cesiumDemo/Source/Scene/Camera.js

import BoundingSphere from '../Core/BoundingSphere.js';
import Cartesian2 from '../Core/Cartesian2.js';
import Cartesian3 from '../Core/Cartesian3.js';
import Cartesian4 from '../Core/Cartesian4.js';
import Cartographic from '../Core/Cartographic.js';
import defaultValue from '../Core/defaultValue.js';
import defined from '../Core/defined.js';
import defineProperties from '../Core/defineProperties.js';
import DeveloperError from '../Core/DeveloperError.js';
import EasingFunction from '../Core/EasingFunction.js';
import Ellipsoid from '../Core/Ellipsoid.js';
import EllipsoidGeodesic from '../Core/EllipsoidGeodesic.js';
import Event from '../Core/Event.js';
import getTimestamp from '../Core/getTimestamp.js';
import HeadingPitchRange from '../Core/HeadingPitchRange.js';
import HeadingPitchRoll from '../Core/HeadingPitchRoll.js';
import Intersect from '../Core/Intersect.js';
import IntersectionTests from '../Core/IntersectionTests.js';
import CesiumMath from '../Core/Math.js';
import Matrix3 from '../Core/Matrix3.js';
import Matrix4 from '../Core/Matrix4.js';
import OrthographicFrustum from '../Core/OrthographicFrustum.js';
import OrthographicOffCenterFrustum from '../Core/OrthographicOffCenterFrustum.js';
import PerspectiveFrustum from '../Core/PerspectiveFrustum.js';
import Quaternion from '../Core/Quaternion.js';
import Ray from '../Core/Ray.js';
import Rectangle from '../Core/Rectangle.js';
import Transforms from '../Core/Transforms.js';
import CameraFlightPath from './CameraFlightPath.js';
import MapMode2D from './MapMode2D.js';
import SceneMode from './SceneMode.js';

    /**
     * The camera is defined by a position, orientation, and view frustum.
     * <br /><br />
     * The orientation forms an orthonormal basis with a view, up and right = view x up unit vectors.
     * <br /><br />
     * The viewing frustum is defined by 6 planes.
     * Each plane is represented by a {@link Cartesian4} object, where the x, y, and z components
     * define the unit vector normal to the plane, and the w component is the distance of the
     * plane from the origin/camera position.
     *
     * @alias Camera
     *
     * @constructor
     *
     * @param {Scene} scene The scene.
     *
     * @demo {@link https://sandcastle.cesium.com/index.html?src=Camera.html|Cesium Sandcastle Camera Demo}
     * @demo {@link https://sandcastle.cesium.com/index.html?src=Camera%20Tutorial.html">Sandcastle Example</a> from the <a href="https://cesium.com/docs/tutorials/camera/|Camera Tutorial}
     *
     * @example
     * // Create a camera looking down the negative z-axis, positioned at the origin,
     * // with a field of view of 60 degrees, and 1:1 aspect ratio.
     * var camera = new Cesium.Camera(scene);
     * camera.position = new Cesium.Cartesian3();
     * camera.direction = Cesium.Cartesian3.negate(Cesium.Cartesian3.UNIT_Z, new Cesium.Cartesian3());
     * camera.up = Cesium.Cartesian3.clone(Cesium.Cartesian3.UNIT_Y);
     * camera.frustum.fov = Cesium.Math.PI_OVER_THREE;
     * camera.frustum.near = 1.0;
     * camera.frustum.far = 2.0;
     */
    function Camera(scene) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(scene)) {
            throw new DeveloperError('scene is required.');
        }
        //>>includeEnd('debug');
        this._scene = scene;

        this._transform = Matrix4.clone(Matrix4.IDENTITY);
        this._invTransform = Matrix4.clone(Matrix4.IDENTITY);
        this._actualTransform = Matrix4.clone(Matrix4.IDENTITY);
        this._actualInvTransform = Matrix4.clone(Matrix4.IDENTITY);
        this._transformChanged = false;

        /**
         * The position of the camera.
         *
         * @type {Cartesian3}
         */
        this.position = new Cartesian3();
        this._position = new Cartesian3();
        this._positionWC = new Cartesian3();
        this._positionCartographic = new Cartographic();
        this._oldPositionWC = undefined;

        /**
         * The position delta magnitude.
         *
         * @private
         */
        this.positionWCDeltaMagnitude = 0.0;

        /**
         * The position delta magnitude last frame.
         *
         * @private
         */
        this.positionWCDeltaMagnitudeLastFrame = 0.0;

        /**
         * How long in seconds since the camera has stopped moving
         *
         * @private
         */
        this.timeSinceMoved = 0.0;
        this._lastMovedTimestamp = 0.0;

        /**
         * The view direction of the camera.
         *
         * @type {Cartesian3}
         */
        this.direction = new Cartesian3();
        this._direction = new Cartesian3();
        this._directionWC = new Cartesian3();

        /**
         * The up direction of the camera.
         *
         * @type {Cartesian3}
         */
        this.up = new Cartesian3();
        this._up = new Cartesian3();
        this._upWC = new Cartesian3();

        /**
         * The right direction of the camera.
         *
         * @type {Cartesian3}
         */
        this.right = new Cartesian3();
        this._right = new Cartesian3();
        this._rightWC = new Cartesian3();

        /**
         * The region of space in view.
         *
         * @type {Frustum}
         * @default PerspectiveFrustum()
         *
         * @see PerspectiveFrustum
         * @see PerspectiveOffCenterFrustum
         * @see OrthographicFrustum
         */
        this.frustum = new PerspectiveFrustum();
        this.frustum.aspectRatio = scene.drawingBufferWidth / scene.drawingBufferHeight;
        this.frustum.fov = CesiumMath.toRadians(60.0);

        /**
         * The default amount to move the camera when an argument is not
         * provided to the move methods.
         * @type {Number}
         * @default 100000.0;
         */
        this.defaultMoveAmount = 100000.0;
        /**
         * The default amount to rotate the camera when an argument is not
         * provided to the look methods.
         * @type {Number}
         * @default Math.PI / 60.0
         */
        this.defaultLookAmount = Math.PI / 60.0;
        /**
         * The default amount to rotate the camera when an argument is not
         * provided to the rotate methods.
         * @type {Number}
         * @default Math.PI / 3600.0
         */
        this.defaultRotateAmount = Math.PI / 3600.0;
        /**
         * The default amount to move the camera when an argument is not
         * provided to the zoom methods.
         * @type {Number}
         * @default 100000.0;
         */
        this.defaultZoomAmount = 100000.0;
        /**
         * If set, the camera will not be able to rotate past this axis in either direction.
         * @type {Cartesian3}
         * @default undefined
         */
        this.constrainedAxis = undefined;
        /**
         * The factor multiplied by the the map size used to determine where to clamp the camera position
         * when zooming out from the surface. The default is 1.5. Only valid for 2D and the map is rotatable.
         * @type {Number}
         * @default 1.5
         */
        this.maximumZoomFactor = 1.5;

        this._moveStart = new Event();
        this._moveEnd = new Event();

        this._changed = new Event();
        this._changedPosition = undefined;
        this._changedDirection = undefined;
        this._changedFrustum = undefined;

        /**
         * The amount the camera has to change before the <code>changed</code> event is raised. The value is a percentage in the [0, 1] range.
         * @type {number}
         * @default 0.5
         */
        this.percentageChanged = 0.5;

        this._viewMatrix = new Matrix4();
        this._invViewMatrix = new Matrix4();
        updateViewMatrix(this);

        this._mode = SceneMode.SCENE3D;
        this._modeChanged = true;
        var projection = scene.mapProjection;
        this._projection = projection;
        this._maxCoord = projection.project(new Cartographic(Math.PI, CesiumMath.PI_OVER_TWO));
        this._max2Dfrustum = undefined;
        this._suspendTerrainAdjustment = false;

        // set default view
        rectangleCameraPosition3D(this, Camera.DEFAULT_VIEW_RECTANGLE, this.position, true);

        var mag = Cartesian3.magnitude(this.position);
        mag += mag * Camera.DEFAULT_VIEW_FACTOR;
        Cartesian3.normalize(this.position, this.position);
        Cartesian3.multiplyByScalar(this.position, mag, this.position);
    }

    /**
     * @private
     */
    Camera.TRANSFORM_2D = new Matrix4(
        0.0, 0.0, 1.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0);

    /**
     * @private
     */
    Camera.TRANSFORM_2D_INVERSE = Matrix4.inverseTransformation(Camera.TRANSFORM_2D, new Matrix4());

    /**
     * The default rectangle the camera will view on creation.
     * @type Rectangle
     */
    Camera.DEFAULT_VIEW_RECTANGLE = Rectangle.fromDegrees(-95.0, -20.0, -70.0, 90.0);

    /**
     * A scalar to multiply to the camera position and add it back after setting the camera to view the rectangle.
     * A value of zero means the camera will view the entire {@link Camera#DEFAULT_VIEW_RECTANGLE}, a value greater than zero
     * will move it further away from the extent, and a value less than zero will move it close to the extent.
     * @type Number
     */
    Camera.DEFAULT_VIEW_FACTOR = 0.5;

    /**
     * The default heading/pitch/range that is used when the camera flies to a location that contains a bounding sphere.
     * @type HeadingPitchRange
     */
    Camera.DEFAULT_OFFSET = new HeadingPitchRange(0.0, -CesiumMath.PI_OVER_FOUR, 0.0);

    function updateViewMatrix(camera) {
        Matrix4.computeView(camera._position, camera._direction, camera._up, camera._right, camera._viewMatrix);
        Matrix4.multiply(camera._viewMatrix, camera._actualInvTransform, camera._viewMatrix);
        Matrix4.inverseTransformation(camera._viewMatrix, camera._invViewMatrix);
    }

    function updateCameraDeltas(camera) {
        if (!defined(camera._oldPositionWC)) {
            camera._oldPositionWC = Cartesian3.clone(camera.positionWC, camera._oldPositionWC);
        } else {
            camera.positionWCDeltaMagnitudeLastFrame = camera.positionWCDeltaMagnitude;
            var delta = Cartesian3.subtract(camera.positionWC, camera._oldPositionWC, camera._oldPositionWC);
            camera.positionWCDeltaMagnitude = Cartesian3.magnitude(delta);
            camera._oldPositionWC = Cartesian3.clone(camera.positionWC, camera._oldPositionWC);

            // Update move timers
            if (camera.positionWCDeltaMagnitude > 0.0) {
                camera.timeSinceMoved = 0.0;
                camera._lastMovedTimestamp = getTimestamp();
            } else {
                camera.timeSinceMoved = Math.max(getTimestamp() - camera._lastMovedTimestamp, 0.0) / 1000.0;
            }
        }
    }

    /**
     * Checks if there's a camera flight for this camera.
     *
     * @returns {Boolean} Whether or not this camera has a current flight with a valid preloadFlightCamera in scene.
     *
     * @private
     *
     */
    Camera.prototype.hasCurrentFlight = function() {
        // The preload flight camera defined check only here since it can be set to undefined when not 3D mode.
        return defined(this._currentFlight) && defined(this._scene.preloadFlightCamera);
    };

    Camera.prototype._updateCameraChanged = function() {
        var camera = this;

        updateCameraDeltas(camera);

        if (camera._changed.numberOfListeners === 0) {
            return;
        }

        var percentageChanged = camera.percentageChanged;

        if (camera._mode === SceneMode.SCENE2D) {
            if (!defined(camera._changedFrustum)) {
                camera._changedPosition = Cartesian3.clone(camera.position, camera._changedPosition);
                camera._changedFrustum = camera.frustum.clone();
                return;
            }

            var position = camera.position;
            var lastPosition = camera._changedPosition;

            var frustum = camera.frustum;
            var lastFrustum = camera._changedFrustum;

            var x0 = position.x + frustum.left;
            var x1 = position.x + frustum.right;
            var x2 = lastPosition.x + lastFrustum.left;
            var x3 = lastPosition.x + lastFrustum.right;

            var y0 = position.y + frustum.bottom;
            var y1 = position.y + frustum.top;
            var y2 = lastPosition.y + lastFrustum.bottom;
            var y3 = lastPosition.y + lastFrustum.top;

            var leftX = Math.max(x0, x2);
            var rightX = Math.min(x1, x3);
            var bottomY = Math.max(y0, y2);
            var topY = Math.min(y1, y3);

            var areaPercentage;
            if (leftX >= rightX || bottomY >= y1) {
                areaPercentage = 1.0;
            } else {
                var areaRef = lastFrustum;
                if (x0 < x2 && x1 > x3 && y0 < y2 && y1 > y3) {
                    areaRef = frustum;
                }
                areaPercentage = 1.0 - ((rightX - leftX) * (topY - bottomY)) / ((areaRef.right - areaRef.left) * (areaRef.top - areaRef.bottom));
            }

            if (areaPercentage > percentageChanged) {
                camera._changed.raiseEvent(areaPercentage);
                camera._changedPosition = Cartesian3.clone(camera.position, camera._changedPosition);
                camera._changedFrustum = camera.frustum.clone(camera._changedFrustum);
            }
            return;
        }

        if (!defined(camera._changedDirection)) {
            camera._changedPosition = Cartesian3.clone(camera.positionWC, camera._changedPosition);
            camera._changedDirection = Cartesian3.clone(camera.directionWC, camera._changedDirection);
            return;
        }

        var dirAngle = CesiumMath.acosClamped(Cartesian3.dot(camera.directionWC, camera._changedDirection));

        var dirPercentage;
        if (defined(camera.frustum.fovy)) {
            dirPercentage = dirAngle / (camera.frustum.fovy * 0.5);
        } else {
            dirPercentage = dirAngle;
        }

        var distance = Cartesian3.distance(camera.positionWC, camera._changedPosition);
        var heightPercentage = distance / camera.positionCartographic.height;

        if (dirPercentage > percentageChanged || heightPercentage > percentageChanged) {
            camera._changed.raiseEvent(Math.max(dirPercentage, heightPercentage));
            camera._changedPosition = Cartesian3.clone(camera.positionWC, camera._changedPosition);
            camera._changedDirection = Cartesian3.clone(camera.directionWC, camera._changedDirection);
        }
    };

    var scratchAdjustHeightTransform = new Matrix4();
    var scratchAdjustHeightCartographic = new Cartographic();

