# Matrix4

#### new Cesium.Matrix4(column0Row0, column1Row0, column2Row0, column3Row0, column0Row1, column1Row1, column2Row1, column3Row1, column0Row2, column1Row2, column2Row2, column3Row2, column0Row3, column1Row3, column2Row3, column3Row3)
Core/Matrix4.js 65

  A 4x4 matrix, indexable as a column-major order array. Constructor parameters are in row-major order for code readability.

  Name | Type | Default | Description
  --- | --- | --- | ---
  `column0Row0` | Number | `0.0` | optional The value for column 0, row 0.
  `column1Row0` | Number | `0.0` | optional The value for column 1, row 0.
  `column2Row0` | Number | `0.0` | optional The value for column 2, row 0.
  `column3Row0` | Number | `0.0` | optional The value for column 3, row 0.
  `column0Row1` | Number | `0.0` | optional The value for column 0, row 1.
  `column1Row1` | Number | `0.0` | optional The value for column 1, row 1.
  `column2Row1` | Number | `0.0` | optional The value for column 2, row 1.
  `column3Row1` | Number | `0.0` | optional The value for column 3, row 1.
  `column0Row2` | Number | `0.0` | optional The value for column 0, row 2.
  `column1Row2` | Number | `0.0` | optional The value for column 1, row 2.
  `column2Row2` | Number | `0.0` | optional The value for column 2, row 2.
  `column3Row2` | Number | `0.0` | optional The value for column 3, row 2.
  `column0Row3` | Number | `0.0` | optional The value for column 0, row 3.
  `column1Row3` | Number | `0.0` | optional The value for column 1, row 3.
  `column2Row3` | Number | `0.0` | optional The value for column 2, row 3.
  `column3Row3` | Number | `0.0` | optional The value for column 3, row 3.

  ##### See:

  - Matrix4.fromColumnMajorArray
  - Matrix4.fromRowMajorArray
  - Matrix4.fromRotationTranslation
  - Matrix4.fromTranslationRotationScale
  - Matrix4.fromTranslationQuaternionRotationScale
  - Matrix4.fromTranslation
  - Matrix4.fromScale
  - Matrix4.fromUniformScale
  - Matrix4.fromCamera
  - Matrix4.computePerspectiveFieldOfView
  - Matrix4.computeOrthographicOffCenter
  - Matrix4.computePerspectiveOffCenter
  - Matrix4.computeInfinitePerspectiveOffCenter
  - Matrix4.computeViewportTransformation
  - Matrix2
  - Matrix3
  - Packable

### Members

#### static constantCesium.Matrix4.COLUMN0ROW0 : Number
Core/Matrix4.js 2585

  The index into Matrix4 for column 0, row 0.

#### static constantCesium.Matrix4.COLUMN0ROW1 : Number
Core/Matrix4.js 2593

  The index into Matrix4 for column 0, row 1.

#### static constantCesium.Matrix4.COLUMN0ROW2 : Number
Core/Matrix4.js 2601

  The index into Matrix4 for column 0, row 2.

#### static constantCesium.Matrix4.COLUMN0ROW3 : Number
Core/Matrix4.js 2609

  The index into Matrix4 for column 0, row 3.

#### static constantCesium.Matrix4.COLUMN1ROW0 : Number
Core/Matrix4.js 2617

  The index into Matrix4 for column 1, row 0.

#### static constantCesium.Matrix4.COLUMN1ROW1 : Number
Core/Matrix4.js 2625

  The index into Matrix4 for column 1, row 1.

#### static constantCesium.Matrix4.COLUMN1ROW2 : Number
Core/Matrix4.js 2633

  The index into Matrix4 for column 1, row 2.

#### static constantCesium.Matrix4.COLUMN1ROW3 : Number
Core/Matrix4.js 2641

  The index into Matrix4 for column 1, row 3.

#### static constantCesium.Matrix4.COLUMN2ROW0 : Number
Core/Matrix4.js 2649

  The index into Matrix4 for column 2, row 0.

#### static constantCesium.Matrix4.COLUMN2ROW1 : Number
Core/Matrix4.js 2657

  The index into Matrix4 for column 2, row 1.

#### static constantCesium.Matrix4.COLUMN2ROW2 : Number
Core/Matrix4.js 2665

  The index into Matrix4 for column 2, row 2.

#### static constantCesium.Matrix4.COLUMN2ROW3 : Number
Core/Matrix4.js 2673

  The index into Matrix4 for column 2, row 3.

