUE; } this._horizonDistance = horizonDistance; this._horizonPlaneNormal = horizonPlaneNormal; this._horizonPlanePosition = horizonPlanePosition; this._cameraPosition = cameraPosition; } } }); /** * Creates an occluder from a bounding sphere and the camera position. * * @param {BoundingSphere} occluderBoundingSphere The bounding sphere surrounding the occluder. * @param {Cartesian3} cameraPosition The coordinate of the viewer/camera. * @param {Occluder} [result] The object onto which to store the result. * @returns {Occluder} The occluder derived from an object's position and radius, as well as the camera position. */ Occluder.fromBoundingSphere = function(occluderBoundingSphere, cameraPosition, result) { //>>includeStart('debug', pragmas.debug); if (!defined(occluderBoundingSphere)) { throw new DeveloperError('occluderBoundingSphere is required.'); } if (!defined(cameraPosition)) { throw new DeveloperError('camera position is required.'); } //>>includeEnd('debug'); if (!defined(result)) { return new Occluder(occluderBoundingSphere, cameraPosition); } Cartesian3.clone(occluderBoundingSphere.center, result._occluderPosition); result._occluderRadius = occluderBoundingSphere.radius; result.cameraPosition = cameraPosition; return result; }; var tempVecScratch = new Cartesian3(); /** * Determines whether or not a point, the occludee, is hidden from view by the occluder. * * @param {Cartesian3} occludee The point surrounding the occludee object. * @returns {Boolean} true if the occludee is visible; otherwise false. * * * @example * var cameraPosition = new Cesium.Cartesian3(0, 0, 0); * var littleSphere = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -1), 0.25); * var occluder = new Cesium.Occluder(littleSphere, cameraPosition); * var point = new Cesium.Cartesian3(0, 0, -3); * occluder.isPointVisible(point); //returns true * * @see Occluder#computeVisibility */ Occluder.prototype.isPointVisible = function(occludee) { if (this._horizonDistance !== Number.MAX_VALUE) { var tempVec = Cartesian3.subtract(occludee, this._occluderPosition, tempVecScratch); var temp = this._occluderRadius; temp = Cartesian3.magnitudeSquared(tempVec) - (temp * temp); if (temp > 0.0) { temp = Math.sqrt(temp) + this._horizonDistance; tempVec = Cartesian3.subtract(occludee, this._cameraPosition, tempVec); return temp * temp > Cartesian3.magnitudeSquared(tempVec); } } return false; }; var occludeePositionScratch = new Cartesian3(); /** * Determines whether or not a sphere, the occludee, is hidden from view by the occluder. * * @param {BoundingSphere} occludee The bounding sphere surrounding the occludee object. * @returns {Boolean} true if the occludee is visible; otherwise false. * * * @example * var cameraPosition = new Cesium.Cartesian3(0, 0, 0); * var littleSphere = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -1), 0.25); * var occluder = new Cesium.Occluder(littleSphere, cameraPosition); * var bigSphere = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -3), 1); * occluder.isBoundingSphereVisible(bigSphere); //returns true * * @see Occluder#computeVisibility */ Occluder.prototype.isBoundingSphereVisible = function(occludee) { var occludeePosition = Cartesian3.clone(occludee.center, occludeePositionScratch); var occludeeRadius = occludee.radius; if (this._horizonDistance !