    Camera.prototype._adjustHeightForTerrain = function() {
        var scene = this._scene;

        var screenSpaceCameraController = scene.screenSpaceCameraController;
        var enableCollisionDetection = screenSpaceCameraController.enableCollisionDetection;
        var minimumCollisionTerrainHeight = screenSpaceCameraController.minimumCollisionTerrainHeight;
        var minimumZoomDistance = screenSpaceCameraController.minimumZoomDistance;

        if (this._suspendTerrainAdjustment || !enableCollisionDetection) {
            return;
        }

        var mode = this._mode;
        var globe = scene.globe;

        if (!defined(globe) || mode === SceneMode.SCENE2D || mode === SceneMode.MORPHING) {
            return;
        }

        var ellipsoid = globe.ellipsoid;
        var projection = scene.mapProjection;

        var transform;
        var mag;
        if (!Matrix4.equals(this.transform, Matrix4.IDENTITY)) {
            transform = Matrix4.clone(this.transform, scratchAdjustHeightTransform);
            mag = Cartesian3.magnitude(this.position);
            this._setTransform(Matrix4.IDENTITY);
        }

        var cartographic = scratchAdjustHeightCartographic;
        if (mode === SceneMode.SCENE3D) {
            ellipsoid.cartesianToCartographic(this.position, cartographic);
        } else {
            projection.unproject(this.position, cartographic);
        }

        var heightUpdated = false;
        if (cartographic.height < minimumCollisionTerrainHeight) {
            var height = globe.getHeight(cartographic);
            if (defined(height)) {
                height += minimumZoomDistance;
                if (cartographic.height < height) {
                    cartographic.height = height;
                    if (mode === SceneMode.SCENE3D) {
                        ellipsoid.cartographicToCartesian(cartographic, this.position);
                    } else {
                        projection.project(cartographic, this.position);
                    }
                    heightUpdated = true;
                }
            }
        }

        if (defined(transform)) {
            this._setTransform(transform);
            if (heightUpdated) {
                Cartesian3.normalize(this.position, this.position);
                Cartesian3.negate(this.position, this.direction);
                Cartesian3.multiplyByScalar(this.position, Math.max(mag, minimumZoomDistance), this.position);
                Cartesian3.normalize(this.direction, this.direction);
                Cartesian3.cross(this.direction, this.up, this.right);
                Cartesian3.cross(this.right, this.direction, this.up);
            }
        }
    };

    function convertTransformForColumbusView(camera) {
        Transforms.basisTo2D(camera._projection, camera._transform, camera._actualTransform);
    }

    var scratchCartographic = new Cartographic();
    var scratchCartesian3Projection = new Cartesian3();
    var scratchCartesian3 = new Cartesian3();
    var scratchCartesian4Origin = new Cartesian4();
    var scratchCartesian4NewOrigin = new Cartesian4();
    var scratchCartesian4NewXAxis = new Cartesian4();
    var scratchCartesian4NewYAxis = new Cartesian4();
    var scratchCartesian4NewZAxis = new Cartesian4();

    function convertTransformFor2D(camera) {
        var projection = camera._projection;
        var ellipsoid = projection.ellipsoid;

        var origin = Matrix4.getColumn(camera._transform, 3, scratchCartesian4Origin);
        var cartographic = ellipsoid.cartesianToCartographic(origin, scratchCartographic);

        var projectedPosition = projection.project(cartographic, scratchCartesian3Projection);
        var newOrigin = scratchCartesian4NewOrigin;
        newOrigin.x = projectedPosition.z;
        newOrigin.y = projectedPosition.x;
        newOrigin.z = projectedPosition.y;
        newOrigin.w = 1.0;

        var newZAxis = Cartesian4.clone(Cartesian4.UNIT_X, scratchCartesian4NewZAxis);

        var xAxis = Cartesian4.add(Matrix4.getColumn(camera._transform, 0, scratchCartesian3), origin, scratchCartesian3);
        ellipsoid.cartesianToCartographic(xAxis, cartographic);

        projection.project(cartographic, projectedPosition);
        var newXAxis = scratchCartesian4NewXAxis;
        newXAxis.x = projectedPosition.z;
        newXAxis.y = projectedPosition.x;
        newXAxis.z = projectedPosition.y;
        newXAxis.w = 0.0;

        Cartesian3.subtract(newXAxis, newOrigin, newXAxis);
        newXAxis.x = 0.0;

        var newYAxis = scratchCartesian4NewYAxis;
        if (Cartesian3.magnitudeSquared(newXAxis) > CesiumMath.EPSILON10) {
            Cartesian3.cross(newZAxis, newXAxis, newYAxis);
        } else {
            var yAxis = Cartesian4.add(Matrix4.getColumn(camera._transform, 1, scratchCartesian3), origin, scratchCartesian3);
            ellipsoid.cartesianToCartographic(yAxis, cartographic);

            projection.project(cartographic, projectedPosition);
            newYAxis.x = projectedPosition.z;
            newYAxis.y = projectedPosition.x;
            newYAxis.z = projectedPosition.y;
            newYAxis.w = 0.0;

            Cartesian3.subtract(newYAxis, newOrigin, newYAxis);
            newYAxis.x = 0.0;

            if (Cartesian3.magnitudeSquared(newYAxis) < CesiumMath.EPSILON10) {
                Cartesian4.clone(Cartesian4.UNIT_Y, newXAxis);
                Cartesian4.clone(Cartesian4.UNIT_Z, newYAxis);
            }
        }

        Cartesian3.cross(newYAxis, newZAxis, newXAxis);
        Cartesian3.normalize(newXAxis, newXAxis);
        Cartesian3.cross(newZAxis, newXAxis, newYAxis);
        Cartesian3.normalize(newYAxis, newYAxis);

        Matrix4.setColumn(camera._actualTransform, 0, newXAxis, camera._actualTransform);
        Matrix4.setColumn(camera._actualTransform, 1, newYAxis, camera._actualTransform);
        Matrix4.setColumn(camera._actualTransform, 2, newZAxis, camera._actualTransform);
        Matrix4.setColumn(camera._actualTransform, 3, newOrigin, camera._actualTransform);
    }

    var scratchCartesian = new Cartesian3();

    function updateMembers(camera) {
        var mode = camera._mode;

        var heightChanged = false;
        var height = 0.0;
        if (mode === SceneMode.SCENE2D) {
            height = camera.frustum.right - camera.frustum.left;
            heightChanged = height !== camera._positionCartographic.height;
        }

        var position = camera._position;
        var positionChanged = !Cartesian3.equals(position, camera.position) || heightChanged;
        if (positionChanged) {
            position = Cartesian3.clone(camera.position, camera._position);
        }

        var direction = camera._direction;
        var directionChanged = !Cartesian3.equals(direction, camera.direction);
        if (directionChanged) {
            Cartesian3.normalize(camera.direction, camera.direction);
            direction = Cartesian3.clone(camera.direction, camera._direction);
        }

        var up = camera._up;
        var upChanged = !Cartesian3.equals(up, camera.up);
        if (upChanged) {
            Cartesian3.normalize(camera.up, camera.up);
            up = Cartesian3.clone(camera.up, camera._up);
        }

        var right = camera._right;
        var rightChanged = !Cartesian3.equals(right, camera.right);
        if (rightChanged) {
            Cartesian3.normalize(camera.right, camera.right);
            right = Cartesian3.clone(camera.right, camera._right);
        }

        var transformChanged = camera._transformChanged || camera._modeChanged;
        camera._transformChanged = false;

        if (transformChanged) {
            Matrix4.inverseTransformation(camera._transform, camera._invTransform);

            if (camera._mode === SceneMode.COLUMBUS_VIEW || camera._mode === SceneMode.SCENE2D) {
                if (Matrix4.equals(Matrix4.IDENTITY, camera._transform)) {
                    Matrix4.clone(Camera.TRANSFORM_2D, camera._actualTransform);
                } else if (camera._mode === SceneMode.COLUMBUS_VIEW) {
                    convertTransformForColumbusView(camera);
                } else {
                    convertTransformFor2D(camera);
                }
            } else {
                Matrix4.clone(camera._transform, camera._actualTransform);
            }

            Matrix4.inverseTransformation(camera._actualTransform, camera._actualInvTransform);

            camera._modeChanged = false;
        }

        var transform = camera._actualTransform;

        if (positionChanged || transformChanged) {
            camera._positionWC = Matrix4.multiplyByPoint(transform, position, camera._positionWC);

            // Compute the Cartographic position of the camera.
            if (mode === SceneMode.SCENE3D || mode === SceneMode.MORPHING) {
                camera._positionCartographic = camera._projection.ellipsoid.cartesianToCartographic(camera._positionWC, camera._positionCartographic);
            } else {
                // The camera position is expressed in the 2D coordinate system where the Y axis is to the East,
                // the Z axis is to the North, and the X axis is out of the map.  Express them instead in the ENU axes where
                // X is to the East, Y is to the North, and Z is out of the local horizontal plane.
                var positionENU = scratchCartesian;
                positionENU.x = camera._positionWC.y;
                positionENU.y = camera._positionWC.z;
                positionENU.z = camera._positionWC.x;

                // In 2D, the camera height is always 12.7 million meters.
                // The apparent height is equal to half the frustum width.
                if (mode === SceneMode.SCENE2D) {
                    positionENU.z = height;
                }

                camera._projection.unproject(positionENU, camera._positionCartographic);
            }
        }

        if (directionChanged || upChanged || rightChanged) {
            var det = Cartesian3.dot(direction, Cartesian3.cross(up, right, scratchCartesian));
            if (Math.abs(1.0 - det) > CesiumMath.EPSILON2) {
                //orthonormalize axes
                var invUpMag = 1.0 / Cartesian3.magnitudeSquared(up);
                var scalar = Cartesian3.dot(up, direction) * invUpMag;
                var w0 = Cartesian3.multiplyByScalar(direction, scalar, scratchCartesian);
                up = Cartesian3.normalize(Cartesian3.subtract(up, w0, camera._up), camera._up);
                Cartesian3.clone(up, camera.up);

                right = Cartesian3.cross(direction, up, camera._right);
                Cartesian3.clone(right, camera.right);
            }
        }

        if (directionChanged || transformChanged) {
            camera._directionWC = Matrix4.multiplyByPointAsVector(transform, direction, camera._directionWC);
            Cartesian3.normalize(camera._directionWC, camera._directionWC);
        }

        if (upChanged || transformChanged) {
            camera._upWC = Matrix4.multiplyByPointAsVector(transform, up, camera._upWC);
            Cartesian3.normalize(camera._upWC, camera._upWC);
        }

        if (rightChanged || transformChanged) {
            camera._rightWC = Matrix4.multiplyByPointAsVector(transform, right, camera._rightWC);
            Cartesian3.normalize(camera._rightWC, camera._rightWC);
        }

        if (positionChanged || directionChanged || upChanged || rightChanged || transformChanged) {
            updateViewMatrix(camera);
        }
    }

    function getHeading(direction, up) {
        var heading;
        if (!CesiumMath.equalsEpsilon(Math.abs(direction.z), 1.0, CesiumMath.EPSILON3)) {
            heading = Math.atan2(direction.y, direction.x) - CesiumMath.PI_OVER_TWO;
        } else {
            heading = Math.atan2(up.y, up.x) - CesiumMath.PI_OVER_TWO;
        }

        return CesiumMath.TWO_PI - CesiumMath.zeroToTwoPi(heading);
    }

    function getPitch(direction) {
        return CesiumMath.PI_OVER_TWO - CesiumMath.acosClamped(direction.z);
    }

    function getRoll(direction, up, right) {
        var roll = 0.0;
        if (!CesiumMath.equalsEpsilon(Math.abs(direction.z), 1.0, CesiumMath.EPSILON3)) {
            roll = Math.atan2(-right.z, up.z);
            roll = CesiumMath.zeroToTwoPi(roll + CesiumMath.TWO_PI);
        }

        return roll;
    }

    var scratchHPRMatrix1 = new Matrix4();
    var scratchHPRMatrix2 = new Matrix4();

    defineProperties(Camera.prototype, {
        /**
         * Gets the camera's reference frame. The inverse of this transformation is appended to the view matrix.
         * @memberof Camera.prototype
         *
         * @type {Matrix4}
         * @readonly
         *
         * @default {@link Matrix4.IDENTITY}
         */
        transform : {
            get : function() {
                return this._transform;
            }
        },

        /**
         * Gets the inverse camera transform.
         * @memberof Camera.prototype
         *
         * @type {Matrix4}
         * @readonly
         *
         * @default {@link Matrix4.IDENTITY}
         */
        inverseTransform : {
            get : function() {
                updateMembers(this);
                return this._invTransform;
            }
        },

        /**
         * Gets the view matrix.
         * @memberof Camera.prototype
         *
         * @type {Matrix4}
         * @readonly
         *
         * @see Camera#inverseViewMatrix
         */
        viewMatrix : {
            get : function() {
                updateMembers(this);
                return this._viewMatrix;
            }
        },

        /**
         * Gets the inverse view matrix.
         * @memberof Camera.prototype
         *
         * @type {Matrix4}
         * @readonly
         *
         * @see Camera#viewMatrix
         */
        inverseViewMatrix : {
            get : function() {
                updateMembers(this);
                return this._invViewMatrix;
            }
        },

        /**
         * Gets the {@link Cartographic} position of the camera, with longitude and latitude
         * expressed in radians and height in meters.  In 2D and Columbus View, it is possible
         * for the returned longitude and latitude to be outside the range of valid longitudes
         * and latitudes when the camera is outside the map.
         * @memberof Camera.prototype
         *
         * @type {Cartographic}
         * @readonly
         */
        positionCartographic : {
            get : function() {
                updateMembers(this);
                return this._positionCartographic;
            }
        },

        /**
         * Gets the position of the camera in world coordinates.
         * @memberof Camera.prototype
         *
         * @type {Cartesian3}
         * @readonly
         */
        positionWC : {
            get : function() {
                updateMembers(this);
                return this._positionWC;
            }
        },

        /**
         * Gets the view direction of the camera in world coordinates.
         * @memberof Camera.prototype
         *
         * @type {Cartesian3}
         * @readonly
         */
        directionWC : {
            get : function() {
                updateMembers(this);
                return this._directionWC;
            }
        },

        /**
         * Gets the up direction of the camera in world coordinates.
         * @memberof Camera.prototype
         *
         * @type {Cartesian3}
         * @readonly
         */
        upWC : {
            get : function() {
                updateMembers(this);
                return this._upWC;
            }
        },

        /**
         * Gets the right direction of the camera in world coordinates.
         * @memberof Camera.prototype
         *
         * @type {Cartesian3}
         * @readonly
         */
        rightWC : {
            get : function() {
                updateMembers(this);
                return this._rightWC;
            }
        },

        /**
         * Gets the camera heading in radians.
         * @memberof Camera.prototype
         *
         * @type {Number}
         * @readonly
         */
        heading : {
            get : function() {
                if (this._mode !== SceneMode.MORPHING) {
                    var ellipsoid = this._projection.ellipsoid;

                    var oldTransform = Matrix4.clone(this._transform, scratchHPRMatrix1);
                    var transform = Transforms.eastNorthUpToFixedFrame(this.positionWC, ellipsoid, scratchHPRMatrix2);
                    this._setTransform(transform);

                    var heading = getHeading(this.direction, this.up);

                    this._setTransform(oldTransform);

                    return heading;
                }

                return undefined;
            }
        },

        /**
         * Gets the camera pitch in radians.
         * @memberof Camera.prototype
         *
         * @type {Number}
         * @readonly
         */
        pitch : {
            get : function() {
                if (this._mode !== SceneMode.MORPHING) {
                    var ellipsoid = this._projection.ellipsoid;

                    var oldTransform = Matrix4.clone(this._transform, scratchHPRMatrix1);
                    var transform = Transforms.eastNorthUpToFixedFrame(this.positionWC, ellipsoid, scratchHPRMatrix2);
                    this._setTransform(transform);

                    var pitch = getPitch(this.direction);

                    this._setTransform(oldTransform);

                    return pitch;
                }

                return undefined;
            }
        },

        /**
         * Gets the camera roll in radians.
         * @memberof Camera.prototype
         *
         * @type {Number}
         * @readonly
         */
        roll : {
            get : function() {
                if (this._mode !== SceneMode.MORPHING) {
                    var ellipsoid = this._projection.ellipsoid;

                    var oldTransform = Matrix4.clone(this._transform, scratchHPRMatrix1);
                    var transform = Transforms.eastNorthUpToFixedFrame(this.positionWC, ellipsoid, scratchHPRMatrix2);
                    this._setTransform(transform);

                    var roll = getRoll(this.direction, this.up, this.right);

                    this._setTransform(oldTransform);

                    return roll;
                }

                return undefined;
            }
        },

        /**
         * Gets the event that will be raised at when the camera starts to move.
         * @memberof Camera.prototype
         * @type {Event}
         * @readonly
         */
        moveStart : {
            get : function() {
                return this._moveStart;
            }
        },