#### static constantCesium.Matrix4.COLUMN3ROW0 : Number
Core/Matrix4.js 2681

  The index into Matrix4 for column 3, row 0.

#### static constantCesium.Matrix4.COLUMN3ROW1 : Number
Core/Matrix4.js 2689

  The index into Matrix4 for column 3, row 1.

#### static constantCesium.Matrix4.COLUMN3ROW2 : Number
Core/Matrix4.js 2697

  The index into Matrix4 for column 3, row 2.

#### static constantCesium.Matrix4.COLUMN3ROW3 : Number
Core/Matrix4.js 2705

  The index into Matrix4 for column 3, row 3.

#### static constantCesium.Matrix4.IDENTITY : Matrix4
Core/Matrix4.js 2563

  An immutable Matrix4 instance initialized to the identity matrix.

#### staticCesium.Matrix4.packedLength : Number
Core/Matrix4.js 91

  The number of elements used to pack the object into an array.

#### static constantCesium.Matrix4.ZERO : Matrix4
Core/Matrix4.js 2574

  An immutable Matrix4 instance initialized to the zero matrix.

### Methods

#### clone(result) → Matrix4
Core/Matrix4.js 2713

  Duplicates the provided Matrix4 instance.

  Name | Type | Description
  --- | --- | ---
  `result` | Matrix4 | optional The object onto which to store the result.

  ##### Returns:

  The modified result parameter or a new Matrix4 instance if one was not provided.

#### equals(right) → Boolean
Core/Matrix4.js 2724

  Compares this matrix to the provided matrix componentwise and returns `true` if they are equal, `false` otherwise.

  Name | Type | Description
  --- | --- | ---
  `right` | Matrix4 | optional The right hand side matrix.

  ##### Returns:

  `true` if they are equal, `false` otherwise.

#### equalsEpsilon(right, epsilon) → Boolean
Core/Matrix4.js 2759

  Compares this matrix to the provided matrix componentwise and returns `true` if they are within the provided epsilon, `false` otherwise.

  Name | Type | Description
  --- | --- | ---
  `right` | Matrix4 | optional The right hand side matrix.
  `epsilon` | Number | The epsilon to use for equality testing.

  ##### Returns:

  `true` if they are within the provided epsilon, `false` otherwise.

#### toString() → String
Core/Matrix4.js 2769

  Computes a string representing this Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.

  ##### Returns:

  A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.

#### staticCesium.Matrix4.abs(matrix, result) → Matrix4
Core/Matrix4.js 2126

  Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix with signed elements.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.add(left, right, result) → Matrix4
Core/Matrix4.js 1434

  Computes the sum of two matrices.

  Name | Type | Description
  --- | --- | ---
  `left` | Matrix4 | The first matrix.
  `right` | Matrix4 | The second matrix.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.clone(matrix, result) → Matrix4
Core/Matrix4.js 178

  Duplicates a Matrix4 instance.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to duplicate.
  `result` | Matrix4 | optional The object onto which to store the result.

  ##### Returns:

  The modified result parameter or a new Matrix4 instance if one was not provided. (Returns undefined if matrix is undefined)

#### staticCesium.Matrix4.computeInfinitePerspectiveOffCenter(left, right, bottom, top, near, far, result) → Matrix4
Core/Matrix4.js 846

  Computes a Matrix4 instance representing an infinite off center perspective transformation.

  Name | Type | Description
  --- | --- | ---
  `left` | Number | The number of meters to the left of the camera that will be in view.
  `right` | Number | The number of meters to the right of the camera that will be in view.
  `bottom` | Number | The number of meters below of the camera that will be in view.
  `top` | Number | The number of meters above of the camera that will be in view.
  `near` | Number | The distance to the near plane in meters.
  `far` | Number | The distance to the far plane in meters.
  `result` | Matrix4 | The object in which the result will be stored.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.computeOrthographicOffCenter(left, right, bottom, top, near, far, result) → Matrix4
Core/Matrix4.js 715

  Computes a Matrix4 instance representing an orthographic transformation matrix.

  Name | Type | Description
  --- | --- | ---
  `left` | Number | The number of meters to the left of the camera that will be in view.
  `right` | Number | The number of meters to the right of the camera that will be in view.
  `bottom` | Number | The number of meters below of the camera that will be in view.
  `top` | Number | The number of meters above of the camera that will be in view.
  `near` | Number | The distance to the near plane in meters.
  `far` | Number | The distance to the far plane in meters.
  `result` | Matrix4 | The object in which the result will be stored.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.computePerspectiveFieldOfView(fovY, aspectRatio, near, far, result) → Matrix4
Core/Matrix4.js 658

  Computes a Matrix4 instance representing a perspective transformation matrix.