== Number.MAX_VALUE) { var tempVec = Cartesian3.subtract(occludeePosition, this._occluderPosition, tempVecScratch); var temp = this._occluderRadius - occludeeRadius; temp = Cartesian3.magnitudeSquared(tempVec) - (temp * temp); if (occludeeRadius < this._occluderRadius) { if (temp > 0.0) { temp = Math.sqrt(temp) + this._horizonDistance; tempVec = Cartesian3.subtract(occludeePosition, this._cameraPosition, tempVec); return ((temp * temp) + (occludeeRadius * occludeeRadius)) > Cartesian3.magnitudeSquared(tempVec); } return false; } // Prevent against the case where the occludee radius is larger than the occluder's; since this is // an uncommon case, the following code should rarely execute. if (temp > 0.0) { tempVec = Cartesian3.subtract(occludeePosition, this._cameraPosition, tempVec); var tempVecMagnitudeSquared = Cartesian3.magnitudeSquared(tempVec); var occluderRadiusSquared = this._occluderRadius * this._occluderRadius; var occludeeRadiusSquared = occludeeRadius * occludeeRadius; if ((((this._horizonDistance * this._horizonDistance) + occluderRadiusSquared) * occludeeRadiusSquared) > (tempVecMagnitudeSquared * occluderRadiusSquared)) { // The occludee is close enough that the occluder cannot possible occlude the occludee return true; } temp = Math.sqrt(temp) + this._horizonDistance; return ((temp * temp) + occludeeRadiusSquared) > tempVecMagnitudeSquared; } // The occludee completely encompasses the occluder return true; } return false; }; var tempScratch = new Cartesian3(); /** * Determine to what extent an occludee is visible (not visible, partially visible, or fully visible). * * @param {BoundingSphere} occludeeBS The bounding sphere of the occludee. * @returns {Number} Visibility.NONE if the occludee is not visible, * Visibility.PARTIAL if the occludee is partially visible, or * Visibility.FULL if the occludee is fully visible. * * * @example * var sphere1 = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -1.5), 0.5); * var sphere2 = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -2.5), 0.5); * var cameraPosition = new Cesium.Cartesian3(0, 0, 0); * var occluder = new Cesium.Occluder(sphere1, cameraPosition); * occluder.computeVisibility(sphere2); //returns Visibility.NONE * * @see Occluder#isVisible */ Occluder.prototype.computeVisibility = function(occludeeBS) { //>>includeStart('debug', pragmas.debug); if (!defined(occludeeBS)) { throw new DeveloperError('occludeeBS is required.'); } //>>includeEnd('debug'); // If the occludee radius is larger than the occluders, this will return that // the entire ocludee is visible, even though that may not be the case, though this should // not occur too often. var occludeePosition = Cartesian3.clone(occludeeBS.center); var occludeeRadius = occludeeBS.radius; if (occludeeRadius > this._occluderRadius) { return Visibility.FULL; } if (this._horizonDistance !== Number.MAX_VALUE) { // The camera is outside the occluder var tempVec = Cartesian3.subtract(occludeePosition, this._occluderPosition, tempScratch); var temp = this._occluderRadius - occludeeRadius; var occluderToOccludeeDistSqrd = Cartesian3.magnitudeSquared(tempVec); temp = occluderToOccludeeDistSqrd - (temp * temp); if (temp > 0.0) { // The occludee is not completely inside the occluder // Check to see if the occluder completely hides the occludee temp = Math.sqrt(temp) + this._horizonDistance; tempVec = Cartesian3.subtract(occludeePosition, this._cameraPosition, tempVec); var cameraToOccludeeDistSqrd = Cartesian3.magnitudeSquared(tempVec); if (((temp * temp) + (occludeeRadius * occludeeRadius)) < cameraToOccludeeDistSqrd) { return Visibility.NONE; } // Check to see whether the occluder is fully or partially visible // when the occludee does not intersect the occluder temp = this._occluderRadius + occludeeRadius; temp = occluderToOccludeeDistSqrd - (temp * temp); if (temp > 0.0) { // The occludee does not intersect the occluder. temp = Math.sqrt(temp) + this._horizonDistance; return (cameraToOccludeeDistSqrd < ((temp * temp)) + (occludeeRadius * occludeeRadius)) ? Visibility.FULL : Visibility.PARTIAL; } //Check to see if the occluder is fully or partially visible when the occludee DOES //intersect the occluder tempVec = Cartesian3.subtract(occludeePosition, this._horizonPlanePosition, tempVec); return (Cartesian3.dot(tempVec, this._horizonPlaneNormal) > -occludeeRadius) ? Visibility.PARTIAL : Visibility.FULL; } } return Visibility.NONE; }; var occludeePointScratch = new Cartesian3(); /** * Computes a point that can be used as the occludee position to the visibility functions. * Use a radius of zero for the occludee radius. Typically, a user computes a bounding sphere around * an object that is used for visibility; however it is also possible to compute a point that if * seen/not seen would also indicate if an object is visible/not visible. This function is better * called for objects that do not move relative to the occluder and is large, such as a chunk of * terrain. You are better off not calling this and using the object's bounding sphere for objects * such as a satellite or ground vehicle. * * @param {BoundingSphere} occluderBoundingSphere The bounding sphere surrounding the occluder. * @param {Cartesian3} occludeePosition The point where the occludee (bounding sphere of radius 0) is located. * @param {Cartesian3[]} positions List of altitude points on the horizon near the surface of the occluder. * @returns {Object} An object containing two attributes: occludeePoint and valid * which is a boolean value. * * @exception {DeveloperError} positions must contain at least one element. * @exception {DeveloperError} occludeePosition must have a value other than occluderBoundingSphere.center. * * @example * var cameraPosition = new Cesium.Cartesian3(0, 0, 0); * var occluderBoundingSphere = new Cesium.BoundingSphere(new Cesium.Cartesian3(0, 0, -8), 2); * var occluder = new Cesium.Occluder(occluderBoundingSphere, cameraPosition); * var positions = [new Cesium.Cartesian3(-0.25, 0, -5.3), new Cesium.Cartesian3(0.25, 0, -5.3)]; * var tileOccluderSphere = Cesium.BoundingSphere.fromPoints(positions); * var occludeePosition = tileOccluderSphere.center; * var occludeePt = Cesium.Occluder.computeOccludeePoint(occluderBoundingSphere, occludeePosition, positions); */ Occluder.computeOccludeePoint = function(occluderBoundingSphere, occludeePosition, positions) { //>>includeStart('debug', pragmas.debug); if (!defined(occluderBoundingSphere)) { throw new DeveloperError('occluderBoundingSphere is required.'); } if (!defined(positions)) { throw new DeveloperError('positions is required.'); } if (positions.length === 0) { throw new DeveloperError('positions must contain at least one element'); } //>>includeEnd('debug'); var occludeePos = Cartesian3.clone(occludeePosition); var occluderPosition = Cartesian3.clone(occluderBoundingSphere.center); var occluderRadius = occluderBoundingSphere.radius; var numPositions = positions.length; //>>includeStart('debug', pragmas.debug); if (Cartesian3.equals(occluderPosition, occludeePosition)) { throw new DeveloperError('occludeePosition must be different than occluderBoundingSphere.center'); } //>>includeEnd('debug'); // Compute a plane with a normal from the occluder to the occludee position. var occluderPlaneNormal = Cartesian3.normalize(Cartesian3.subtract(occludeePos, occluderPosition, occludeePointScratch), occludeePointScratch); var occluderPlaneD = -(Cartesian3.dot(occluderPlaneNormal, occluderPosition)); //For each position, determine the horizon intersection. Choose the position and intersection //that results in the greatest angle with the occcluder plane. var aRotationVector = Occluder._anyRotationVector(occluderPosition, occluderPlaneNormal, occluderPlaneD); var dot = Occluder._horizonToPlaneNormalDotProduct(occluderBoundingSphere, occluderPlaneNormal, occluderPlaneD, aRotationVector, positions[0]); if (!dot) { //The position is inside the mimimum radius, which is invalid return undefined; } var tempDot; for ( var i = 1; i < numPositions; ++i) { tempDot = Occluder._horizonToPlaneNormalDotProduct(occluderBoundingSphere, occluderPlaneNormal, occluderPlaneD, aRotationVector, positions[i]); if (!tempDot) { //The position is inside the minimum radius, which is invalid return undefined; } if (tempDot < dot) { dot = tempDot; } } //Verify that the dot is not near 90 degress if (dot < 0.00174532836589830883577820272085) { return undefined; } var distance = occluderRadius / dot; return Cartesian3.add(occluderPosition, Cartesian3.multiplyByScalar(occluderPlaneNormal, distance, occludeePointScratch), occludeePointScratch); }; var computeOccludeePointFromRectangleScratch = []; /** * Computes a point that can be used as the occludee position to the visibility functions from a rectangle. * * @param {Rectangle} rectangle The rectangle used to create a bounding sphere. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid used to determine positions of the rectangle. * @returns {Object} An object containing two attributes: occludeePoint and valid * which is a boolean value. */ Occluder.computeOccludeePointFromRectangle = function(rectangle, ellipsoid) { //>>includeStart('debug', pragmas.debug); if (!defined(rectangle)) { throw new DeveloperError('rectangle is required.'); } //>>includeEnd('debug'); ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84); var positions = Rectangle.subsample(rectangle, ellipsoid, 0.0, computeOccludeePointFromRectangleScratch); var bs = BoundingSphere.fromPoints(positions); // TODO: get correct ellipsoid center var ellipsoidCenter = Cartesian3.ZERO; if (!Cartesian3.equals(ellipsoidCenter, bs.center)) { return Occluder.computeOccludeePoint(new BoundingSphere(ellipsoidCenter, ellipsoid.minimumRadius), bs.center, positions); } return undefined; }; var tempVec0Scratch = new Cartesian3(); Occluder._anyRotationVector = function(occluderPosition, occluderPlaneNormal, occluderPlaneD) { var tempVec0 = Cartesian3.abs(occluderPlaneNormal, tempVec0Scratch); var majorAxis = tempVec0.x > tempVec0.y ? 0 : 1; if (((majorAxis === 0) && (tempVec0.z > tempVec0.x)) || ((majorAxis === 1) && (tempVec0.z > tempVec0.y))) { majorAxis = 2; } var tempVec = new Cartesian3(); var tempVec1; if (majorAxis === 0) { tempVec0.x = occluderPosition.x; tempVec0.y = occluderPosition.y + 1.0; tempVec0.z = occluderPosition.z + 1.0; tempVec1 = Cartesian3.UNIT_X; } else if (majorAxis === 1) { tempVec0.x = occluderPosition.x + 1.0; tempVec0.y = occluderPosition.y; tempVec0.z = occluderPosition.z + 1.0; tempVec1 = Cartesian3.UNIT_Y; } else { tempVec0.x = occluderPosition.x + 1.0; tempVec0.y = occluderPosition.y + 1.0; tempVec0.z = occluderPosition.z; tempVec1 = Cartesian3.UNIT_Z; } var u = (Cartesian3.dot(occluderPlaneNormal, tempVec0) + occluderPlaneD) / -(Cartesian3.dot(occluderPlaneNormal, tempVec1)); return Cartesian3.normalize(Cartesian3.subtract(Cartesian3.add(tempVec0, Cartesian3.multiplyByScalar(tempVec1, u, tempVec), tempVec0), occluderPosition, tempVec0), tempVec0); }; var posDirectionScratch = new Cartesian3(); Occluder._rotationVector = function(occluderPosition, occluderPlaneNormal, occluderPlaneD, position, anyRotationVector) { //Determine the angle between the occluder plane normal and the position direction var positionDirection = Cartesian3.subtract(position, occluderPosition, posDirectionScratch); positionDirection = Cartesian3.normalize(positionDirection, positionDirection); if (Cartesian3.dot(occluderPlaneNormal, positionDirection) < 0.99999998476912904932780850903444) { var crossProduct = Cartesian3.cross(occluderPlaneNormal, positionDirection, positionDirection); var length = Cartesian3.magnitude(crossProduct); if (length > CesiumMath.EPSILON13) { return Cartesian3.normalize(crossProduct, new Cartesian3()); } } //The occluder plane normal and the position direction are colinear. Use any //vector in the occluder plane as the rotation vector return anyRotationVector; }; var posScratch1 = new Cartesian3(); var occluerPosScratch = new Cartesian3(); var posScratch2 = new Cartesian3(); var horizonPlanePosScratch = new Cartesian3(); Occluder._horizonToPlaneNormalDotProduct = function(occluderBS, occluderPlaneNormal, occluderPlaneD, anyRotationVector, position) { var pos = Cartesian3.clone(position, posScratch1); var occluderPosition = Cartesian3.clone(occluderBS.center, occluerPosScratch); var occluderRadius = occluderBS.radius; //Verify that the position is outside the occluder var positionToOccluder = Cartesian3.subtract(occluderPosition, pos, posScratch2); var occluderToPositionDistanceSquared = Cartesian3.magnitudeSquared(positionToOccluder); var occluderRadiusSquared = occluderRadius * occluderRadius; if (occluderToPositionDistanceSquared < occluderRadiusSquared) { return false; } //Horizon parameters var horizonDistanceSquared = occluderToPositionDistanceSquared - occluderRadiusSquared; var horizonDistance = Math.sqrt(horizonDistanceSquared); var occluderToPositionDistance = Math.sqrt(occluderToPositionDistanceSquared); var invOccluderToPositionDistance = 1.0 / occluderToPositionDistance; var cosTheta = horizonDistance * invOccluderToPositionDistance; var horizonPlaneDistance = cosTheta * horizonDistance; positionToOccluder = Cartesian3.normalize(positionToOccluder, positionToOccluder); var horizonPlanePosition = Cartesian3.add(pos, Cartesian3.multiplyByScalar(positionToOccluder, horizonPlaneDistance, horizonPlanePosScratch), horizonPlanePosScratch); var horizonCrossDistance = Math.sqrt(horizonDistanceSquared - (horizonPlaneDistance * horizonPlaneDistance)); //Rotate the position to occluder vector 90 degrees var tempVec = this._rotationVector(occluderPosition, occluderPlaneNormal, occluderPlaneD, pos, anyRotationVector); var horizonCrossDirection = Cartesian3.fromElements( (tempVec.x * tempVec.x * positionToOccluder.x) + ((tempVec.x * tempVec.y - tempVec.z) * positionToOccluder.y) + ((tempVec.x * tempVec.z + tempVec.y) * positionToOccluder.z), ((tempVec.x * tempVec.y + tempVec.z) * positionToOccluder.x) + (tempVec.y * tempVec.y * positionToOccluder.y) + ((tempVec.y * tempVec.z - tempVec.x) * positionToOccluder.z), ((tempVec.x * tempVec.z - tempVec.y) * positionToOccluder.x) + ((tempVec.y * tempVec.z + tempVec.x) * positionToOccluder.y) + (tempVec.z * tempVec.z * positionToOccluder.z), posScratch1); horizonCrossDirection = Cartesian3.normalize(horizonCrossDirection, horizonCrossDirection); //Horizon positions var offset = Cartesian3.multiplyByScalar(horizonCrossDirection, horizonCrossDistance, posScratch1); tempVec = Cartesian3.normalize(Cartesian3.subtract(Cartesian3.add(horizonPlanePosition, offset, posScratch2), occluderPosition, posScratch2), posScratch2); var dot0 = Cartesian3.dot(occluderPlaneNormal, tempVec); tempVec = Cartesian3.normalize(Cartesian3.subtract(Cartesian3.subtract(horizonPlanePosition, offset, tempVec), occluderPosition, tempVec), tempVec); var dot1 = Cartesian3.dot(occluderPlaneNormal, tempVec); return (dot0 < dot1) ? dot0 : dot1; }; export default Occluder;