        /**
         * Gets the event that will be raised when the camera has stopped moving.
         * @memberof Camera.prototype
         * @type {Event}
         * @readonly
         */
        moveEnd : {
            get : function() {
                return this._moveEnd;
            }
        },

        /**
         * Gets the event that will be raised when the camera has changed by <code>percentageChanged</code>.
         * @memberof Camera.prototype
         * @type {Event}
         * @readonly
         */
        changed : {
            get : function() {
                return this._changed;
            }
        }
    });

    /**
     * @private
     */
    Camera.prototype.update = function(mode) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(mode)) {
            throw new DeveloperError('mode is required.');
        }
        if (mode === SceneMode.SCENE2D && !(this.frustum instanceof OrthographicOffCenterFrustum)) {
            throw new DeveloperError('An OrthographicOffCenterFrustum is required in 2D.');
        }
        if ((mode === SceneMode.SCENE3D || mode === SceneMode.COLUMBUS_VIEW) &&
            (!(this.frustum instanceof PerspectiveFrustum) && !(this.frustum instanceof OrthographicFrustum))) {
            throw new DeveloperError('A PerspectiveFrustum or OrthographicFrustum is required in 3D and Columbus view');
        }
        //>>includeEnd('debug');

        var updateFrustum = false;
        if (mode !== this._mode) {
            this._mode = mode;
            this._modeChanged = mode !== SceneMode.MORPHING;
            updateFrustum = this._mode === SceneMode.SCENE2D;
        }

        if (updateFrustum) {
            var frustum = this._max2Dfrustum = this.frustum.clone();

            //>>includeStart('debug', pragmas.debug);
            if (!(frustum instanceof OrthographicOffCenterFrustum)) {
                throw new DeveloperError('The camera frustum is expected to be orthographic for 2D camera control.');
            }
            //>>includeEnd('debug');

            var maxZoomOut = 2.0;
            var ratio = frustum.top / frustum.right;
            frustum.right = this._maxCoord.x * maxZoomOut;
            frustum.left = -frustum.right;
            frustum.top = ratio * frustum.right;
            frustum.bottom = -frustum.top;
        }

        if (this._mode === SceneMode.SCENE2D) {
            clampMove2D(this, this.position);
        }

        var globe = this._scene.globe;
        var globeFinishedUpdating = !defined(globe) || (globe._surface.tileProvider.ready && globe._surface._tileLoadQueueHigh.length === 0 && globe._surface._tileLoadQueueMedium.length === 0 && globe._surface._tileLoadQueueLow.length === 0 && globe._surface._debug.tilesWaitingForChildren === 0);
        if (this._suspendTerrainAdjustment) {
            this._suspendTerrainAdjustment = !globeFinishedUpdating;
        }

        if (globeFinishedUpdating) {
            this._adjustHeightForTerrain();
        }
    };

    var setTransformPosition = new Cartesian3();
    var setTransformUp = new Cartesian3();
    var setTransformDirection = new Cartesian3();

    Camera.prototype._setTransform = function(transform) {
        var position = Cartesian3.clone(this.positionWC, setTransformPosition);
        var up = Cartesian3.clone(this.upWC, setTransformUp);
        var direction = Cartesian3.clone(this.directionWC, setTransformDirection);

        Matrix4.clone(transform, this._transform);
        this._transformChanged = true;
        updateMembers(this);
        var inverse = this._actualInvTransform;

        Matrix4.multiplyByPoint(inverse, position, this.position);
        Matrix4.multiplyByPointAsVector(inverse, direction, this.direction);
        Matrix4.multiplyByPointAsVector(inverse, up, this.up);
        Cartesian3.cross(this.direction, this.up, this.right);

        updateMembers(this);
    };

    var scratchAdjustOrtghographicFrustumMousePosition = new Cartesian2();
    var pickGlobeScratchRay = new Ray();
    var scratchRayIntersection = new Cartesian3();
    var scratchDepthIntersection = new Cartesian3();

    Camera.prototype._adjustOrthographicFrustum = function(zooming) {
        if (!(this.frustum instanceof OrthographicFrustum)) {
            return;
        }

        if (!zooming && this._positionCartographic.height < 150000.0) {
            return;
        }

        if (!Matrix4.equals(Matrix4.IDENTITY, this.transform)) {
            this.frustum.width = Cartesian3.magnitude(this.position);
            return;
        }

        var scene = this._scene;
        var globe = scene.globe;
        var rayIntersection;
        var depthIntersection;

        if (defined(globe)) {
            var mousePosition = scratchAdjustOrtghographicFrustumMousePosition;
            mousePosition.x = scene.drawingBufferWidth / 2.0;
            mousePosition.y = scene.drawingBufferHeight / 2.0;

            var ray = this.getPickRay(mousePosition, pickGlobeScratchRay);
            rayIntersection = globe.pickWorldCoordinates(ray, scene, scratchRayIntersection);

            if (scene.pickPositionSupported) {
                depthIntersection = scene.pickPositionWorldCoordinates(mousePosition, scratchDepthIntersection);
            }

            if (defined(rayIntersection) && defined(depthIntersection)) {
                var depthDistance = defined(depthIntersection) ? Cartesian3.distance(depthIntersection, this.positionWC) : Number.POSITIVE_INFINITY;
                var rayDistance = defined(rayIntersection) ? Cartesian3.distance(rayIntersection, this.positionWC) : Number.POSITIVE_INFINITY;
                this.frustum.width = Math.min(depthDistance, rayDistance);
            } else if (defined(depthIntersection)) {
                this.frustum.width = Cartesian3.distance(depthIntersection, this.positionWC);
            } else if (defined(rayIntersection)) {
                this.frustum.width = Cartesian3.distance(rayIntersection, this.positionWC);
            }
        }

        if (!defined(globe) || (!defined(rayIntersection) && !defined(depthIntersection))) {
            var distance = Math.max(this.positionCartographic.height, 0.0);
            this.frustum.width = distance;
        }
    };

    var scratchSetViewCartesian = new Cartesian3();
    var scratchSetViewTransform1 = new Matrix4();
    var scratchSetViewTransform2 = new Matrix4();
    var scratchSetViewQuaternion = new Quaternion();
    var scratchSetViewMatrix3 = new Matrix3();
    var scratchSetViewCartographic = new Cartographic();

    function setView3D(camera, position, hpr) {
        var currentTransform = Matrix4.clone(camera.transform, scratchSetViewTransform1);
        var localTransform = Transforms.eastNorthUpToFixedFrame(position, camera._projection.ellipsoid, scratchSetViewTransform2);
        camera._setTransform(localTransform);

        Cartesian3.clone(Cartesian3.ZERO, camera.position);
        hpr.heading = hpr.heading - CesiumMath.PI_OVER_TWO;

        var rotQuat = Quaternion.fromHeadingPitchRoll(hpr, scratchSetViewQuaternion);
        var rotMat = Matrix3.fromQuaternion(rotQuat, scratchSetViewMatrix3);

        Matrix3.getColumn(rotMat, 0, camera.direction);
        Matrix3.getColumn(rotMat, 2, camera.up);
        Cartesian3.cross(camera.direction, camera.up, camera.right);

        camera._setTransform(currentTransform);

        camera._adjustOrthographicFrustum(true);
    }

    function setViewCV(camera, position,hpr, convert) {
        var currentTransform = Matrix4.clone(camera.transform, scratchSetViewTransform1);
        camera._setTransform(Matrix4.IDENTITY);

        if (!Cartesian3.equals(position, camera.positionWC)) {
            if (convert) {
                var projection = camera._projection;
                var cartographic = projection.ellipsoid.cartesianToCartographic(position, scratchSetViewCartographic);
                position = projection.project(cartographic, scratchSetViewCartesian);
            }
            Cartesian3.clone(position, camera.position);
        }
        hpr.heading = hpr.heading - CesiumMath.PI_OVER_TWO;

        var rotQuat = Quaternion.fromHeadingPitchRoll(hpr, scratchSetViewQuaternion);
        var rotMat = Matrix3.fromQuaternion(rotQuat, scratchSetViewMatrix3);

        Matrix3.getColumn(rotMat, 0, camera.direction);
        Matrix3.getColumn(rotMat, 2, camera.up);
        Cartesian3.cross(camera.direction, camera.up, camera.right);

        camera._setTransform(currentTransform);

        camera._adjustOrthographicFrustum(true);
    }

    function setView2D(camera, position, hpr, convert) {
        var currentTransform = Matrix4.clone(camera.transform, scratchSetViewTransform1);
        camera._setTransform(Matrix4.IDENTITY);

        if (!Cartesian3.equals(position, camera.positionWC)) {
            if (convert) {
                var projection = camera._projection;
                var cartographic = projection.ellipsoid.cartesianToCartographic(position, scratchSetViewCartographic);
                position = projection.project(cartographic, scratchSetViewCartesian);
            }

            Cartesian2.clone(position, camera.position);

            var newLeft = -position.z * 0.5;
            var newRight = -newLeft;

            var frustum = camera.frustum;
            if (newRight > newLeft) {
                var ratio = frustum.top / frustum.right;
                frustum.right = newRight;
                frustum.left = newLeft;
                frustum.top = frustum.right * ratio;
                frustum.bottom = -frustum.top;
            }
        }

        if (camera._scene.mapMode2D === MapMode2D.ROTATE) {
            hpr.heading = hpr.heading  - CesiumMath.PI_OVER_TWO;
            hpr.pitch = -CesiumMath.PI_OVER_TWO;
            hpr.roll =  0.0;
            var rotQuat = Quaternion.fromHeadingPitchRoll(hpr, scratchSetViewQuaternion);
            var rotMat = Matrix3.fromQuaternion(rotQuat, scratchSetViewMatrix3);

            Matrix3.getColumn(rotMat, 2, camera.up);
            Cartesian3.cross(camera.direction, camera.up, camera.right);
        }

        camera._setTransform(currentTransform);
    }

    var scratchToHPRDirection = new Cartesian3();
    var scratchToHPRUp = new Cartesian3();
    var scratchToHPRRight = new Cartesian3();

    function directionUpToHeadingPitchRoll(camera, position, orientation, result) {
        var direction = Cartesian3.clone(orientation.direction, scratchToHPRDirection);
        var up = Cartesian3.clone(orientation.up, scratchToHPRUp);

        if (camera._scene.mode === SceneMode.SCENE3D) {
            var ellipsoid = camera._projection.ellipsoid;
            var transform = Transforms.eastNorthUpToFixedFrame(position, ellipsoid, scratchHPRMatrix1);
            var invTransform = Matrix4.inverseTransformation(transform, scratchHPRMatrix2);

            Matrix4.multiplyByPointAsVector(invTransform, direction, direction);
            Matrix4.multiplyByPointAsVector(invTransform, up, up);
        }

        var right = Cartesian3.cross(direction, up, scratchToHPRRight);

        result.heading = getHeading(direction, up);
        result.pitch = getPitch(direction);
        result.roll = getRoll(direction, up, right);

        return result;
    }

    var scratchSetViewOptions = {
        destination : undefined,
        orientation : {
            direction : undefined,
            up : undefined,
            heading : undefined,
            pitch : undefined,
            roll : undefined
        },
        convert : undefined,
        endTransform : undefined
    };

    var scratchHpr = new HeadingPitchRoll();
    /**
     * Sets the camera position, orientation and transform.
     *
     * @param {Object} options Object with the following properties:
     * @param {Cartesian3|Rectangle} [options.destination] The final position of the camera in WGS84 (world) coordinates or a rectangle that would be visible from a top-down view.
     * @param {Object} [options.orientation] An object that contains either direction and up properties or heading, pitch and roll properties. By default, the direction will point
     * towards the center of the frame in 3D and in the negative z direction in Columbus view. The up direction will point towards local north in 3D and in the positive
     * y direction in Columbus view. Orientation is not used in 2D when in infinite scrolling mode.
     * @param {Matrix4} [options.endTransform] Transform matrix representing the reference frame of the camera.
     * @param {Boolean} [options.convert] Whether to convert the destination from world coordinates to scene coordinates (only relevant when not using 3D). Defaults to <code>true</code>.
     *
     * @example
     * // 1. Set position with a top-down view
     * viewer.camera.setView({
     *     destination : Cesium.Cartesian3.fromDegrees(-117.16, 32.71, 15000.0)
     * });
     *
     * // 2 Set view with heading, pitch and roll
     * viewer.camera.setView({
     *     destination : cartesianPosition,
     *     orientation: {
     *         heading : Cesium.Math.toRadians(90.0), // east, default value is 0.0 (north)
     *         pitch : Cesium.Math.toRadians(-90),    // default value (looking down)
     *         roll : 0.0                             // default value
     *     }
     * });
     *
     * // 3. Change heading, pitch and roll with the camera position remaining the same.
     * viewer.camera.setView({
     *     orientation: {
     *         heading : Cesium.Math.toRadians(90.0), // east, default value is 0.0 (north)
     *         pitch : Cesium.Math.toRadians(-90),    // default value (looking down)
     *         roll : 0.0                             // default value
     *     }
     * });
     *
     *
     * // 4. View rectangle with a top-down view
     * viewer.camera.setView({
     *     destination : Cesium.Rectangle.fromDegrees(west, south, east, north)
     * });
     *
     * // 5. Set position with an orientation using unit vectors.
     * viewer.camera.setView({
     *     destination : Cesium.Cartesian3.fromDegrees(-122.19, 46.25, 5000.0),
     *     orientation : {
     *         direction : new Cesium.Cartesian3(-0.04231243104240401, -0.20123236049443421, -0.97862924300734),
     *         up : new Cesium.Cartesian3(-0.47934589305293746, -0.8553216253114552, 0.1966022179118339)
     *     }
     * });
     */
    Camera.prototype.setView = function(options) {
        options = defaultValue(options, defaultValue.EMPTY_OBJECT);
        var orientation = defaultValue(options.orientation, defaultValue.EMPTY_OBJECT);

        var mode = this._mode;
        if (mode === SceneMode.MORPHING) {
            return;
        }

        if (defined(options.endTransform)) {
            this._setTransform(options.endTransform);
        }

        var convert = defaultValue(options.convert, true);
        var destination = defaultValue(options.destination, Cartesian3.clone(this.positionWC, scratchSetViewCartesian));
        if (defined(destination) && defined(destination.west)) {
            destination = this.getRectangleCameraCoordinates(destination, scratchSetViewCartesian);
            convert = false;
        }

        if (defined(orientation.direction)) {
            orientation = directionUpToHeadingPitchRoll(this, destination, orientation, scratchSetViewOptions.orientation);
        }

        scratchHpr.heading = defaultValue(orientation.heading, 0.0);
        scratchHpr.pitch = defaultValue(orientation.pitch, -CesiumMath.PI_OVER_TWO);
        scratchHpr.roll = defaultValue(orientation.roll, 0.0);

        this._suspendTerrainAdjustment = true;

        if (mode === SceneMode.SCENE3D) {
            setView3D(this, destination, scratchHpr);
        } else if (mode === SceneMode.SCENE2D) {
            setView2D(this, destination, scratchHpr, convert);
        } else {
            setViewCV(this, destination, scratchHpr, convert);
        }
    };

    var pitchScratch = new Cartesian3();
    /**
     * Fly the camera to the home view.  Use {@link Camera#.DEFAULT_VIEW_RECTANGLE} to set
     * the default view for the 3D scene.  The home view for 2D and columbus view shows the
     * entire map.
     *
     * @param {Number} [duration] The duration of the flight in seconds. If omitted, Cesium attempts to calculate an ideal duration based on the distance to be traveled by the flight. See {@link Camera#flyTo}
     */
    Camera.prototype.flyHome = function(duration) {
        var mode = this._mode;

        if (mode === SceneMode.MORPHING) {
            this._scene.completeMorph();
        }

        if (mode === SceneMode.SCENE2D) {
            this.flyTo({
                destination : Camera.DEFAULT_VIEW_RECTANGLE,
                duration : duration,
                endTransform : Matrix4.IDENTITY
            });
        } else if (mode === SceneMode.SCENE3D) {
            var destination = this.getRectangleCameraCoordinates(Camera.DEFAULT_VIEW_RECTANGLE);

            var mag = Cartesian3.magnitude(destination);
            mag += mag * Camera.DEFAULT_VIEW_FACTOR;
            Cartesian3.normalize(destination, destination);
            Cartesian3.multiplyByScalar(destination, mag, destination);

            this.flyTo({
                destination : destination,
                duration : duration,
                endTransform : Matrix4.IDENTITY
            });
        } else if (mode === SceneMode.COLUMBUS_VIEW) {
            var maxRadii = this._projection.ellipsoid.maximumRadius;
            var position = new Cartesian3(0.0, -1.0, 1.0);
            position = Cartesian3.multiplyByScalar(Cartesian3.normalize(position, position), 5.0 * maxRadii, position);
            this.flyTo({
                destination : position,
                duration : duration,
                orientation : {
                    heading : 0.0,
                    pitch : -Math.acos(Cartesian3.normalize(position, pitchScratch).z),
                    roll : 0.0
                },
                endTransform : Matrix4.IDENTITY,
                convert : false
            });
        }
    };