  Name | Type | Description
  --- | --- | ---
  `fovY` | Number | The field of view along the Y axis in radians.
  `aspectRatio` | Number | The aspect ratio.
  `near` | Number | The distance to the near plane in meters.
  `far` | Number | The distance to the far plane in meters.
  `result` | Matrix4 | The object in which the result will be stored.

  ##### Returns:

  The modified result parameter.

  ##### Throws:

  - DeveloperError : fovY must be in [0, PI).
  - DeveloperError : aspectRatio must be greater than zero.
  - DeveloperError : near must be greater than zero.
  - DeveloperError : far must be greater than zero.

#### staticCesium.Matrix4.computePerspectiveOffCenter(left, right, bottom, top, near, far, result) → Matrix4
Core/Matrix4.js 782

  Computes a Matrix4 instance representing an off center perspective transformation.

  Name | Type | Description
  --- | --- | ---
  `left` | Number | The number of meters to the left of the camera that will be in view.
  `right` | Number | The number of meters to the right of the camera that will be in view.
  `bottom` | Number | The number of meters below of the camera that will be in view.
  `top` | Number | The number of meters above of the camera that will be in view.
  `near` | Number | The distance to the near plane in meters.
  `far` | Number | The distance to the far plane in meters.
  `result` | Matrix4 | The object in which the result will be stored.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.computeViewportTransformation(viewport, nearDepthRange, farDepthRange, result) → Matrix4
Core/Matrix4.js 913

  Computes a Matrix4 instance that transforms from normalized device coordinates to window coordinates.

  Name | Type | Default | Description
  --- | --- | --- | ---
  `viewport` | Object | `{ x : 0.0, y : 0.0, width : 0.0, height : 0.0 }` | optional The viewport's corners as shown in Example 1.
  `nearDepthRange` | Number | `0.0` | optional The near plane distance in window coordinates.
  `farDepthRange` | Number | `1.0` | optional The far plane distance in window coordinates.
  `result` | Matrix4 |  | The object in which the result will be stored.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      // Create viewport transformation using an explicit viewport and depth range.
      var m = Cesium.Matrix4.computeViewportTransformation({
          x : 0.0,
          y : 0.0,
          width : 1024.0,
          height : 768.0
      }, 0.0, 1.0, new Cesium.Matrix4());

#### staticCesium.Matrix4.equals(left, right) → Boolean
Core/Matrix4.js 2185

  Compares the provided matrices componentwise and returns `true` if they are equal, `false` otherwise.

  Name | Type | Description
  --- | --- | ---
  `left` | Matrix4 | optional The first matrix.
  `right` | Matrix4 | optional The second matrix.

  ##### Returns:

  `true` if left and right are equal, `false` otherwise.

  ##### Example:

      //compares two Matrix4 instances

      // a = [10.0, 14.0, 18.0, 22.0]
      //     [11.0, 15.0, 19.0, 23.0]
      //     [12.0, 16.0, 20.0, 24.0]
      //     [13.0, 17.0, 21.0, 25.0]

      // b = [10.0, 14.0, 18.0, 22.0]
      //     [11.0, 15.0, 19.0, 23.0]
      //     [12.0, 16.0, 20.0, 24.0]
      //     [13.0, 17.0, 21.0, 25.0]

      if(Cesium.Matrix4.equals(a,b)) {
           console.log("Both matrices are equal");
      } else {
           console.log("They are not equal");
      }

      //Prints "Both matrices are equal" on the console

#### staticCesium.Matrix4.equalsEpsilon(left, right, epsilon) → Boolean
Core/Matrix4.js 2247

  Compares the provided matrices componentwise and returns `true` if they are within the provided epsilon, `false` otherwise.

  Name | Type | Description
  --- | --- | ---
  `left` | Matrix4 | optional The first matrix.
  `right` | Matrix4 | optional The second matrix.
  `epsilon` | Number | The epsilon to use for equality testing.

  ##### Returns:

  `true` if left and right are within the provided epsilon, `false` otherwise.

