Camera.js

/*global define*/
define([
        '../Core/BoundingSphere',
        '../Core/Cartesian2',
        '../Core/Cartesian3',
        '../Core/Cartesian4',
        '../Core/Cartographic',
        '../Core/defaultValue',
        '../Core/defined',
        '../Core/defineProperties',
        '../Core/DeveloperError',
        '../Core/EasingFunction',
        '../Core/Ellipsoid',
        '../Core/EllipsoidGeodesic',
        '../Core/Event',
        '../Core/HeadingPitchRange',
        '../Core/Intersect',
        '../Core/IntersectionTests',
        '../Core/Math',
        '../Core/Matrix3',
        '../Core/Matrix4',
        '../Core/Quaternion',
        '../Core/Ray',
        '../Core/Rectangle',
        '../Core/Transforms',
        './CameraFlightPath',
        './PerspectiveFrustum',
        './SceneMode'
    ], function(
        BoundingSphere,
        Cartesian2,
        Cartesian3,
        Cartesian4,
        Cartographic,
        defaultValue,
        defined,
        defineProperties,
        DeveloperError,
        EasingFunction,
        Ellipsoid,
        EllipsoidGeodesic,
        Event,
        HeadingPitchRange,
        Intersect,
        IntersectionTests,
        CesiumMath,
        Matrix3,
        Matrix4,
        Quaternion,
        Ray,
        Rectangle,
        Transforms,
        CameraFlightPath,
        PerspectiveFrustum,
        SceneMode) {
    'use strict';

    /**
     * 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 http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Camera.html|Cesium Sandcastle Camera Demo}
     * @demo {@link http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Camera%20Tutorial.html">Sandcastle Example</a> from the <a href="http://cesiumjs.org/2013/02/13/Cesium-Camera-Tutorial/|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();

        /**
         * 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 translating across the surface. The default is 1.5. Only valid for 2D and Columbus view.
         * @type {Number}
         * @default 1.5
         */
        this.maximumTranslateFactor = 1.5;
        /**
         * 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 2.5. Only valid for 2D.
         * @type {Number}
         * @default 2.5
         */
        this.maximumZoomFactor = 2.5;

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

        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;

        // 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;

    function updateViewMatrix(camera) {
        var r = camera._right;
        var u = camera._up;
        var d = camera._direction;
        var e = camera._position;

        var viewMatrix = camera._viewMatrix;
        viewMatrix[0] = r.x;
        viewMatrix[1] = u.x;
        viewMatrix[2] = -d.x;
        viewMatrix[3] = 0.0;
        viewMatrix[4] = r.y;
        viewMatrix[5] = u.y;
        viewMatrix[6] = -d.y;
        viewMatrix[7] = 0.0;
        viewMatrix[8] = r.z;
        viewMatrix[9] = u.z;
        viewMatrix[10] = -d.z;
        viewMatrix[11] = 0.0;
        viewMatrix[12] = -Cartesian3.dot(r, e);
        viewMatrix[13] = -Cartesian3.dot(u, e);
        viewMatrix[14] = Cartesian3.dot(d, e);
        viewMatrix[15] = 1.0;

        Matrix4.multiply(viewMatrix, camera._actualInvTransform, camera._viewMatrix);
        Matrix4.inverseTransformation(camera._viewMatrix, camera._invViewMatrix);
    }

    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 convertTransformForColumbusView(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 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);

        var yAxis = Cartesian4.add(Matrix4.getColumn(camera._transform, 1, scratchCartesian3), origin, scratchCartesian3);
        ellipsoid.cartesianToCartographic(yAxis, cartographic);

        projection.project(cartographic, projectedPosition);
        var newYAxis = scratchCartesian4NewYAxis;
        newYAxis.x = projectedPosition.z;
        newYAxis.y = projectedPosition.x;
        newYAxis.z = projectedPosition.y;
        newYAxis.w = 0.0;

        Cartesian3.subtract(newYAxis, newOrigin, newYAxis);

        var newZAxis = scratchCartesian4NewZAxis;
        Cartesian3.cross(newXAxis, newYAxis, newZAxis);
        Cartesian3.normalize(newZAxis, newZAxis);
        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);
    }