    /**
     * Transform a vector or point from world coordinates to the camera's reference frame.
     *
     * @param {Cartesian4} cartesian The vector or point to transform.
     * @param {Cartesian4} [result] The object onto which to store the result.
     * @returns {Cartesian4} The transformed vector or point.
     */
    Camera.prototype.worldToCameraCoordinates = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Cartesian4();
        }
        updateMembers(this);
        return Matrix4.multiplyByVector(this._actualInvTransform, cartesian, result);
    };

    /**
     * Transform a point from world coordinates to the camera's reference frame.
     *
     * @param {Cartesian3} cartesian The point to transform.
     * @param {Cartesian3} [result] The object onto which to store the result.
     * @returns {Cartesian3} The transformed point.
     */
    Camera.prototype.worldToCameraCoordinatesPoint = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Cartesian3();
        }
        updateMembers(this);
        return Matrix4.multiplyByPoint(this._actualInvTransform, cartesian, result);
    };

    /**
     * Transform a vector from world coordinates to the camera's reference frame.
     *
     * @param {Cartesian3} cartesian The vector to transform.
     * @param {Cartesian3} [result] The object onto which to store the result.
     * @returns {Cartesian3} The transformed vector.
     */
    Camera.prototype.worldToCameraCoordinatesVector = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Cartesian3();
        }
        updateMembers(this);
        return Matrix4.multiplyByPointAsVector(this._actualInvTransform, cartesian, result);
    };

    /**
     * Transform a vector or point from the camera's reference frame to world coordinates.
     *
     * @param {Cartesian4} cartesian The vector or point to transform.
     * @param {Cartesian4} [result] The object onto which to store the result.
     * @returns {Cartesian4} The transformed vector or point.
     */
    Camera.prototype.cameraToWorldCoordinates = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Cartesian4();
        }
        updateMembers(this);
        return Matrix4.multiplyByVector(this._actualTransform, cartesian, result);
    };

    /**
     * Transform a point from the camera's reference frame to world coordinates.
     *
     * @param {Cartesian3} cartesian The point to transform.
     * @param {Cartesian3} [result] The object onto which to store the result.
     * @returns {Cartesian3} The transformed point.
     */
    Camera.prototype.cameraToWorldCoordinatesPoint = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Cartesian3();
        }
        updateMembers(this);
        return Matrix4.multiplyByPoint(this._actualTransform, cartesian, result);
    };

    /**
     * Transform a vector from the camera's reference frame to world coordinates.
     *
     * @param {Cartesian3} cartesian The vector to transform.
     * @param {Cartesian3} [result] The object onto which to store the result.
     * @returns {Cartesian3} The transformed vector.
     */
    Camera.prototype.cameraToWorldCoordinatesVector = function(cartesian, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(cartesian)) {
            throw new DeveloperError('cartesian is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Cartesian3();
        }
        updateMembers(this);
        return Matrix4.multiplyByPointAsVector(this._actualTransform, cartesian, result);
    };

    function clampMove2D(camera, position) {
        var rotatable2D = camera._scene.mapMode2D === MapMode2D.ROTATE;
        var maxProjectedX = camera._maxCoord.x;
        var maxProjectedY = camera._maxCoord.y;

        var minX;
        var maxX;
        if (rotatable2D) {
            maxX = maxProjectedX;
            minX = -maxX;
        } else {
            maxX = position.x - maxProjectedX * 2.0;
            minX = position.x + maxProjectedX * 2.0;
        }

        if (position.x > maxProjectedX) {
            position.x = maxX;
        }
        if (position.x < -maxProjectedX) {
            position.x = minX;
        }

        if (position.y > maxProjectedY) {
            position.y = maxProjectedY;
        }
        if (position.y < -maxProjectedY) {
            position.y = -maxProjectedY;
        }
    }

    var moveScratch = new Cartesian3();
    /**
     * Translates the camera's position by <code>amount</code> along <code>direction</code>.
     *
     * @param {Cartesian3} direction The direction to move.
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveBackward
     * @see Camera#moveForward
     * @see Camera#moveLeft
     * @see Camera#moveRight
     * @see Camera#moveUp
     * @see Camera#moveDown
     */
    Camera.prototype.move = function(direction, amount) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(direction)) {
            throw new DeveloperError('direction is required.');
        }
        //>>includeEnd('debug');

        var cameraPosition = this.position;
        Cartesian3.multiplyByScalar(direction, amount, moveScratch);
        Cartesian3.add(cameraPosition, moveScratch, cameraPosition);

        if (this._mode === SceneMode.SCENE2D) {
            clampMove2D(this, cameraPosition);
        }
        this._adjustOrthographicFrustum(true);
    };

    /**
     * Translates the camera's position by <code>amount</code> along the camera's view vector.
     * When in 2D mode, this will zoom in the camera instead of translating the camera's position.
     *
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveBackward
     */
    Camera.prototype.moveForward = function(amount) {
        amount = defaultValue(amount, this.defaultMoveAmount);

        if (this._mode === SceneMode.SCENE2D) {
            // 2D mode
            zoom2D(this, amount);
        } else {
            // 3D or Columbus view mode
            this.move(this.direction, amount);
        }
    };

    /**
     * Translates the camera's position by <code>amount</code> along the opposite direction
     * of the camera's view vector.
     * When in 2D mode, this will zoom out the camera instead of translating the camera's position.
     *
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveForward
     */
    Camera.prototype.moveBackward = function(amount) {
        amount = defaultValue(amount, this.defaultMoveAmount);

        if (this._mode === SceneMode.SCENE2D) {
            // 2D mode
            zoom2D(this, -amount);
        } else {
            // 3D or Columbus view mode
            this.move(this.direction, -amount);
        }
    };

    /**
     * Translates the camera's position by <code>amount</code> along the camera's up vector.
     *
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveDown
     */
    Camera.prototype.moveUp = function(amount) {
        amount = defaultValue(amount, this.defaultMoveAmount);
        this.move(this.up, amount);
    };

    /**
     * Translates the camera's position by <code>amount</code> along the opposite direction
     * of the camera's up vector.
     *
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveUp
     */
    Camera.prototype.moveDown = function(amount) {
        amount = defaultValue(amount, this.defaultMoveAmount);
        this.move(this.up, -amount);
    };

    /**
     * Translates the camera's position by <code>amount</code> along the camera's right vector.
     *
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveLeft
     */
    Camera.prototype.moveRight = function(amount) {
        amount = defaultValue(amount, this.defaultMoveAmount);
        this.move(this.right, amount);
    };

    /**
     * Translates the camera's position by <code>amount</code> along the opposite direction
     * of the camera's right vector.
     *
     * @param {Number} [amount] The amount, in meters, to move. Defaults to <code>defaultMoveAmount</code>.
     *
     * @see Camera#moveRight
     */
    Camera.prototype.moveLeft = function(amount) {
        amount = defaultValue(amount, this.defaultMoveAmount);
        this.move(this.right, -amount);
    };

    /**
     * Rotates the camera around its up vector by amount, in radians, in the opposite direction
     * of its right vector if not in 2D mode.
     *
     * @param {Number} [amount] The amount, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#lookRight
     */
    Camera.prototype.lookLeft = function(amount) {
        amount = defaultValue(amount, this.defaultLookAmount);

        // only want view of map to change in 3D mode, 2D visual is incorrect when look changes
        if (this._mode !== SceneMode.SCENE2D) {
            this.look(this.up, -amount);
        }
    };

    /**
     * Rotates the camera around its up vector by amount, in radians, in the direction
     * of its right vector if not in 2D mode.
     *
     * @param {Number} [amount] The amount, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#lookLeft
     */
    Camera.prototype.lookRight = function(amount) {
        amount = defaultValue(amount, this.defaultLookAmount);

        // only want view of map to change in 3D mode, 2D visual is incorrect when look changes
        if (this._mode !== SceneMode.SCENE2D) {
            this.look(this.up, amount);
        }
    };

    /**
     * Rotates the camera around its right vector by amount, in radians, in the direction
     * of its up vector if not in 2D mode.
     *
     * @param {Number} [amount] The amount, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#lookDown
     */
    Camera.prototype.lookUp = function(amount) {
        amount = defaultValue(amount, this.defaultLookAmount);

        // only want view of map to change in 3D mode, 2D visual is incorrect when look changes
        if (this._mode !== SceneMode.SCENE2D) {
            this.look(this.right, -amount);
        }
    };

    /**
     * Rotates the camera around its right vector by amount, in radians, in the opposite direction
     * of its up vector if not in 2D mode.
     *
     * @param {Number} [amount] The amount, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#lookUp
     */
    Camera.prototype.lookDown = function(amount) {
        amount = defaultValue(amount, this.defaultLookAmount);

        // only want view of map to change in 3D mode, 2D visual is incorrect when look changes
        if (this._mode !== SceneMode.SCENE2D) {
            this.look(this.right, amount);
        }
    };

    var lookScratchQuaternion = new Quaternion();
    var lookScratchMatrix = new Matrix3();
    /**
     * Rotate each of the camera's orientation vectors around <code>axis</code> by <code>angle</code>
     *
     * @param {Cartesian3} axis The axis to rotate around.
     * @param {Number} [angle] The angle, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#lookUp
     * @see Camera#lookDown
     * @see Camera#lookLeft
     * @see Camera#lookRight
     */
    Camera.prototype.look = function(axis, angle) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(axis)) {
            throw new DeveloperError('axis is required.');
        }
        //>>includeEnd('debug');

        var turnAngle = defaultValue(angle, this.defaultLookAmount);
        var quaternion = Quaternion.fromAxisAngle(axis, -turnAngle, lookScratchQuaternion);
        var rotation = Matrix3.fromQuaternion(quaternion, lookScratchMatrix);

        var direction = this.direction;
        var up = this.up;
        var right = this.right;

        Matrix3.multiplyByVector(rotation, direction, direction);
        Matrix3.multiplyByVector(rotation, up, up);
        Matrix3.multiplyByVector(rotation, right, right);
    };

    /**
     * Rotate the camera counter-clockwise around its direction vector by amount, in radians.
     *
     * @param {Number} [amount] The amount, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#twistRight
     */
    Camera.prototype.twistLeft = function(amount) {
        amount = defaultValue(amount, this.defaultLookAmount);
        this.look(this.direction, amount);
    };

    /**
     * Rotate the camera clockwise around its direction vector by amount, in radians.
     *
     * @param {Number} [amount] The amount, in radians, to rotate by. Defaults to <code>defaultLookAmount</code>.
     *
     * @see Camera#twistLeft
     */
    Camera.prototype.twistRight = function(amount) {
        amount = defaultValue(amount, this.defaultLookAmount);
        this.look(this.direction, -amount);
    };

    var rotateScratchQuaternion = new Quaternion();
    var rotateScratchMatrix = new Matrix3();
    /**
     * Rotates the camera around <code>axis</code> by <code>angle</code>. The distance
     * of the camera's position to the center of the camera's reference frame remains the same.
     *
     * @param {Cartesian3} axis The axis to rotate around given in world coordinates.
     * @param {Number} [angle] The angle, in radians, to rotate by. Defaults to <code>defaultRotateAmount</code>.
     *
     * @see Camera#rotateUp
     * @see Camera#rotateDown
     * @see Camera#rotateLeft
     * @see Camera#rotateRight
     */
    Camera.prototype.rotate = function(axis, angle) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(axis)) {
            throw new DeveloperError('axis is required.');
        }
        //>>includeEnd('debug');

        var turnAngle = defaultValue(angle, this.defaultRotateAmount);
        var quaternion = Quaternion.fromAxisAngle(axis, -turnAngle, rotateScratchQuaternion);
        var rotation = Matrix3.fromQuaternion(quaternion, rotateScratchMatrix);
        Matrix3.multiplyByVector(rotation, this.position, this.position);
        Matrix3.multiplyByVector(rotation, this.direction, this.direction);
        Matrix3.multiplyByVector(rotation, this.up, this.up);
        Cartesian3.cross(this.direction, this.up, this.right);
        Cartesian3.cross(this.right, this.direction, this.up);

        this._adjustOrthographicFrustum(false);
    };

    /**
     * Rotates the camera around the center of the camera's reference frame by angle downwards.
     *
     * @param {Number} [angle] The angle, in radians, to rotate by. Defaults to <code>defaultRotateAmount</code>.
     *
     * @see Camera#rotateUp
     * @see Camera#rotate
     */
    Camera.prototype.rotateDown = function(angle) {
        angle = defaultValue(angle, this.defaultRotateAmount);
        rotateVertical(this, angle);
    };

    /**
     * Rotates the camera around the center of the camera's reference frame by angle upwards.
     *
     * @param {Number} [angle] The angle, in radians, to rotate by. Defaults to <code>defaultRotateAmount</code>.
     *
     * @see Camera#rotateDown
     * @see Camera#rotate
     */
    Camera.prototype.rotateUp = function(angle) {
        angle = defaultValue(angle, this.defaultRotateAmount);
        rotateVertical(this, -angle);
    };

    var rotateVertScratchP = new Cartesian3();
    var rotateVertScratchA = new Cartesian3();
    var rotateVertScratchTan = new Cartesian3();
    var rotateVertScratchNegate = new Cartesian3();
    function rotateVertical(camera, angle) {
        var position = camera.position;
        if (defined(camera.constrainedAxis) && !Cartesian3.equalsEpsilon(camera.position, Cartesian3.ZERO, CesiumMath.EPSILON2)) {
            var p = Cartesian3.normalize(position, rotateVertScratchP);
            var northParallel = Cartesian3.equalsEpsilon(p, camera.constrainedAxis, CesiumMath.EPSILON2);
            var southParallel = Cartesian3.equalsEpsilon(p, Cartesian3.negate(camera.constrainedAxis, rotateVertScratchNegate), CesiumMath.EPSILON2);
            if ((!northParallel && !southParallel)) {
                var constrainedAxis = Cartesian3.normalize(camera.constrainedAxis, rotateVertScratchA);

                var dot = Cartesian3.dot(p, constrainedAxis);
                var angleToAxis = CesiumMath.acosClamped(dot);
                if (angle > 0 && angle > angleToAxis) {
                    angle = angleToAxis - CesiumMath.EPSILON4;
                }

                dot = Cartesian3.dot(p, Cartesian3.negate(constrainedAxis, rotateVertScratchNegate));
                angleToAxis = CesiumMath.acosClamped(dot);
                if (angle < 0 && -angle > angleToAxis) {
                    angle = -angleToAxis + CesiumMath.EPSILON4;
                }

                var tangent = Cartesian3.cross(constrainedAxis, p, rotateVertScratchTan);
                camera.rotate(tangent, angle);
            } else if ((northParallel && angle < 0) || (southParallel && angle > 0)) {
                camera.rotate(camera.right, angle);
            }
        } else {
            camera.rotate(camera.right, angle);
        }
    }