  ##### Example:

      //compares two Matrix4 instances

      // a = [10.5, 14.5, 18.5, 22.5]
      //     [11.5, 15.5, 19.5, 23.5]
      //     [12.5, 16.5, 20.5, 24.5]
      //     [13.5, 17.5, 21.5, 25.5]

      // b = [10.0, 14.0, 18.0, 22.0]
      //     [11.0, 15.0, 19.0, 23.0]
      //     [12.0, 16.0, 20.0, 24.0]
      //     [13.0, 17.0, 21.0, 25.0]

      if(Cesium.Matrix4.equalsEpsilon(a,b,0.1)){
           console.log("Difference between both the matrices is less than 0.1");
      } else {
           console.log("Difference between both the matrices is not less than 0.1");
      }

      //Prints "Difference between both the matrices is not less than 0.1" on the console

#### staticCesium.Matrix4.fromArray(array, startingIndex, result) → Matrix4
Core/Matrix4.js 230

  Creates a Matrix4 from 16 consecutive elements in an array.

  Name | Type | Default | Description
  --- | --- | --- | ---
  `array` | Array.<Number> |  | The array whose 16 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
  `startingIndex` | Number | `0` | optional The offset into the array of the first element, which corresponds to first column first row position in the matrix.
  `result` | Matrix4 |  | optional The object onto which to store the result.

  ##### Returns:

  The modified result parameter or a new Matrix4 instance if one was not provided.

  ##### Example:

      // Create the Matrix4:
      // [1.0, 2.0, 3.0, 4.0]
      // [1.0, 2.0, 3.0, 4.0]
      // [1.0, 2.0, 3.0, 4.0]
      // [1.0, 2.0, 3.0, 4.0]

      var v = [1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
      var m = Cesium.Matrix4.fromArray(v);

      // Create same Matrix4 with using an offset into an array
      var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
      var m2 = Cesium.Matrix4.fromArray(v2, 2);

#### staticCesium.Matrix4.fromCamera(camera, result) → Matrix4
Core/Matrix4.js 558

  Computes a Matrix4 instance from a Camera.

  Name | Type | Description
  --- | --- | ---
  `camera` | Camera | The camera to use.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

#### staticCesium.Matrix4.fromColumnMajorArray(values, result) → Matrix4
Core/Matrix4.js 239

  Computes a Matrix4 instance from a column-major order array.

  Name | Type | Description
  --- | --- | ---
  `values` | Array.<Number> | The column-major order array.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

#### staticCesium.Matrix4.fromRotationTranslation(rotation, translation, result) → Matrix4
Core/Matrix4.js 298

  Computes a Matrix4 instance from a Matrix3 representing the rotation and a Cartesian3 representing the translation.

  Name | Type | Default | Description
  --- | --- | --- | ---
  `rotation` | Matrix3 |  | The upper left portion of the matrix representing the rotation.
  `translation` | Cartesian3 | `Cartesian3.ZERO` | optional The upper right portion of the matrix representing the translation.
  `result` | Matrix4 |  | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

#### staticCesium.Matrix4.fromRowMajorArray(values, result) → Matrix4
Core/Matrix4.js 257

  Computes a Matrix4 instance from a row-major order array. The resulting matrix will be in column-major order.

  Name | Type | Description
  --- | --- | ---
  `values` | Array.<Number> | The row-major order array.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

#### staticCesium.Matrix4.fromScale(scale, result) → Matrix4
Core/Matrix4.js 465

  Computes a Matrix4 instance representing a non-uniform scale.

  Name | Type | Description
  --- | --- | ---
  `scale` | Cartesian3 | The x, y, and z scale factors.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

  ##### Example:

      // Creates
      //   [7.0, 0.0, 0.0, 0.0]
      //   [0.0, 8.0, 0.0, 0.0]
      //   [0.0, 0.0, 9.0, 0.0]
      //   [0.0, 0.0, 0.0, 1.0]
      var m = Cesium.Matrix4.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));

#### staticCesium.Matrix4.fromTranslation(translation, result) → Matrix4
Core/Matrix4.js 440

  Creates a Matrix4 instance from a Cartesian3 representing the translation.

  Name | Type | Description
  --- | --- | ---
  `translation` | Cartesian3 | The upper right portion of the matrix representing the translation.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

  ##### See:

  - Matrix4.multiplyByTranslation

#### staticCesium.Matrix4.fromTranslationQuaternionRotationScale(translation, rotation, scale, result) → Matrix4
Core/Matrix4.js 350

  Computes a Matrix4 instance from a translation, rotation, and scale (TRS) representation with the rotation represented as a quaternion.