    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);
        }

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

        if (rightChanged || transformChanged) {
            camera._rightWC = Matrix4.multiplyByPointAsVector(transform, right, 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}
         */
        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 at when the camera has stopped moving.
         * @memberof Camera.prototype
         * @type {Event}
         * @readonly
         */
        moveEnd : {
            get : function() {
                return this._moveEnd;
            }
        }
    });

    /**
     * @private
     */
    Camera.prototype.update = function(mode) {
        //>>includeStart('debug', pragmas.debug);
        if (!defined(mode)) {
            throw new DeveloperError('mode is required.');
        }
        //>>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 (!defined(frustum.left) || !defined(frustum.right) ||
               !defined(frustum.top) || !defined(frustum.bottom)) {
                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 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 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, heading, pitch, roll) {
        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);

        var rotQuat = Quaternion.fromHeadingPitchRoll(heading - CesiumMath.PI_OVER_TWO, pitch, roll, 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);
    }

    function setViewCV(camera, position, heading, pitch, roll, 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);
        }

        var rotQuat = Quaternion.fromHeadingPitchRoll(heading - CesiumMath.PI_OVER_TWO, pitch, roll, 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);
    }

    function setView2D(camera, position, 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;
            }
        }

        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
    };

    /**
     * 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, pith 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.
     * @param {Matrix4} [options.endTransform] Transform matrix representing the reference frame of the camera.
     *
     * @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. Setposition 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);
        }

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

        if (mode === SceneMode.SCENE3D) {
            setView3D(this, destination, heading, pitch, roll);
        } else if (mode === SceneMode.SCENE2D) {
            setView2D(this, destination, convert);
        } else {
            setViewCV(this, destination, heading, pitch, roll, 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 number of seconds to complete the camera flight to home. 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 : Rectangle.MAX_VALUE,
                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 maxX = camera._maxCoord.x;
        if (position.x > maxX) {
            position.x = position.x - maxX * 2.0;
        }
        if (position.x < -maxX) {
            position.x = position.x + maxX * 2.0;
        }

        var maxY = camera._maxCoord.y;
        if (position.y > maxY) {
            position.y = maxY;
        }
        if (position.y < -maxY) {
            position.y = -maxY;
        }
    }

    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);
        }
    };

    /**
     * Translates the camera's position by <code>amount</code> along the camera's view vector.
     *
     * @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);
        this.move(this.direction, amount);
    };

    /**
     * Translates the camera's position by <code>amount</code> along the opposite direction
     * of the camera's view vector.
     *
     * @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);
        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.
     *
     * @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);
        this.look(this.up, -amount);
    };

    /**
     * Rotates the camera around its up vector by amount, in radians, in the direction
     * of its right vector.
     *
     * @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);
        this.look(this.up, amount);
    };

    /**
     * Rotates the camera around its right vector by amount, in radians, in the direction
     * of its up vector.
     *
     * @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);
        this.look(this.right, -amount);
    };

    /**
     * Rotates the camera around its right vector by amount, in radians, in the opposite direction
     * of its up vector.
     *
     * @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);
        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);
    };

    /**
     * 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;
        var p = Cartesian3.normalize(position, rotateVertScratchP);
        if (defined(camera.constrainedAxis)) {
            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 (!defined(frustum.left) || !defined(frustum.right) || !defined(frustum.top) || !defined(frustum.bottom)) {
            throw new DeveloperError('The camera frustum is expected to be orthographic for 2D camera control.');
        }
        //>>includeEnd('debug');

        amount = amount * 0.5;
        var newRight = frustum.right - amount;
        var newLeft = frustum.left + amount;

        var maxRight = camera._maxCoord.x;
        if (newRight > maxRight) {
            newRight = maxRight;
            newLeft = -maxRight;
        }

        if (newRight <= newLeft) {
            newRight = 1.0;
            newLeft = -1.0;
        }

        var 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);
    };

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

        var 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);