    /**
     * Rotates the camera around the center of the camera's reference frame by angle to the right.
     *
     * @param {Number} [angle] The angle, in radians, to rotate by. Defaults to <code>defaultRotateAmount</code>.
     *
     * @see Camera#rotateLeft
     * @see Camera#rotate
     */
    Camera.prototype.rotateRight = function(angle) {
        angle = defaultValue(angle, this.defaultRotateAmount);
        rotateHorizontal(this, -angle);
    };

    /**
     * Rotates the camera around the center of the camera's reference frame by angle to the left.
     *
     * @param {Number} [angle] The angle, in radians, to rotate by. Defaults to <code>defaultRotateAmount</code>.
     *
     * @see Camera#rotateRight
     * @see Camera#rotate
     */
    Camera.prototype.rotateLeft = function(angle) {
        angle = defaultValue(angle, this.defaultRotateAmount);
        rotateHorizontal(this, angle);
    };

    function rotateHorizontal(camera, angle) {
        if (defined(camera.constrainedAxis)) {
            camera.rotate(camera.constrainedAxis, angle);
        } else {
            camera.rotate(camera.up, angle);
        }
    }

    function zoom2D(camera, amount) {
        var frustum = camera.frustum;

        //>>includeStart('debug', pragmas.debug);
        if (!(frustum instanceof OrthographicOffCenterFrustum) || !defined(frustum.left) || !defined(frustum.right) ||
            !defined(frustum.bottom) || !defined(frustum.top)) {
            throw new DeveloperError('The camera frustum is expected to be orthographic for 2D camera control.');
        }
        //>>includeEnd('debug');

        var ratio;
        amount = amount * 0.5;

        if((Math.abs(frustum.top) + Math.abs(frustum.bottom)) > (Math.abs(frustum.left) + Math.abs(frustum.right))) {
            var newTop = frustum.top - amount;
            var newBottom = frustum.bottom + amount;

            var maxBottom = camera._maxCoord.y;
            if (camera._scene.mapMode2D === MapMode2D.ROTATE) {
                maxBottom *= camera.maximumZoomFactor;
            }

            if (newBottom > maxBottom) {
                newBottom = maxBottom;
                newTop = -maxBottom;
            }

            if (newTop <= newBottom) {
                newTop = 1.0;
                newBottom = -1.0;
            }

            ratio = frustum.right / frustum.top;
            frustum.top = newTop;
            frustum.bottom = newBottom;
            frustum.right = frustum.top * ratio;
            frustum.left = -frustum.right;
        } else {
            var newRight = frustum.right - amount;
            var newLeft = frustum.left + amount;

            var maxRight = camera._maxCoord.x;
            if (camera._scene.mapMode2D === MapMode2D.ROTATE) {
                maxRight *= camera.maximumZoomFactor;
            }

            if (newRight > maxRight) {
                newRight = maxRight;
                newLeft = -maxRight;
            }

            if (newRight <= newLeft) {
                newRight = 1.0;
                newLeft = -1.0;
            }
            ratio = frustum.top / frustum.right;
            frustum.right = newRight;
            frustum.left = newLeft;
            frustum.top = frustum.right * ratio;
            frustum.bottom = -frustum.top;
        }
    }

    function zoom3D(camera, amount) {
        camera.move(camera.direction, amount);
    }

    /**
     * Zooms <code>amount</code> along the camera's view vector.
     *
     * @param {Number} [amount] The amount to move. Defaults to <code>defaultZoomAmount</code>.
     *
     * @see Camera#zoomOut
     */
    Camera.prototype.zoomIn = function(amount) {
        amount = defaultValue(amount, this.defaultZoomAmount);
        if (this._mode === SceneMode.SCENE2D) {
            zoom2D(this, amount);
        } else {
            zoom3D(this, amount);
        }
    };

    /**
     * Zooms <code>amount</code> along the opposite direction of
     * the camera's view vector.
     *
     * @param {Number} [amount] The amount to move. Defaults to <code>defaultZoomAmount</code>.
     *
     * @see Camera#zoomIn
     */
    Camera.prototype.zoomOut = function(amount) {
        amount = defaultValue(amount, this.defaultZoomAmount);
        if (this._mode === SceneMode.SCENE2D) {
            zoom2D(this, -amount);
        } else {
            zoom3D(this, -amount);
        }
    };

    /**
     * Gets the magnitude of the camera position. In 3D, this is the vector magnitude. In 2D and
     * Columbus view, this is the distance to the map.
     *
     * @returns {Number} The magnitude of the position.
     */
    Camera.prototype.getMagnitude = function() {
        if (this._mode === SceneMode.SCENE3D) {
            return Cartesian3.magnitude(this.position);
        } else if (this._mode === SceneMode.COLUMBUS_VIEW) {
            return Math.abs(this.position.z);
        } else if (this._mode === SceneMode.SCENE2D) {
            return Math.max(this.frustum.right - this.frustum.left, this.frustum.top - this.frustum.bottom);
        }
    };

    var scratchLookAtMatrix4 = new Matrix4();

    /**
     * Sets the camera position and orientation using a target and offset. The target must be given in
     * world coordinates. The offset can be either a cartesian or heading/pitch/range in the local east-north-up reference frame centered at the target.
     * If the offset is a cartesian, then it is an offset from the center of the reference frame defined by the transformation matrix. If the offset
     * is heading/pitch/range, then the heading and the pitch angles are defined in the reference frame defined by the transformation matrix.
     * The heading is the angle from y axis and increasing towards the x axis. Pitch is the rotation from the xy-plane. Positive pitch
     * angles are below the plane. Negative pitch angles are above the plane. The range is the distance from the center.
     *
     * In 2D, there must be a top down view. The camera will be placed above the target looking down. The height above the
     * target will be the magnitude of the offset. The heading will be determined from the offset. If the heading cannot be
     * determined from the offset, the heading will be north.
     *
     * @param {Cartesian3} target The target position in world coordinates.
     * @param {Cartesian3|HeadingPitchRange} offset The offset from the target in the local east-north-up reference frame centered at the target.
     *
     * @exception {DeveloperError} lookAt is not supported while morphing.
     *
     * @example
     * // 1. Using a cartesian offset
     * var center = Cesium.Cartesian3.fromDegrees(-98.0, 40.0);
     * viewer.camera.lookAt(center, new Cesium.Cartesian3(0.0, -4790000.0, 3930000.0));
     *
     * // 2. Using a HeadingPitchRange offset
     * var center = Cesium.Cartesian3.fromDegrees(-72.0, 40.0);
     * var heading = Cesium.Math.toRadians(50.0);
     * var pitch = Cesium.Math.toRadians(-20.0);
     * var range = 5000.0;
     * viewer.camera.lookAt(center, new Cesium.HeadingPitchRange(heading, pitch, range));
     */
    Camera.prototype.lookAt = function(target, offset) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(target)) {
            throw new DeveloperError('target is required');
        }
        if (!defined(offset)) {
            throw new DeveloperError('offset is required');
        }
        if (this._mode === SceneMode.MORPHING) {
            throw new DeveloperError('lookAt is not supported while morphing.');
        }
        //>>includeEnd('debug');

        var transform = Transforms.eastNorthUpToFixedFrame(target, Ellipsoid.WGS84, scratchLookAtMatrix4);
        this.lookAtTransform(transform, offset);
    };

    var scratchLookAtHeadingPitchRangeOffset = new Cartesian3();
    var scratchLookAtHeadingPitchRangeQuaternion1 = new Quaternion();
    var scratchLookAtHeadingPitchRangeQuaternion2 = new Quaternion();
    var scratchHeadingPitchRangeMatrix3 = new Matrix3();

    function offsetFromHeadingPitchRange(heading, pitch, range) {
        pitch = CesiumMath.clamp(pitch, -CesiumMath.PI_OVER_TWO, CesiumMath.PI_OVER_TWO);
        heading = CesiumMath.zeroToTwoPi(heading) - CesiumMath.PI_OVER_TWO;

        var pitchQuat = Quaternion.fromAxisAngle(Cartesian3.UNIT_Y, -pitch, scratchLookAtHeadingPitchRangeQuaternion1);
        var headingQuat = Quaternion.fromAxisAngle(Cartesian3.UNIT_Z, -heading, scratchLookAtHeadingPitchRangeQuaternion2);
        var rotQuat = Quaternion.multiply(headingQuat, pitchQuat, headingQuat);
        var rotMatrix = Matrix3.fromQuaternion(rotQuat, scratchHeadingPitchRangeMatrix3);

        var offset = Cartesian3.clone(Cartesian3.UNIT_X, scratchLookAtHeadingPitchRangeOffset);
        Matrix3.multiplyByVector(rotMatrix, offset, offset);
        Cartesian3.negate(offset, offset);
        Cartesian3.multiplyByScalar(offset, range, offset);
        return offset;
    }

    /**
     * Sets the camera position and orientation using a target and transformation matrix. The offset can be either a cartesian or heading/pitch/range.
     * If the offset is a cartesian, then it is an offset from the center of the reference frame defined by the transformation matrix. If the offset
     * is heading/pitch/range, then the heading and the pitch angles are defined in the reference frame defined by the transformation matrix.
     * The heading is the angle from y axis and increasing towards the x axis. Pitch is the rotation from the xy-plane. Positive pitch
     * angles are below the plane. Negative pitch angles are above the plane. The range is the distance from the center.
     *
     * In 2D, there must be a top down view. The camera will be placed above the center of the reference frame. The height above the
     * target will be the magnitude of the offset. The heading will be determined from the offset. If the heading cannot be
     * determined from the offset, the heading will be north.
     *
     * @param {Matrix4} transform The transformation matrix defining the reference frame.
     * @param {Cartesian3|HeadingPitchRange} [offset] The offset from the target in a reference frame centered at the target.
     *
     * @exception {DeveloperError} lookAtTransform is not supported while morphing.
     *
     * @example
     * // 1. Using a cartesian offset
     * var transform = Cesium.Transforms.eastNorthUpToFixedFrame(Cesium.Cartesian3.fromDegrees(-98.0, 40.0));
     * viewer.camera.lookAtTransform(transform, new Cesium.Cartesian3(0.0, -4790000.0, 3930000.0));
     *
     * // 2. Using a HeadingPitchRange offset
     * var transform = Cesium.Transforms.eastNorthUpToFixedFrame(Cesium.Cartesian3.fromDegrees(-72.0, 40.0));
     * var heading = Cesium.Math.toRadians(50.0);
     * var pitch = Cesium.Math.toRadians(-20.0);
     * var range = 5000.0;
     * viewer.camera.lookAtTransform(transform, new Cesium.HeadingPitchRange(heading, pitch, range));
     */
    Camera.prototype.lookAtTransform = function(transform, offset) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(transform)) {
            throw new DeveloperError('transform is required');
        }
        if (this._mode === SceneMode.MORPHING) {
            throw new DeveloperError('lookAtTransform is not supported while morphing.');
        }
        //>>includeEnd('debug');

        this._setTransform(transform);
        if (!defined(offset)) {
            return;
        }

        var cartesianOffset;
        if (defined(offset.heading)) {
            cartesianOffset = offsetFromHeadingPitchRange(offset.heading, offset.pitch, offset.range);
        } else {
            cartesianOffset = offset;
        }

        if (this._mode === SceneMode.SCENE2D) {
            Cartesian2.clone(Cartesian2.ZERO, this.position);

            Cartesian3.negate(cartesianOffset, this.up);
            this.up.z = 0.0;

            if (Cartesian3.magnitudeSquared(this.up) < CesiumMath.EPSILON10) {
                Cartesian3.clone(Cartesian3.UNIT_Y, this.up);
            }

            Cartesian3.normalize(this.up, this.up);

            this._setTransform(Matrix4.IDENTITY);

            Cartesian3.negate(Cartesian3.UNIT_Z, this.direction);
            Cartesian3.cross(this.direction, this.up, this.right);
            Cartesian3.normalize(this.right, this.right);

            var frustum = this.frustum;
            var ratio = frustum.top / frustum.right;
            frustum.right = Cartesian3.magnitude(cartesianOffset) * 0.5;
            frustum.left = -frustum.right;
            frustum.top = ratio * frustum.right;
            frustum.bottom = -frustum.top;

            this._setTransform(transform);

            return;
        }

        Cartesian3.clone(cartesianOffset, this.position);
        Cartesian3.negate(this.position, this.direction);
        Cartesian3.normalize(this.direction, this.direction);
        Cartesian3.cross(this.direction, Cartesian3.UNIT_Z, this.right);

        if (Cartesian3.magnitudeSquared(this.right) < CesiumMath.EPSILON10) {
            Cartesian3.clone(Cartesian3.UNIT_X, this.right);
        }

        Cartesian3.normalize(this.right, this.right);
        Cartesian3.cross(this.right, this.direction, this.up);
        Cartesian3.normalize(this.up, this.up);

        this._adjustOrthographicFrustum(true);
    };

    var viewRectangle3DCartographic1 = new Cartographic();
    var viewRectangle3DCartographic2 = new Cartographic();
    var viewRectangle3DNorthEast = new Cartesian3();
    var viewRectangle3DSouthWest = new Cartesian3();
    var viewRectangle3DNorthWest = new Cartesian3();
    var viewRectangle3DSouthEast = new Cartesian3();
    var viewRectangle3DNorthCenter = new Cartesian3();
    var viewRectangle3DSouthCenter = new Cartesian3();
    var viewRectangle3DCenter = new Cartesian3();
    var viewRectangle3DEquator = new Cartesian3();
    var defaultRF = {
        direction : new Cartesian3(),
        right : new Cartesian3(),
        up : new Cartesian3()
    };
    var viewRectangle3DEllipsoidGeodesic;

    function computeD(direction, upOrRight, corner, tanThetaOrPhi) {
        var opposite = Math.abs(Cartesian3.dot(upOrRight, corner));
        return opposite / tanThetaOrPhi - Cartesian3.dot(direction, corner);
    }

    function rectangleCameraPosition3D(camera, rectangle, result, updateCamera) {
        var ellipsoid = camera._projection.ellipsoid;
        var cameraRF = updateCamera ? camera : defaultRF;

        var north = rectangle.north;
        var south = rectangle.south;
        var east = rectangle.east;
        var west = rectangle.west;

        // If we go across the International Date Line
        if (west > east) {
            east += CesiumMath.TWO_PI;
        }