  Name | Type | Description
  --- | --- | ---
  `translation` | Cartesian3 | The translation transformation.
  `rotation` | Quaternion | The rotation transformation.
  `scale` | Cartesian3 | The non-uniform scale transformation.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

  ##### Example:

      var result = Cesium.Matrix4.fromTranslationQuaternionRotationScale(
        new Cesium.Cartesian3(1.0, 2.0, 3.0), // translation
        Cesium.Quaternion.IDENTITY,           // rotation
        new Cesium.Cartesian3(7.0, 8.0, 9.0), // scale
        result);

#### staticCesium.Matrix4.fromTranslationRotationScale(translationRotationScale, result) → Matrix4
Core/Matrix4.js 421

  Creates a Matrix4 instance from a `TranslationRotationScale` instance.

  Name | Type | Description
  --- | --- | ---
  `translationRotationScale` | TranslationRotationScale | The instance.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

#### staticCesium.Matrix4.fromUniformScale(scale, result) → Matrix4
Core/Matrix4.js 514

  Computes a Matrix4 instance representing a uniform scale.

  Name | Type | Description
  --- | --- | ---
  `scale` | Number | The uniform scale factor.
  `result` | Matrix4 | optional The object in which the result will be stored, if undefined a new instance will be created.

  ##### Returns:

  The modified result parameter, or a new Matrix4 instance if one was not provided.

  ##### Example:

      // Creates
      //   [2.0, 0.0, 0.0, 0.0]
      //   [0.0, 2.0, 0.0, 0.0]
      //   [0.0, 0.0, 2.0, 0.0]
      //   [0.0, 0.0, 0.0, 1.0]
      var m = Cesium.Matrix4.fromUniformScale(2.0);

#### staticCesium.Matrix4.getColumn(matrix, index, result) → Cartesian4
Core/Matrix4.js 1066

  Retrieves a copy of the matrix column at the provided index as a Cartesian4 instance.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `index` | Number | The zero-based index of the column to retrieve.
  `result` | Cartesian4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Throws:

  - DeveloperError : index must be 0, 1, 2, or 3.

  ##### Examples:

      //returns a Cartesian4 instance with values from the specified column
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      //Example 1: Creates an instance of Cartesian
      var a = Cesium.Matrix4.getColumn(m, 2, new Cesium.Cartesian4());

      //Example 2: Sets values for Cartesian instance
      var a = new Cesium.Cartesian4();
      Cesium.Matrix4.getColumn(m, 2, a);

      // a.x = 12.0; a.y = 16.0; a.z = 20.0; a.w = 24.0;

#### staticCesium.Matrix4.getElementIndex(row, column) → Number
Core/Matrix4.js 1026

  Computes the array index of the element at the provided row and column.

  Name | Type | Description
  --- | --- | ---
  `row` | Number | The zero-based index of the row.
  `column` | Number | The zero-based index of the column.

  ##### Returns:

  The index of the element at the provided row and column.

  ##### Throws:

  - DeveloperError : row must be 0, 1, 2, or 3.
  - DeveloperError : column must be 0, 1, 2, or 3.

  ##### Example:

      var myMatrix = new Cesium.Matrix4();
      var column1Row0Index = Cesium.Matrix4.getElementIndex(1, 0);
      var column1Row0 = myMatrix[column1Row0Index];
      myMatrix[column1Row0Index] = 10.0;

#### staticCesium.Matrix4.getMaximumScale(matrix) → Number
Core/Matrix4.js 1327

  Computes the maximum scale assuming the matrix is an affine transformation. The maximum scale is the maximum length of the column vectors in the upper-left 3x3 matrix.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix.

  ##### Returns:

  The maximum scale.

#### staticCesium.Matrix4.getRotation(matrix, result) → Matrix3
Core/Matrix4.js 2320

  Gets the upper left 3x3 rotation matrix of the provided matrix, assuming the matrix is a affine transformation matrix.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `result` | Matrix3 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      // returns a Matrix3 instance from a Matrix4 instance

      // m = [10.0, 14.0, 18.0, 22.0]
      //     [11.0, 15.0, 19.0, 23.0]
      //     [12.0, 16.0, 20.0, 24.0]
      //     [13.0, 17.0, 21.0, 25.0]

      var b = new Cesium.Matrix3();
      Cesium.Matrix4.getRotation(m,b);

      // b = [10.0, 14.0, 18.0]
      //     [11.0, 15.0, 19.0]
      //     [12.0, 16.0, 20.0]

#### staticCesium.Matrix4.getRow(matrix, index, result) → Cartesian4
Core/Matrix4.js 1216

  Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `index` | Number | The zero-based index of the row to retrieve.
  `result` | Cartesian4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Throws:

  - DeveloperError : index must be 0, 1, 2, or 3.