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

        result.x = (northEast.x - southWest.x) * 0.5 + southWest.x;
        result.y = (northEast.y - southWest.y) * 0.5 + southWest.y;
        result.z = Math.max((northEast.x - southWest.x) / tanTheta, (northEast.y - southWest.y) / tanPhi) * 0.5;

        return result;
    }

    var viewRectangle2DCartographic = new Cartographic();
    var viewRectangle2DNorthEast = new Cartesian3();
    var viewRectangle2DSouthWest = new Cartesian3();
    function rectangleCameraPosition2D (camera, rectangle, result) {
        var projection = camera._projection;
        if (rectangle.west > rectangle.east) {
            rectangle = Rectangle.MAX_VALUE;
        }

        var cart = viewRectangle2DCartographic;
        cart.longitude = rectangle.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 an 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.z = 0.0;
        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');

        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 x = (2.0 / width) * windowPosition.x - 1.0;
        x *= (camera.frustum.right - camera.frustum.left) * 0.5;
        var y = (2.0 / height) * (height - windowPosition.y) - 1.0;
        y *= (camera.frustum.top - camera.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);

        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, 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 scratchFlyToCarto = new Cartographic();
    var newOptions = {
        destination : undefined,
        heading : undefined,
        pitch : undefined,
        roll : undefined,
        duration : undefined,
        complete : undefined,
        cancel : undefined,
        endTransform : undefined,
        maximumHeight : undefined,
        easingFunction : 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, pith 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.
     * @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 {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;
        }

        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 sscc = this._scene.screenSpaceCameraController;

        if (defined(sscc) || mode === SceneMode.SCENE2D) {
            var ellipsoid = this._scene.mapProjection.ellipsoid;
            var destinationCartographic = ellipsoid.cartesianToCartographic(destination, scratchFlyToCarto);
            var height = destinationCartographic.height;

            // Make sure camera doesn't zoom outside set limits
            if (defined(sscc)) {
                //The computed height for rectangle in 2D/CV is stored in the 'z' component of Cartesian3
                if (mode !== SceneMode.SCENE3D && isRectangle) {
                    destination.z = CesiumMath.clamp(destination.z, sscc.minimumZoomDistance, sscc.maximumZoomDistance);
                } else {
                    destinationCartographic.height = CesiumMath.clamp(destinationCartographic.height, sscc.minimumZoomDistance, sscc.maximumZoomDistance);
                }
            }

            // The max height in 2D might be lower than the max height for sscc.
            if (mode === SceneMode.SCENE2D) {
                var maxHeight = ellipsoid.maximumRadius * Math.PI * 2.0;
                if (isRectangle) {
                    destination.z = Math.min(destination.z, maxHeight);
                } else {
                    destinationCartographic.height = Math.min(destinationCartographic.height, maxHeight);
                }
            }

            //Only change if we clamped the height
            if (destinationCartographic.height !== height) {
                destination = ellipsoid.cartographicToCartesian(destinationCartographic, scratchFlyToDestination);
            }
        }

        newOptions.destination = destination;
        newOptions.heading = orientation.heading;
        newOptions.pitch = orientation.pitch;
        newOptions.roll = orientation.roll;
        newOptions.duration = options.duration;
        newOptions.complete = options.complete;
        newOptions.cancel = options.cancel;
        newOptions.endTransform = options.endTransform;
        newOptions.convert = isRectangle ? false : options.convert;
        newOptions.maximumHeight = options.maximumHeight;
        newOptions.easingFunction = options.easingFunction;

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

    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;

        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 scratchDefaultOffset = new HeadingPitchRange(0.0, -CesiumMath.PI_OVER_FOUR, 0.0);
    var MINIMUM_ZOOM = 100.0;

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

        var range = offset.range;
        if (!defined(range) || range === 0.0) {
            var radius = boundingSphere.radius;
            if (radius === 0.0) {
                offset.range = MINIMUM_ZOOM;
            } else {
                offset.range = camera._mode === SceneMode.SCENE2D ? distanceToBoundingSphere2D(camera, radius) : distanceToBoundingSphere3D(camera, radius);
            }
        }

        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.');
        }
        //>>includeEnd('debug');

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

        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 {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
        });
    };

    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 = Cartesian3.normalize(Cartesian3.cross(Cartesian3.UNIT_Z, q, scratchCartesian3_3), scratchCartesian3_3);
        var 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;
    };

    /**
     * @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);

        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
     */

    return Camera;
});