        // Find the midpoint latitude.
        //
        // EllipsoidGeodesic will fail if the north and south edges are very close to being on opposite sides of the ellipsoid.
        // Ideally we'd just call EllipsoidGeodesic.setEndPoints and let it throw when it detects this case, but sadly it doesn't
        // even look for this case in optimized builds, so we have to test for it here instead.
        //
        // Fortunately, this case can only happen (here) when north is very close to the north pole and south is very close to the south pole,
        // so handle it just by using 0 latitude as the center.  It's certainliy possible to use a smaller tolerance
        // than one degree here, but one degree is safe and putting the center at 0 latitude should be good enough for any
        // rectangle that spans 178+ of the 180 degrees of latitude.
        var longitude = (west + east) * 0.5;
        var latitude;
        if (south < -CesiumMath.PI_OVER_TWO + CesiumMath.RADIANS_PER_DEGREE && north > CesiumMath.PI_OVER_TWO - CesiumMath.RADIANS_PER_DEGREE) {
            latitude = 0.0;
        } else {
            var northCartographic = viewRectangle3DCartographic1;
            northCartographic.longitude = longitude;
            northCartographic.latitude = north;
            northCartographic.height = 0.0;

            var southCartographic = viewRectangle3DCartographic2;
            southCartographic.longitude = longitude;
            southCartographic.latitude = south;
            southCartographic.height = 0.0;

            var ellipsoidGeodesic = viewRectangle3DEllipsoidGeodesic;
            if (!defined(ellipsoidGeodesic) || ellipsoidGeodesic.ellipsoid !== ellipsoid) {
                viewRectangle3DEllipsoidGeodesic = ellipsoidGeodesic = new EllipsoidGeodesic(undefined, undefined, ellipsoid);
            }

            ellipsoidGeodesic.setEndPoints(northCartographic, southCartographic);
            latitude = ellipsoidGeodesic.interpolateUsingFraction(0.5, viewRectangle3DCartographic1).latitude;
        }

        var centerCartographic = viewRectangle3DCartographic1;
        centerCartographic.longitude = longitude;
        centerCartographic.latitude = latitude;
        centerCartographic.height = 0.0;

        var center = ellipsoid.cartographicToCartesian(centerCartographic, viewRectangle3DCenter);

        var cart = viewRectangle3DCartographic1;
        cart.longitude = east;
        cart.latitude = north;
        var northEast = ellipsoid.cartographicToCartesian(cart, viewRectangle3DNorthEast);
        cart.longitude = west;
        var northWest = ellipsoid.cartographicToCartesian(cart, viewRectangle3DNorthWest);
        cart.longitude = longitude;
        var northCenter = ellipsoid.cartographicToCartesian(cart, viewRectangle3DNorthCenter);
        cart.latitude = south;
        var southCenter = ellipsoid.cartographicToCartesian(cart, viewRectangle3DSouthCenter);
        cart.longitude = east;
        var southEast = ellipsoid.cartographicToCartesian(cart, viewRectangle3DSouthEast);
        cart.longitude = west;
        var southWest = ellipsoid.cartographicToCartesian(cart, viewRectangle3DSouthWest);

        Cartesian3.subtract(northWest, center, northWest);
        Cartesian3.subtract(southEast, center, southEast);
        Cartesian3.subtract(northEast, center, northEast);
        Cartesian3.subtract(southWest, center, southWest);
        Cartesian3.subtract(northCenter, center, northCenter);
        Cartesian3.subtract(southCenter, center, southCenter);

        var direction = ellipsoid.geodeticSurfaceNormal(center, cameraRF.direction);
        Cartesian3.negate(direction, direction);
        var right = Cartesian3.cross(direction, Cartesian3.UNIT_Z, cameraRF.right);
        Cartesian3.normalize(right, right);
        var up = Cartesian3.cross(right, direction, cameraRF.up);

        var d;
        if (camera.frustum instanceof OrthographicFrustum) {
            var width = Math.max(Cartesian3.distance(northEast, northWest), Cartesian3.distance(southEast, southWest));
            var height = Math.max(Cartesian3.distance(northEast, southEast), Cartesian3.distance(northWest, southWest));

            var rightScalar;
            var topScalar;
            var ratio = camera.frustum._offCenterFrustum.right / camera.frustum._offCenterFrustum.top;
            var heightRatio = height * ratio;
            if (width > heightRatio) {
                rightScalar = width;
                topScalar = rightScalar / ratio;
            } else {
                topScalar = height;
                rightScalar = heightRatio;
            }

            d = Math.max(rightScalar, topScalar);
        } else {
            var tanPhi = Math.tan(camera.frustum.fovy * 0.5);
            var tanTheta = camera.frustum.aspectRatio * tanPhi;

            d = Math.max(
                computeD(direction, up, northWest, tanPhi),
                computeD(direction, up, southEast, tanPhi),
                computeD(direction, up, northEast, tanPhi),
                computeD(direction, up, southWest, tanPhi),
                computeD(direction, up, northCenter, tanPhi),
                computeD(direction, up, southCenter, tanPhi),
                computeD(direction, right, northWest, tanTheta),
                computeD(direction, right, southEast, tanTheta),
                computeD(direction, right, northEast, tanTheta),
                computeD(direction, right, southWest, tanTheta),
                computeD(direction, right, northCenter, tanTheta),
                computeD(direction, right, southCenter, tanTheta));

            // If the rectangle crosses the equator, compute D at the equator, too, because that's the
            // widest part of the rectangle when projected onto the globe.
            if (south < 0 && north > 0) {
                var equatorCartographic = viewRectangle3DCartographic1;
                equatorCartographic.longitude = west;
                equatorCartographic.latitude = 0.0;
                equatorCartographic.height = 0.0;
                var equatorPosition = ellipsoid.cartographicToCartesian(equatorCartographic, viewRectangle3DEquator);
                Cartesian3.subtract(equatorPosition, center, equatorPosition);
                d = Math.max(d, computeD(direction, up, equatorPosition, tanPhi), computeD(direction, right, equatorPosition, tanTheta));

                equatorCartographic.longitude = east;
                equatorPosition = ellipsoid.cartographicToCartesian(equatorCartographic, viewRectangle3DEquator);
                Cartesian3.subtract(equatorPosition, center, equatorPosition);
                d = Math.max(d, computeD(direction, up, equatorPosition, tanPhi), computeD(direction, right, equatorPosition, tanTheta));
            }
        }

        return Cartesian3.add(center, Cartesian3.multiplyByScalar(direction, -d, viewRectangle3DEquator), result);
    }

    var viewRectangleCVCartographic = new Cartographic();
    var viewRectangleCVNorthEast = new Cartesian3();
    var viewRectangleCVSouthWest = new Cartesian3();
    function rectangleCameraPositionColumbusView(camera, rectangle, result) {
        var projection = camera._projection;
        if (rectangle.west > rectangle.east) {
            rectangle = Rectangle.MAX_VALUE;
        }
        var transform = camera._actualTransform;
        var invTransform = camera._actualInvTransform;

        var cart = viewRectangleCVCartographic;
        cart.longitude = rectangle.east;
        cart.latitude = rectangle.north;
        var northEast = projection.project(cart, viewRectangleCVNorthEast);
        Matrix4.multiplyByPoint(transform, northEast, northEast);
        Matrix4.multiplyByPoint(invTransform, northEast, northEast);

        cart.longitude = rectangle.west;
        cart.latitude = rectangle.south;
        var southWest = projection.project(cart, viewRectangleCVSouthWest);
        Matrix4.multiplyByPoint(transform, southWest, southWest);
        Matrix4.multiplyByPoint(invTransform, southWest, southWest);

        result.x = (northEast.x - southWest.x) * 0.5 + southWest.x;
        result.y = (northEast.y - southWest.y) * 0.5 + southWest.y;

        if (defined(camera.frustum.fovy)) {
            var tanPhi = Math.tan(camera.frustum.fovy * 0.5);
            var tanTheta = camera.frustum.aspectRatio * tanPhi;
            result.z = Math.max((northEast.x - southWest.x) / tanTheta, (northEast.y - southWest.y) / tanPhi) * 0.5;
        } else {
            var width = northEast.x - southWest.x;
            var height = northEast.y - southWest.y;
            result.z = Math.max(width, height);
        }

        return result;
    }

    var viewRectangle2DCartographic = new Cartographic();
    var viewRectangle2DNorthEast = new Cartesian3();
    var viewRectangle2DSouthWest = new Cartesian3();
    function rectangleCameraPosition2D(camera, rectangle, result) {
        var projection = camera._projection;

        // Account for the rectangle crossing the International Date Line in 2D mode
        var east = rectangle.east;
        if (rectangle.west > rectangle.east) {
            if(camera._scene.mapMode2D === MapMode2D.INFINITE_SCROLL) {
                east += CesiumMath.TWO_PI;
            } else {
                rectangle = Rectangle.MAX_VALUE;
                east = rectangle.east;
            }
        }

        var cart = viewRectangle2DCartographic;
        cart.longitude = east;
        cart.latitude = rectangle.north;
        var northEast = projection.project(cart, viewRectangle2DNorthEast);
        cart.longitude = rectangle.west;
        cart.latitude = rectangle.south;
        var southWest = projection.project(cart, viewRectangle2DSouthWest);

        var width = Math.abs(northEast.x - southWest.x) * 0.5;
        var height = Math.abs(northEast.y - southWest.y) * 0.5;

        var right, top;
        var ratio = camera.frustum.right / camera.frustum.top;
        var heightRatio = height * ratio;
        if (width > heightRatio) {
            right = width;
            top = right / ratio;
        } else {
            top = height;
            right = heightRatio;
        }

        height = Math.max(2.0 * right, 2.0 * top);

        result.x = (northEast.x - southWest.x) * 0.5 + southWest.x;
        result.y = (northEast.y - southWest.y) * 0.5 + southWest.y;

        cart = projection.unproject(result, cart);
        cart.height = height;
        result = projection.project(cart, result);

        return result;
    }

    /**
     * Get the camera position needed to view a rectangle on an ellipsoid or map
     *
     * @param {Rectangle} rectangle The rectangle to view.
     * @param {Cartesian3} [result] The camera position needed to view the rectangle
     * @returns {Cartesian3} The camera position needed to view the rectangle
     */
    Camera.prototype.getRectangleCameraCoordinates = function(rectangle, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(rectangle)) {
            throw new DeveloperError('rectangle is required');
        }
        //>>includeEnd('debug');
        var mode = this._mode;

        if (!defined(result)) {
            result = new Cartesian3();
        }

        if (mode === SceneMode.SCENE3D) {
            return rectangleCameraPosition3D(this, rectangle, result);
        } else if (mode === SceneMode.COLUMBUS_VIEW) {
            return rectangleCameraPositionColumbusView(this, rectangle, result);
        } else if (mode === SceneMode.SCENE2D) {
            return rectangleCameraPosition2D(this, rectangle, result);
        }

        return undefined;
    };

    var pickEllipsoid3DRay = new Ray();
    function pickEllipsoid3D(camera, windowPosition, ellipsoid, result) {
        ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
        var ray = camera.getPickRay(windowPosition, pickEllipsoid3DRay);
        var intersection = IntersectionTests.rayEllipsoid(ray, ellipsoid);
        if (!intersection) {
            return undefined;
        }

        var t = intersection.start > 0.0 ? intersection.start : intersection.stop;
        return Ray.getPoint(ray, t, result);
    }

    var pickEllipsoid2DRay = new Ray();
    function pickMap2D(camera, windowPosition, projection, result) {
        var ray = camera.getPickRay(windowPosition, pickEllipsoid2DRay);
        var position = ray.origin;
        position = Cartesian3.fromElements(position.y, position.z, 0.0, position);
        var cart = projection.unproject(position);

        if (cart.latitude < -CesiumMath.PI_OVER_TWO || cart.latitude > CesiumMath.PI_OVER_TWO) {
            return undefined;
        }

        return projection.ellipsoid.cartographicToCartesian(cart, result);
    }

    var pickEllipsoidCVRay = new Ray();
    function pickMapColumbusView(camera, windowPosition, projection, result) {
        var ray = camera.getPickRay(windowPosition, pickEllipsoidCVRay);
        var scalar = -ray.origin.x / ray.direction.x;
        Ray.getPoint(ray, scalar, result);

        var cart = projection.unproject(new Cartesian3(result.y, result.z, 0.0));

        if (cart.latitude < -CesiumMath.PI_OVER_TWO || cart.latitude > CesiumMath.PI_OVER_TWO ||
            cart.longitude < -Math.PI || cart.longitude > Math.PI) {
            return undefined;
        }

        return projection.ellipsoid.cartographicToCartesian(cart, result);
    }

    /**
     * Pick an ellipsoid or map.
     *
     * @param {Cartesian2} windowPosition The x and y coordinates of a pixel.
     * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to pick.
     * @param {Cartesian3} [result] The object onto which to store the result.
     * @returns {Cartesian3} If the ellipsoid or map was picked, returns the point on the surface of the ellipsoid or map
     * in world coordinates. If the ellipsoid or map was not picked, returns undefined.
     */
    Camera.prototype.pickEllipsoid = function(windowPosition, ellipsoid, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(windowPosition)) {
            throw new DeveloperError('windowPosition is required.');
        }
        //>>includeEnd('debug');

        var canvas = this._scene.canvas;
        if (canvas.clientWidth === 0 || canvas.clientHeight === 0) {
            return undefined;
        }

        if (!defined(result)) {
            result = new Cartesian3();
        }

        ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);

        if (this._mode === SceneMode.SCENE3D) {
            result = pickEllipsoid3D(this, windowPosition, ellipsoid, result);
        } else if (this._mode === SceneMode.SCENE2D) {
            result = pickMap2D(this, windowPosition, this._projection, result);
        } else if (this._mode === SceneMode.COLUMBUS_VIEW) {
            result = pickMapColumbusView(this, windowPosition, this._projection, result);
        } else {
            return undefined;
        }

        return result;
    };

    var pickPerspCenter = new Cartesian3();
    var pickPerspXDir = new Cartesian3();
    var pickPerspYDir = new Cartesian3();
    function getPickRayPerspective(camera, windowPosition, result) {
        var canvas = camera._scene.canvas;
        var width = canvas.clientWidth;
        var height = canvas.clientHeight;

        var tanPhi = Math.tan(camera.frustum.fovy * 0.5);
        var tanTheta = camera.frustum.aspectRatio * tanPhi;
        var near = camera.frustum.near;

        var x = (2.0 / width) * windowPosition.x - 1.0;
        var y = (2.0 / height) * (height - windowPosition.y) - 1.0;

        var position = camera.positionWC;
        Cartesian3.clone(position, result.origin);

        var nearCenter = Cartesian3.multiplyByScalar(camera.directionWC, near, pickPerspCenter);
        Cartesian3.add(position, nearCenter, nearCenter);
        var xDir = Cartesian3.multiplyByScalar(camera.rightWC, x * near * tanTheta, pickPerspXDir);
        var yDir = Cartesian3.multiplyByScalar(camera.upWC, y * near * tanPhi, pickPerspYDir);
        var direction = Cartesian3.add(nearCenter, xDir, result.direction);
        Cartesian3.add(direction, yDir, direction);
        Cartesian3.subtract(direction, position, direction);
        Cartesian3.normalize(direction, direction);

        return result;
    }

    var scratchDirection = new Cartesian3();

    function getPickRayOrthographic(camera, windowPosition, result) {
        var canvas = camera._scene.canvas;
        var width = canvas.clientWidth;
        var height = canvas.clientHeight;

        var frustum = camera.frustum;
        if (defined(frustum._offCenterFrustum)) {
            frustum = frustum._offCenterFrustum;
        }
        var x = (2.0 / width) * windowPosition.x - 1.0;
        x *= (frustum.right - frustum.left) * 0.5;
        var y = (2.0 / height) * (height - windowPosition.y) - 1.0;
        y *= (frustum.top - frustum.bottom) * 0.5;

        var origin = result.origin;
        Cartesian3.clone(camera.position, origin);