  ##### Examples:

      //returns a Cartesian4 instance with values from the specified column
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      //Example 1: Returns an instance of Cartesian
      var a = Cesium.Matrix4.getRow(m, 2, new Cesium.Cartesian4());

      //Example 2: Sets values for a Cartesian instance
      var a = new Cesium.Cartesian4();
      Cesium.Matrix4.getRow(m, 2, a);

      // a.x = 18.0; a.y = 19.0; a.z = 20.0; a.w = 21.0;

#### staticCesium.Matrix4.getScale(matrix, result) → Cartesian3
Core/Matrix4.js 1301

  Extracts the non-uniform scale assuming the matrix is an affine transformation.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix.
  `result` | Cartesian3 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter

#### staticCesium.Matrix4.getTranslation(matrix, result) → Cartesian3
Core/Matrix4.js 2282

  Gets the translation portion of the provided matrix, assuming the matrix is a affine transformation matrix.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `result` | Cartesian3 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.inverse(matrix, result) → Matrix4
Core/Matrix4.js 2359

  Computes the inverse of the provided matrix using Cramers Rule. If the determinant is zero, the matrix can not be inverted, and an exception is thrown. If the matrix is an affine transformation matrix, it is more efficient to invert it with `Matrix4.inverseTransformation`.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to invert.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Throws:

  - RuntimeError : matrix is not invertible because its determinate is zero.

#### staticCesium.Matrix4.inverseTransformation(matrix, result) → Matrix4
Core/Matrix4.js 2504

  Computes the inverse of the provided matrix assuming it is an affine transformation matrix, where the upper left 3x3 elements are a rotation matrix, and the upper three elements in the fourth column are the translation. The bottom row is assumed to be [0, 0, 0, 1]. The matrix is not verified to be in the proper form. This method is faster than computing the inverse for a general 4x4 matrix using `Matrix4.inverse`.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to invert.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.multiply(left, right, result) → Matrix4
Core/Matrix4.js 1340

  Computes the product of two matrices.

  Name | Type | Description
  --- | --- | ---
  `left` | Matrix4 | The first matrix.
  `right` | Matrix4 | The second matrix.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.multiplyByMatrix3(matrix, rotation, result) → Matrix4
Core/Matrix4.js 1613

  Multiplies a transformation matrix (with a bottom row of `[0.0, 0.0, 0.0, 1.0]`) by a 3x3 rotation matrix. This is an optimization for `Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m);` with less allocations and arithmetic operations.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix on the left-hand side.
  `rotation` | Matrix3 | The 3x3 rotation matrix on the right-hand side.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromRotationTranslation(rotation), m);
      Cesium.Matrix4.multiplyByMatrix3(m, rotation, m);

#### staticCesium.Matrix4.multiplyByPoint(matrix, cartesian, result) → Cartesian3
Core/Matrix4.js 1927

  Computes the product of a matrix and a `Cartesian3`. This is equivalent to calling `Matrix4.multiplyByVector` with a `Cartesian4` with a `w` component of 1, but returns a `Cartesian3` instead of a `Cartesian4`.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix.
  `cartesian` | Cartesian3 | The point.
  `result` | Cartesian3 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
      var result = Cesium.Matrix4.multiplyByPoint(matrix, p, new Cesium.Cartesian3());

#### staticCesium.Matrix4.multiplyByPointAsVector(matrix, cartesian, result) → Cartesian3
Core/Matrix4.js 1887

  Computes the product of a matrix and a `Cartesian3`. This is equivalent to calling `Matrix4.multiplyByVector` with a `Cartesian4` with a `w` component of zero.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix.
  `cartesian` | Cartesian3 | The point.
  `result` | Cartesian3 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
      var result = Cesium.Matrix4.multiplyByPointAsVector(matrix, p, new Cesium.Cartesian3());
      // A shortcut for
      //   Cartesian3 p = ...
      //   Cesium.Matrix4.multiplyByVector(matrix, new Cesium.Cartesian4(p.x, p.y, p.z, 0.0), result);

#### staticCesium.Matrix4.multiplyByScalar(matrix, scalar, result) → Matrix4
Core/Matrix4.js 1978

  Computes the product of a matrix and a scalar.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix.
  `scalar` | Number | The number to multiply by.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      //create a Matrix4 instance which is a scaled version of the supplied Matrix4
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      var a = Cesium.Matrix4.multiplyByScalar(m, -2, new Cesium.Matrix4());

