cesium/Source/Scene/Camera.js

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/**
 * Checks if there's a camera flight with preload for this camera.
 *
 * @returns {Boolean} Whether or not this camera has a current flight with a valid preloadFlightCamera in scene.
 *
 * @private
 *
 */
Camera.prototype.canPreloadFlight = function () {
  return defined(this._currentFlight) && this._mode !== SceneMode.SCENE2D;
};

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

  updateCameraDeltas(camera);

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

  var percentageChanged = camera.percentageChanged;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

var scratchCartesian = new Cartesian3();

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

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

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

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

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

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

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

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

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

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

    camera._modeChanged = false;
  }

  var transform = camera._actualTransform;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  return roll;
}

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

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

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

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

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

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

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

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

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

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

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

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

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

        this._setTransform(oldTransform);

        return heading;
      }

      return undefined;
    },
  },

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

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

        var pitch = getPitch(this.direction);

        this._setTransform(oldTransform);

        return pitch;
      }

      return undefined;
    },
  },

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

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

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

        this._setTransform(oldTransform);

        return roll;
      }

      return undefined;
    },
  },

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

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

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

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

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

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

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

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

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

var 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 scratchAdjustOrthographicFrustumMousePosition = new Cartesian2();
var scratchPickRay = new Ray();
var scratchRayIntersection = new Cartesian3();
var scratchDepthIntersection = new Cartesian3();

function calculateOrthographicFrustumWidth(camera) {
  // Camera is fixed to an object, so keep frustum width constant.
  if (!Matrix4.equals(Matrix4.IDENTITY, camera.transform)) {
    return Cartesian3.magnitude(camera.position);
  }

  var scene = camera._scene;
  var globe = scene.globe;

  var mousePosition = scratchAdjustOrthographicFrustumMousePosition;
  mousePosition.x = scene.drawingBufferWidth / 2.0;
  mousePosition.y = scene.drawingBufferHeight / 2.0;

  var rayIntersection;
  if (defined(globe)) {
    var ray = camera.getPickRay(mousePosition, scratchPickRay);
    rayIntersection = globe.pickWorldCoordinates(
      ray,
      scene,
      true,
      scratchRayIntersection
    );
  }

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

  var distance;
  if (defined(rayIntersection) || defined(depthIntersection)) {
    var depthDistance = defined(depthIntersection)
      ? Cartesian3.distance(depthIntersection, camera.positionWC)
      : Number.POSITIVE_INFINITY;
    var rayDistance = defined(rayIntersection)
      ? Cartesian3.distance(rayIntersection, camera.positionWC)
      : Number.POSITIVE_INFINITY;
    distance = Math.min(depthDistance, rayDistance);
  } else {
    distance = Math.max(camera.positionCartographic.height, 0.0);
  }
  return distance;
}

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

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

  this.frustum.width = calculateOrthographicFrustumWidth(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, hpr) {
  var currentTransform = Matrix4.clone(
    camera.transform,
    scratchSetViewTransform1
  );
  var localTransform = Transforms.eastNorthUpToFixedFrame(
    position,
    camera._projection.ellipsoid,
    scratchSetViewTransform2
  );
  camera._setTransform(localTransform);

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

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

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

  camera._setTransform(currentTransform);

  camera._adjustOrthographicFrustum(true);
}

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

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

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

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

  camera._setTransform(currentTransform);

  camera._adjustOrthographicFrustum(true);
}

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

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

    Cartesian2.clone(position, camera.position);

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

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

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

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

  camera._setTransform(currentTransform);
}

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

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

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

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

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

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

  return result;
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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