        Cartesian3.multiplyByScalar(camera.right, x, scratchDirection);
        Cartesian3.add(scratchDirection, origin, origin);
        Cartesian3.multiplyByScalar(camera.up, y, scratchDirection);
        Cartesian3.add(scratchDirection, origin, origin);

        Cartesian3.clone(camera.directionWC, result.direction);

        if (camera._mode === SceneMode.COLUMBUS_VIEW || camera._mode === SceneMode.SCENE2D) {
            Cartesian3.fromElements(result.origin.z, result.origin.x, result.origin.y, result.origin);
        }

        return result;
    }

    /**
     * Create a ray from the camera position through the pixel at <code>windowPosition</code>
     * in world coordinates.
     *
     * @param {Cartesian2} windowPosition The x and y coordinates of a pixel.
     * @param {Ray} [result] The object onto which to store the result.
     * @returns {Ray} Returns the {@link Cartesian3} position and direction of the ray.
     */
    Camera.prototype.getPickRay = function(windowPosition, result) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(windowPosition)) {
            throw new DeveloperError('windowPosition is required.');
        }
        //>>includeEnd('debug');

        if (!defined(result)) {
            result = new Ray();
        }

        var frustum = this.frustum;
        if (defined(frustum.aspectRatio) && defined(frustum.fov) && defined(frustum.near)) {
            return getPickRayPerspective(this, windowPosition, result);
        }

        return getPickRayOrthographic(this, windowPosition, result);
    };

    var scratchToCenter = new Cartesian3();
    var scratchProj = new Cartesian3();

    /**
     * Return the distance from the camera to the front of the bounding sphere.
     *
     * @param {BoundingSphere} boundingSphere The bounding sphere in world coordinates.
     * @returns {Number} The distance to the bounding sphere.
     */
    Camera.prototype.distanceToBoundingSphere = function(boundingSphere) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(boundingSphere)) {
            throw new DeveloperError('boundingSphere is required.');
        }
        //>>includeEnd('debug');

        var toCenter = Cartesian3.subtract(this.positionWC, boundingSphere.center, scratchToCenter);
        var proj = Cartesian3.multiplyByScalar(this.directionWC, Cartesian3.dot(toCenter, this.directionWC), scratchProj);
        return Math.max(0.0, Cartesian3.magnitude(proj) - boundingSphere.radius);
    };

    var scratchPixelSize = new Cartesian2();

    /**
     * Return the pixel size in meters.
     *
     * @param {BoundingSphere} boundingSphere The bounding sphere in world coordinates.
     * @param {Number} drawingBufferWidth The drawing buffer width.
     * @param {Number} drawingBufferHeight The drawing buffer height.
     * @returns {Number} The pixel size in meters.
     */
    Camera.prototype.getPixelSize = function(boundingSphere, drawingBufferWidth, drawingBufferHeight) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(boundingSphere)) {
            throw new DeveloperError('boundingSphere is required.');
        }
        if (!defined(drawingBufferWidth)) {
            throw new DeveloperError('drawingBufferWidth is required.');
        }
        if (!defined(drawingBufferHeight)) {
            throw new DeveloperError('drawingBufferHeight is required.');
        }
        //>>includeEnd('debug');

        var distance = this.distanceToBoundingSphere(boundingSphere);
        var pixelSize = this.frustum.getPixelDimensions(drawingBufferWidth, drawingBufferHeight, distance, this._scene.pixelRatio, scratchPixelSize);
        return Math.max(pixelSize.x, pixelSize.y);
    };

    function createAnimationTemplateCV(camera, position, center, maxX, maxY, duration) {
        var newPosition = Cartesian3.clone(position);

        if (center.y > maxX) {
            newPosition.y -= center.y - maxX;
        } else if (center.y < -maxX) {
            newPosition.y += -maxX - center.y;
        }

        if (center.z > maxY) {
            newPosition.z -= center.z - maxY;
        } else if (center.z < -maxY) {
            newPosition.z += -maxY - center.z;
        }

        function updateCV(value) {
            var interp = Cartesian3.lerp(position, newPosition, value.time, new Cartesian3());
            camera.worldToCameraCoordinatesPoint(interp, camera.position);
        }
        return {
            easingFunction : EasingFunction.EXPONENTIAL_OUT,
            startObject : {
                time : 0.0
            },
            stopObject : {
                time : 1.0
            },
            duration : duration,
            update : updateCV
        };
    }

    var normalScratch = new Cartesian3();
    var centerScratch = new Cartesian3();
    var posScratch = new Cartesian3();
    var scratchCartesian3Subtract = new Cartesian3();

    function createAnimationCV(camera, duration) {
        var position = camera.position;
        var direction = camera.direction;

        var normal = camera.worldToCameraCoordinatesVector(Cartesian3.UNIT_X, normalScratch);
        var scalar = -Cartesian3.dot(normal, position) / Cartesian3.dot(normal, direction);
        var center = Cartesian3.add(position, Cartesian3.multiplyByScalar(direction, scalar, centerScratch), centerScratch);
        camera.cameraToWorldCoordinatesPoint(center, center);

        position = camera.cameraToWorldCoordinatesPoint(camera.position, posScratch);

        var tanPhi = Math.tan(camera.frustum.fovy * 0.5);
        var tanTheta = camera.frustum.aspectRatio * tanPhi;
        var distToC = Cartesian3.magnitude(Cartesian3.subtract(position, center, scratchCartesian3Subtract));
        var dWidth = tanTheta * distToC;
        var dHeight = tanPhi * distToC;

        var mapWidth = camera._maxCoord.x;
        var mapHeight = camera._maxCoord.y;

        var maxX = Math.max(dWidth - mapWidth, mapWidth);
        var maxY = Math.max(dHeight - mapHeight, mapHeight);

        if (position.z < -maxX || position.z > maxX || position.y < -maxY || position.y > maxY) {
            var translateX = center.y < -maxX || center.y > maxX;
            var translateY = center.z < -maxY || center.z > maxY;
            if (translateX || translateY) {
                return createAnimationTemplateCV(camera, position, center, maxX, maxY, duration);
            }
        }

        return undefined;
    }

    /**
     * Create an animation to move the map into view. This method is only valid for 2D and Columbus modes.
     *
     * @param {Number} duration The duration, in seconds, of the animation.
     * @returns {Object} The animation or undefined if the scene mode is 3D or the map is already ion view.
     *
     * @private
     */
    Camera.prototype.createCorrectPositionTween = function(duration) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(duration)) {
            throw new DeveloperError('duration is required.');
        }
        //>>includeEnd('debug');

        if (this._mode === SceneMode.COLUMBUS_VIEW) {
            return createAnimationCV(this, duration);
        }

        return undefined;
    };

    var scratchFlyToDestination = new Cartesian3();
    var newOptions = {
        destination : undefined,
        heading : undefined,
        pitch : undefined,
        roll : undefined,
        duration : undefined,
        complete : undefined,
        cancel : undefined,
        endTransform : undefined,
        maximumHeight : undefined,
        easingFunction : undefined
    };

    /**
     * Cancels the current camera flight if one is in progress.
     * The camera is left at it's current location.
     */
    Camera.prototype.cancelFlight = function () {
        if (defined(this._currentFlight)) {
            this._currentFlight.cancelTween();
            this._currentFlight = undefined;
        }
    };

    /**
     * Flies the camera from its current position to a new position.
     *
     * @param {Object} options Object with the following properties:
     * @param {Cartesian3|Rectangle} options.destination The final position of the camera in WGS84 (world) coordinates or a rectangle that would be visible from a top-down view.
     * @param {Object} [options.orientation] An object that contains either direction and up properties or heading, pitch and roll properties. By default, the direction will point
     * towards the center of the frame in 3D and in the negative z direction in Columbus view. The up direction will point towards local north in 3D and in the positive
     * y direction in Columbus view.  Orientation is not used in 2D when in infinite scrolling mode.
     * @param {Number} [options.duration] The duration of the flight in seconds. If omitted, Cesium attempts to calculate an ideal duration based on the distance to be traveled by the flight.
     * @param {Camera~FlightCompleteCallback} [options.complete] The function to execute when the flight is complete.
     * @param {Camera~FlightCancelledCallback} [options.cancel] The function to execute if the flight is cancelled.
     * @param {Matrix4} [options.endTransform] Transform matrix representing the reference frame the camera will be in when the flight is completed.
     * @param {Number} [options.maximumHeight] The maximum height at the peak of the flight.
     * @param {Number} [options.pitchAdjustHeight] If camera flyes higher than that value, adjust pitch duiring the flight to look down, and keep Earth in viewport.
     * @param {Number} [options.flyOverLongitude] There are always two ways between 2 points on globe. This option force camera to choose fight direction to fly over that longitude.
     * @param {Number} [options.flyOverLongitudeWeight] Fly over the lon specifyed via flyOverLongitude only if that way is not longer than short way times flyOverLongitudeWeight.
     * @param {Boolean} [options.convert] Whether to convert the destination from world coordinates to scene coordinates (only relevant when not using 3D). Defaults to <code>true</code>.
     * @param {EasingFunction|EasingFunction~Callback} [options.easingFunction] Controls how the time is interpolated over the duration of the flight.
     *
     * @exception {DeveloperError} If either direction or up is given, then both are required.
     *
     * @example
     * // 1. Fly to a position with a top-down view
     * viewer.camera.flyTo({
     *     destination : Cesium.Cartesian3.fromDegrees(-117.16, 32.71, 15000.0)
     * });
     *
     * // 2. Fly to a Rectangle with a top-down view
     * viewer.camera.flyTo({
     *     destination : Cesium.Rectangle.fromDegrees(west, south, east, north)
     * });
     *
     * // 3. Fly to a position with an orientation using unit vectors.
     * viewer.camera.flyTo({
     *     destination : Cesium.Cartesian3.fromDegrees(-122.19, 46.25, 5000.0),
     *     orientation : {
     *         direction : new Cesium.Cartesian3(-0.04231243104240401, -0.20123236049443421, -0.97862924300734),
     *         up : new Cesium.Cartesian3(-0.47934589305293746, -0.8553216253114552, 0.1966022179118339)
     *     }
     * });
     *
     * // 4. Fly to a position with an orientation using heading, pitch and roll.
     * viewer.camera.flyTo({
     *     destination : Cesium.Cartesian3.fromDegrees(-122.19, 46.25, 5000.0),
     *     orientation : {
     *         heading : Cesium.Math.toRadians(175.0),
     *         pitch : Cesium.Math.toRadians(-35.0),
     *         roll : 0.0
     *     }
     * });
     */
    Camera.prototype.flyTo = function(options) {
        options = defaultValue(options, defaultValue.EMPTY_OBJECT);
        var destination = options.destination;
        //>>includeStart('debug', pragmas.debug);
        if (!defined(destination)) {
            throw new DeveloperError('destination is required.');
        }
        //>>includeEnd('debug');

        var mode = this._mode;
        if (mode === SceneMode.MORPHING) {
            return;
        }

        this.cancelFlight();

        var orientation = defaultValue(options.orientation, defaultValue.EMPTY_OBJECT);
        if (defined(orientation.direction)) {
            orientation = directionUpToHeadingPitchRoll(this, destination, orientation, scratchSetViewOptions.orientation);
        }

        if (defined(options.duration) && options.duration <= 0.0) {
            var setViewOptions = scratchSetViewOptions;
            setViewOptions.destination = options.destination;
            setViewOptions.orientation.heading = orientation.heading;
            setViewOptions.orientation.pitch = orientation.pitch;
            setViewOptions.orientation.roll = orientation.roll;
            setViewOptions.convert = options.convert;
            setViewOptions.endTransform = options.endTransform;
            this.setView(setViewOptions);
            if (typeof options.complete === 'function') {
                options.complete();
            }
            return;
        }

        var isRectangle = defined(destination.west);
        if (isRectangle) {
            destination = this.getRectangleCameraCoordinates(destination, scratchFlyToDestination);
        }

        var that = this;
        var flightTween;

        newOptions.destination = destination;
        newOptions.heading = orientation.heading;
        newOptions.pitch = orientation.pitch;
        newOptions.roll = orientation.roll;
        newOptions.duration = options.duration;
        newOptions.complete = function () {
            if(flightTween === that._currentFlight){
                that._currentFlight = undefined;
            }
            if (defined(options.complete)) {
                options.complete();
            }
        };
        newOptions.cancel = options.cancel;
        newOptions.endTransform = options.endTransform;
        newOptions.convert = isRectangle ? false : options.convert;
        newOptions.maximumHeight = options.maximumHeight;
        newOptions.pitchAdjustHeight = options.pitchAdjustHeight;
        newOptions.flyOverLongitude = options.flyOverLongitude;
        newOptions.flyOverLongitudeWeight = options.flyOverLongitudeWeight;
        newOptions.easingFunction = options.easingFunction;

        var scene = this._scene;
        flightTween = scene.tweens.add(CameraFlightPath.createTween(scene, newOptions));
        this._currentFlight = flightTween;

        // Save the final destination view information for the PRELOAD_FLIGHT pass.
        var preloadFlightCamera = this._scene.preloadFlightCamera;
        if (this._mode !== SceneMode.SCENE2D) {
            if (!defined(preloadFlightCamera)) {
                preloadFlightCamera = Camera.clone(this);
            }
            preloadFlightCamera.setView({ destination: destination, orientation: orientation });

            this._scene.preloadFlightCullingVolume = preloadFlightCamera.frustum.computeCullingVolume(preloadFlightCamera.positionWC, preloadFlightCamera.directionWC, preloadFlightCamera.upWC);
        } else {
            preloadFlightCamera = undefined;
        }
    };

    function distanceToBoundingSphere3D(camera, radius) {
        var frustum = camera.frustum;
        var tanPhi = Math.tan(frustum.fovy * 0.5);
        var tanTheta = frustum.aspectRatio * tanPhi;
        return Math.max(radius / tanTheta, radius / tanPhi);
    }

    function distanceToBoundingSphere2D(camera, radius) {
        var frustum = camera.frustum;
        if (defined(frustum._offCenterFrustum)) {
            frustum = frustum._offCenterFrustum;
        }

        var right, top;
        var ratio = frustum.right / frustum.top;
        var heightRatio = radius * ratio;
        if (radius > heightRatio) {
            right = radius;
            top = right / ratio;
        } else {
            top = radius;
            right = heightRatio;
        }

        return Math.max(right, top) * 1.50;
    }

    var MINIMUM_ZOOM = 100.0;

    function adjustBoundingSphereOffset(camera, boundingSphere, offset) {
        if (!defined(offset)) {
            offset = HeadingPitchRange.clone(Camera.DEFAULT_OFFSET);
        }

        var minimumZoom = camera._scene.screenSpaceCameraController.minimumZoomDistance;
        var maximumZoom = camera._scene.screenSpaceCameraController.maximumZoomDistance;
        var range = offset.range;
        if (!defined(range) || range === 0.0) {
            var radius = boundingSphere.radius;
            if (radius === 0.0) {
                offset.range = MINIMUM_ZOOM;
            } else if (camera.frustum instanceof OrthographicFrustum || camera._mode === SceneMode.SCENE2D) {
                offset.range = distanceToBoundingSphere2D(camera, radius);
            } else {
                offset.range = distanceToBoundingSphere3D(camera, radius);
            }
            offset.range = CesiumMath.clamp(offset.range, minimumZoom, maximumZoom);
        }

        return offset;
    }

    /**
     * Sets the camera so that the current view contains the provided bounding sphere.
     *
     * <p>The offset is heading/pitch/range in the local east-north-up reference frame centered at the center of the bounding sphere.
     * The heading and the pitch angles are defined in the local east-north-up reference frame.
     * The heading is the angle from y axis and increasing towards the x axis. Pitch is the rotation from the xy-plane. Positive pitch
     * angles are below the plane. Negative pitch angles are above the plane. The range is the distance from the center. If the range is
     * zero, a range will be computed such that the whole bounding sphere is visible.</p>
     *
     * <p>In 2D, there must be a top down view. The camera will be placed above the target looking down. The height above the
     * target will be the range. The heading will be determined from the offset. If the heading cannot be
     * determined from the offset, the heading will be north.</p>
     *
     * @param {BoundingSphere} boundingSphere The bounding sphere to view, in world coordinates.
     * @param {HeadingPitchRange} [offset] The offset from the target in the local east-north-up reference frame centered at the target.
     *
     * @exception {DeveloperError} viewBoundingSphere is not supported while morphing.
     */
    Camera.prototype.viewBoundingSphere = function(boundingSphere, offset) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(boundingSphere)) {
            throw new DeveloperError('boundingSphere is required.');
        }

        if (this._mode === SceneMode.MORPHING) {
            throw new DeveloperError('viewBoundingSphere is not supported while morphing.');
        }
        //>>includeEnd('debug');

        offset = adjustBoundingSphereOffset(this, boundingSphere, offset);
        this.lookAt(boundingSphere.center, offset);
    };

    var scratchflyToBoundingSphereTransform = new Matrix4();
    var scratchflyToBoundingSphereDestination = new Cartesian3();
    var scratchflyToBoundingSphereDirection = new Cartesian3();
    var scratchflyToBoundingSphereUp = new Cartesian3();
    var scratchflyToBoundingSphereRight = new Cartesian3();
    var scratchFlyToBoundingSphereCart4 = new Cartesian4();
    var scratchFlyToBoundingSphereQuaternion = new Quaternion();
    var scratchFlyToBoundingSphereMatrix3 = new Matrix3();