      // m remains the same
      // a = [-20.0, -22.0, -24.0, -26.0]
      //     [-28.0, -30.0, -32.0, -34.0]
      //     [-36.0, -38.0, -40.0, -42.0]
      //     [-44.0, -46.0, -48.0, -50.0]

#### staticCesium.Matrix4.multiplyByScale(matrix, scale, result) → Matrix4
Core/Matrix4.js 1792

  Multiplies an affine transformation matrix (with a bottom row of `[0.0, 0.0, 0.0, 1.0]`) by an implicit non-uniform scale matrix. This is an optimization for `Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);`, where `m` must be an affine matrix. This function performs fewer allocations and arithmetic operations.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The affine matrix on the left-hand side.
  `scale` | Cartesian3 | The non-uniform scale on the right-hand side.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromScale(scale), m);
      Cesium.Matrix4.multiplyByScale(m, scale, m);

  ##### See:

  - Matrix4.fromScale
  - Matrix4.multiplyByUniformScale

#### staticCesium.Matrix4.multiplyByTranslation(matrix, translation, result) → Matrix4
Core/Matrix4.js 1691

  Multiplies a transformation matrix (with a bottom row of `[0.0, 0.0, 0.0, 1.0]`) by an implicit translation matrix defined by a `Cartesian3`. This is an optimization for `Matrix4.multiply(m, Matrix4.fromTranslation(position), m);` with less allocations and arithmetic operations.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix on the left-hand side.
  `translation` | Cartesian3 | The translation on the right-hand side.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromTranslation(position), m);
      Cesium.Matrix4.multiplyByTranslation(m, position, m);

#### staticCesium.Matrix4.multiplyByUniformScale(matrix, scale, result) → Matrix4
Core/Matrix4.js 1753

  Multiplies an affine transformation matrix (with a bottom row of `[0.0, 0.0, 0.0, 1.0]`) by an implicit uniform scale matrix. This is an optimization for `Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);`, where `m` must be an affine matrix. This function performs fewer allocations and arithmetic operations.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The affine matrix on the left-hand side.
  `scale` | Number | The uniform scale on the right-hand side.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromUniformScale(scale), m);
      Cesium.Matrix4.multiplyByUniformScale(m, scale, m);

  ##### See:

  - Matrix4.fromUniformScale
  - Matrix4.multiplyByScale

#### staticCesium.Matrix4.multiplyByVector(matrix, cartesian, result) → Cartesian4
Core/Matrix4.js 1841

  Computes the product of a matrix and a column vector.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix.
  `cartesian` | Cartesian4 | The vector.
  `result` | Cartesian4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.multiplyTransformation(left, right, result) → Matrix4
Core/Matrix4.js 1525

  Computes the product of two matrices assuming the matrices are affine transformation matrices, where the upper left 3x3 elements are a rotation matrix, and the upper three elements in the fourth column are the translation. The bottom row is assumed to be [0, 0, 0, 1]. The matrix is not verified to be in the proper form. This method is faster than computing the product for general 4x4 matrices using `Matrix4.multiply`.

  Name | Type | Description
  --- | --- | ---
  `left` | Matrix4 | The first matrix.
  `right` | Matrix4 | The second matrix.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      var m1 = new Cesium.Matrix4(1.0, 6.0, 7.0, 0.0, 2.0, 5.0, 8.0, 0.0, 3.0, 4.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0);
      var m2 = Cesium.Transforms.eastNorthUpToFixedFrame(new Cesium.Cartesian3(1.0, 1.0, 1.0));
      var m3 = Cesium.Matrix4.multiplyTransformation(m1, m2, new Cesium.Matrix4());

#### staticCesium.Matrix4.negate(matrix, result) → Matrix4
Core/Matrix4.js 2032

  Computes a negated copy of the provided matrix.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to negate.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      //create a new Matrix4 instance which is a negation of a Matrix4
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      var a = Cesium.Matrix4.negate(m, new Cesium.Matrix4());

      // m remains the same
      // a = [-10.0, -11.0, -12.0, -13.0]
      //     [-14.0, -15.0, -16.0, -17.0]
      //     [-18.0, -19.0, -20.0, -21.0]
      //     [-22.0, -23.0, -24.0, -25.0]

#### staticCesium.Matrix4.pack(value, array, startingIndex)
Core/Matrix4.js 100

  Stores the provided instance into the provided array.

  Name | Type | Default | Description
  --- | --- | --- | ---
  `value` | Matrix4 |  | The value to pack.
  `array` | Array.<Number> |  | The array to pack into.
  `startingIndex` | Number | `0` | optional The index into the array at which to start packing the elements.