    /**
     * Flies the camera to a location where the current view contains the provided bounding sphere.
     *
     * <p> The offset is heading/pitch/range in the local east-north-up reference frame centered at the center of the bounding sphere.
     * The heading and the pitch angles are defined in the local east-north-up reference frame.
     * The heading is the angle from y axis and increasing towards the x axis. Pitch is the rotation from the xy-plane. Positive pitch
     * angles are below the plane. Negative pitch angles are above the plane. The range is the distance from the center. If the range is
     * zero, a range will be computed such that the whole bounding sphere is visible.</p>
     *
     * <p>In 2D and Columbus View, there must be a top down view. The camera will be placed above the target looking down. The height above the
     * target will be the range. The heading will be aligned to local north.</p>
     *
     * @param {BoundingSphere} boundingSphere The bounding sphere to view, in world coordinates.
     * @param {Object} [options] Object with the following properties:
     * @param {Number} [options.duration] The duration of the flight in seconds. If omitted, Cesium attempts to calculate an ideal duration based on the distance to be traveled by the flight.
     * @param {HeadingPitchRange} [options.offset] The offset from the target in the local east-north-up reference frame centered at the target.
     * @param {Camera~FlightCompleteCallback} [options.complete] The function to execute when the flight is complete.
     * @param {Camera~FlightCancelledCallback} [options.cancel] The function to execute if the flight is cancelled.
     * @param {Matrix4} [options.endTransform] Transform matrix representing the reference frame the camera will be in when the flight is completed.
     * @param {Number} [options.maximumHeight] The maximum height at the peak of the flight.
     * @param {Number} [options.pitchAdjustHeight] If camera flyes higher than that value, adjust pitch duiring the flight to look down, and keep Earth in viewport.
     * @param {Number} [options.flyOverLongitude] There are always two ways between 2 points on globe. This option force camera to choose fight direction to fly over that longitude.
     * @param {Number} [options.flyOverLongitudeWeight] Fly over the lon specifyed via flyOverLongitude only if that way is not longer than short way times flyOverLongitudeWeight.
     * @param {EasingFunction|EasingFunction~Callback} [options.easingFunction] Controls how the time is interpolated over the duration of the flight.
     */
    Camera.prototype.flyToBoundingSphere = function(boundingSphere, options) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(boundingSphere)) {
            throw new DeveloperError('boundingSphere is required.');
        }
        //>>includeEnd('debug');

        options = defaultValue(options, defaultValue.EMPTY_OBJECT);
        var scene2D = this._mode === SceneMode.SCENE2D || this._mode === SceneMode.COLUMBUS_VIEW;
        this._setTransform(Matrix4.IDENTITY);
        var offset = adjustBoundingSphereOffset(this, boundingSphere, options.offset);

        var position;
        if (scene2D) {
            position = Cartesian3.multiplyByScalar(Cartesian3.UNIT_Z, offset.range, scratchflyToBoundingSphereDestination);
        } else {
            position = offsetFromHeadingPitchRange(offset.heading, offset.pitch, offset.range);
        }

        var transform = Transforms.eastNorthUpToFixedFrame(boundingSphere.center, Ellipsoid.WGS84, scratchflyToBoundingSphereTransform);
        Matrix4.multiplyByPoint(transform, position, position);

        var direction;
        var up;

        if (!scene2D) {
            direction = Cartesian3.subtract(boundingSphere.center, position, scratchflyToBoundingSphereDirection);
            Cartesian3.normalize(direction, direction);

            up = Matrix4.multiplyByPointAsVector(transform, Cartesian3.UNIT_Z, scratchflyToBoundingSphereUp);
            if (1.0 - Math.abs(Cartesian3.dot(direction, up)) < CesiumMath.EPSILON6) {
                var rotateQuat = Quaternion.fromAxisAngle(direction, offset.heading, scratchFlyToBoundingSphereQuaternion);
                var rotation = Matrix3.fromQuaternion(rotateQuat, scratchFlyToBoundingSphereMatrix3);

                Cartesian3.fromCartesian4(Matrix4.getColumn(transform, 1, scratchFlyToBoundingSphereCart4), up);
                Matrix3.multiplyByVector(rotation, up, up);
            }

            var right = Cartesian3.cross(direction, up, scratchflyToBoundingSphereRight);
            Cartesian3.cross(right, direction, up);
            Cartesian3.normalize(up, up);
        }

        this.flyTo({
            destination : position,
            orientation : {
                direction : direction,
                up : up
            },
            duration : options.duration,
            complete : options.complete,
            cancel : options.cancel,
            endTransform : options.endTransform,
            maximumHeight : options.maximumHeight,
            easingFunction : options.easingFunction,
            flyOverLongitude : options.flyOverLongitude,
            flyOverLongitudeWeight : options.flyOverLongitudeWeight,
            pitchAdjustHeight : options.pitchAdjustHeight
        });
    };

    var scratchCartesian3_1 = new Cartesian3();
    var scratchCartesian3_2 = new Cartesian3();
    var scratchCartesian3_3 = new Cartesian3();
    var scratchCartesian3_4 = new Cartesian3();
    var horizonPoints = [new Cartesian3(), new Cartesian3(), new Cartesian3(), new Cartesian3()];

    function computeHorizonQuad(camera, ellipsoid) {
        var radii = ellipsoid.radii;
        var p = camera.positionWC;

        // Find the corresponding position in the scaled space of the ellipsoid.
        var q = Cartesian3.multiplyComponents(ellipsoid.oneOverRadii, p, scratchCartesian3_1);

        var qMagnitude = Cartesian3.magnitude(q);
        var qUnit = Cartesian3.normalize(q, scratchCartesian3_2);

        // Determine the east and north directions at q.
        var eUnit;
        var nUnit;
        if (Cartesian3.equalsEpsilon(qUnit, Cartesian3.UNIT_Z, CesiumMath.EPSILON10)) {
            eUnit = new Cartesian3(0, 1, 0);
            nUnit = new Cartesian3(0, 0, 1);
        } else {
            eUnit = Cartesian3.normalize(Cartesian3.cross(Cartesian3.UNIT_Z, qUnit, scratchCartesian3_3), scratchCartesian3_3);
            nUnit = Cartesian3.normalize(Cartesian3.cross(qUnit, eUnit, scratchCartesian3_4), scratchCartesian3_4);
        }

        // Determine the radius of the 'limb' of the ellipsoid.
        var wMagnitude = Math.sqrt(Cartesian3.magnitudeSquared(q) - 1.0);

        // Compute the center and offsets.
        var center = Cartesian3.multiplyByScalar(qUnit, 1.0 / qMagnitude, scratchCartesian3_1);
        var scalar = wMagnitude / qMagnitude;
        var eastOffset = Cartesian3.multiplyByScalar(eUnit, scalar, scratchCartesian3_2);
        var northOffset = Cartesian3.multiplyByScalar(nUnit, scalar, scratchCartesian3_3);

        // A conservative measure for the longitudes would be to use the min/max longitudes of the bounding frustum.
        var upperLeft = Cartesian3.add(center, northOffset, horizonPoints[0]);
        Cartesian3.subtract(upperLeft, eastOffset, upperLeft);
        Cartesian3.multiplyComponents(radii, upperLeft, upperLeft);

        var lowerLeft = Cartesian3.subtract(center, northOffset, horizonPoints[1]);
        Cartesian3.subtract(lowerLeft, eastOffset, lowerLeft);
        Cartesian3.multiplyComponents(radii, lowerLeft, lowerLeft);

        var lowerRight = Cartesian3.subtract(center, northOffset, horizonPoints[2]);
        Cartesian3.add(lowerRight, eastOffset, lowerRight);
        Cartesian3.multiplyComponents(radii, lowerRight, lowerRight);

        var upperRight = Cartesian3.add(center, northOffset, horizonPoints[3]);
        Cartesian3.add(upperRight, eastOffset, upperRight);
        Cartesian3.multiplyComponents(radii, upperRight, upperRight);

        return horizonPoints;
    }

    var scratchPickCartesian2 = new Cartesian2();
    var scratchRectCartesian = new Cartesian3();
    var cartoArray = [new Cartographic(), new Cartographic(), new Cartographic(), new Cartographic()];
    function addToResult(x, y, index, camera, ellipsoid, computedHorizonQuad) {
        scratchPickCartesian2.x = x;
        scratchPickCartesian2.y = y;
        var r = camera.pickEllipsoid(scratchPickCartesian2, ellipsoid, scratchRectCartesian);
        if (defined(r)) {
            cartoArray[index] = ellipsoid.cartesianToCartographic(r, cartoArray[index]);
            return 1;
        }
        cartoArray[index] = ellipsoid.cartesianToCartographic(computedHorizonQuad[index], cartoArray[index]);
        return 0;
    }
    /**
     * Computes the approximate visible rectangle on the ellipsoid.
     *
     * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid that you want to know the visible region.
     * @param {Rectangle} [result] The rectangle in which to store the result
     *
     * @returns {Rectangle|undefined} The visible rectangle or undefined if the ellipsoid isn't visible at all.
     */
    Camera.prototype.computeViewRectangle = function(ellipsoid, result) {
        ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
        var cullingVolume = this.frustum.computeCullingVolume(this.positionWC, this.directionWC, this.upWC);
        var boundingSphere = new BoundingSphere(Cartesian3.ZERO, ellipsoid.maximumRadius);
        var visibility = cullingVolume.computeVisibility(boundingSphere);
        if (visibility === Intersect.OUTSIDE) {
            return undefined;
        }

        var canvas = this._scene.canvas;
        var width = canvas.clientWidth;
        var height = canvas.clientHeight;

        var successfulPickCount = 0;

        var computedHorizonQuad = computeHorizonQuad(this, ellipsoid);

        successfulPickCount += addToResult(0, 0, 0, this, ellipsoid, computedHorizonQuad);
        successfulPickCount += addToResult(0, height, 1, this, ellipsoid, computedHorizonQuad);
        successfulPickCount += addToResult(width, height, 2, this, ellipsoid, computedHorizonQuad);
        successfulPickCount += addToResult(width, 0, 3, this, ellipsoid, computedHorizonQuad);

        if (successfulPickCount < 2) {
            // If we have space non-globe in 3 or 4 corners then return the whole globe
            return Rectangle.MAX_VALUE;
        }

        result = Rectangle.fromCartographicArray(cartoArray, result);

        // Detect if we go over the poles
        var distance = 0;
        var lastLon = cartoArray[3].longitude;
        for (var i = 0; i < 4; ++i) {
            var lon = cartoArray[i].longitude;
            var diff = Math.abs(lon - lastLon);
            if (diff > CesiumMath.PI) {
                // Crossed the dateline
                distance += CesiumMath.TWO_PI - diff;
            } else {
                distance += diff;
            }

            lastLon = lon;
        }

        // We are over one of the poles so adjust the rectangle accordingly
        if (CesiumMath.equalsEpsilon(Math.abs(distance), CesiumMath.TWO_PI, CesiumMath.EPSILON9)) {
            result.west = -CesiumMath.PI;
            result.east = CesiumMath.PI;
            if (cartoArray[0].latitude >= 0.0) {
                result.north = CesiumMath.PI_OVER_TWO;
            } else {
                result.south = -CesiumMath.PI_OVER_TWO;
            }
        }

        return result;
    };

    /**
     * Switches the frustum/projection to perspective.
     *
     * This function is a no-op in 2D which must always be orthographic.
     */
    Camera.prototype.switchToPerspectiveFrustum = function() {
        if (this._mode === SceneMode.SCENE2D || this.frustum instanceof PerspectiveFrustum) {
            return;
        }

        var scene = this._scene;
        this.frustum = new PerspectiveFrustum();
        this.frustum.aspectRatio = scene.drawingBufferWidth / scene.drawingBufferHeight;
        this.frustum.fov = CesiumMath.toRadians(60.0);
    };

    /**
     * Switches the frustum/projection to orthographic.
     *
     * This function is a no-op in 2D which will always be orthographic.
     */
    Camera.prototype.switchToOrthographicFrustum = function() {
        if (this._mode === SceneMode.SCENE2D || this.frustum instanceof OrthographicFrustum) {
            return;
        }

        var scene = this._scene;
        this.frustum = new OrthographicFrustum();
        this.frustum.aspectRatio = scene.drawingBufferWidth / scene.drawingBufferHeight;

        // It doesn't matter what we set this to. The adjust below will correct the width based on the camera position.
        this.frustum.width = Cartesian3.magnitude(this.position);

        // Check the projection matrix. It will always be defined, but we need to force an off-center update.
        var projectionMatrix = this.frustum.projectionMatrix;
        if (defined(projectionMatrix)) {
            this._adjustOrthographicFrustum(true);
        }
    };

    /**
     * @private
     */
    Camera.clone = function(camera, result) {
        if (!defined(result)) {
            result = new Camera(camera._scene);
        }

        Cartesian3.clone(camera.position, result.position);
        Cartesian3.clone(camera.direction, result.direction);
        Cartesian3.clone(camera.up, result.up);
        Cartesian3.clone(camera.right, result.right);
        Matrix4.clone(camera._transform, result.transform);
        result._transformChanged = true;
        result.frustum = camera.frustum.clone();

        return result;
    };

    /**
     * A function that will execute when a flight completes.
     * @callback Camera~FlightCompleteCallback
     */

    /**
     * A function that will execute when a flight is cancelled.
     * @callback Camera~FlightCancelledCallback
     */
export default Camera;