#### staticCesium.Matrix4.setColumn(matrix, index, cartesian, result) → Matrix4
Core/Matrix4.js 1119

  Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian4 instance.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `index` | Number | The zero-based index of the column to set.
  `cartesian` | Cartesian4 | The Cartesian whose values will be assigned to the specified column.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Throws:

  - DeveloperError : index must be 0, 1, 2, or 3.

  ##### Example:

      //creates a new Matrix4 instance with new column values from the Cartesian4 instance
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      var a = Cesium.Matrix4.setColumn(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());

      // m remains the same
      // a = [10.0, 11.0, 99.0, 13.0]
      //     [14.0, 15.0, 98.0, 17.0]
      //     [18.0, 19.0, 97.0, 21.0]
      //     [22.0, 23.0, 96.0, 25.0]

#### staticCesium.Matrix4.setRow(matrix, index, cartesian, result) → Matrix4
Core/Matrix4.js 1268

  Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian4 instance.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `index` | Number | The zero-based index of the row to set.
  `cartesian` | Cartesian4 | The Cartesian whose values will be assigned to the specified row.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Throws:

  - DeveloperError : index must be 0, 1, 2, or 3.

  ##### Example:

      //create a new Matrix4 instance with new row values from the Cartesian4 instance
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      var a = Cesium.Matrix4.setRow(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());

      // m remains the same
      // a = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [99.0, 98.0, 97.0, 96.0]
      //     [22.0, 23.0, 24.0, 25.0]

#### staticCesium.Matrix4.setTranslation(matrix, translation, result) → Matrix4
Core/Matrix4.js 1153

  Computes a new matrix that replaces the translation in the rightmost column of the provided matrix with the provided translation. This assumes the matrix is an affine transformation

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use.
  `translation` | Cartesian3 | The translation that replaces the translation of the provided matrix.
  `result` | Cartesian4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.subtract(left, right, result) → Matrix4
Core/Matrix4.js 1474

  Computes the difference of two matrices.

  Name | Type | Description
  --- | --- | ---
  `left` | Matrix4 | The first matrix.
  `right` | Matrix4 | The second matrix.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

#### staticCesium.Matrix4.toArray(matrix, result) → Array.<Number>
Core/Matrix4.js 978

  Computes an Array from the provided Matrix4 instance. The array will be in column-major order.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to use..
  `result` | Array.<Number> | optional The Array onto which to store the result.

  ##### Returns:

  The modified Array parameter or a new Array instance if one was not provided.

  ##### Example:

      //create an array from an instance of Matrix4
      // m = [10.0, 14.0, 18.0, 22.0]
      //     [11.0, 15.0, 19.0, 23.0]
      //     [12.0, 16.0, 20.0, 24.0]
      //     [13.0, 17.0, 21.0, 25.0]
      var a = Cesium.Matrix4.toArray(m);

      // m remains the same
      //creates a = [10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0]

#### staticCesium.Matrix4.transpose(matrix, result) → Matrix4
Core/Matrix4.js 2083

  Computes the transpose of the provided matrix.

  Name | Type | Description
  --- | --- | ---
  `matrix` | Matrix4 | The matrix to transpose.
  `result` | Matrix4 | The object onto which to store the result.

  ##### Returns:

  The modified result parameter.

  ##### Example:

      //returns transpose of a Matrix4
      // m = [10.0, 11.0, 12.0, 13.0]
      //     [14.0, 15.0, 16.0, 17.0]
      //     [18.0, 19.0, 20.0, 21.0]
      //     [22.0, 23.0, 24.0, 25.0]

      var a = Cesium.Matrix4.transpose(m, new Cesium.Matrix4());

      // m remains the same
      // a = [10.0, 14.0, 18.0, 22.0]
      //     [11.0, 15.0, 19.0, 23.0]
      //     [12.0, 16.0, 20.0, 24.0]
      //     [13.0, 17.0, 21.0, 25.0]

#### staticCesium.Matrix4.unpack(array, startingIndex, result) → Matrix4
Core/Matrix4.js 139

  Retrieves an instance from a packed array.

  Name | Type | Default | Description
  --- | --- | --- | ---
  `array` | Array.<Number> |  | The packed array.
  `startingIndex` | Number | `0` | optional The starting index of the element to be unpacked.
  `result` | Matrix4 |  | optional The object into which to store the result.

  ##### Returns:

  The modified result parameter or a new Matrix4 instance if one was not provided.