Matrix4 - Cesium Documentation

# Matrix4

#### new Matrix4(column0Row0, column1Row0, column2Row0, column3Row0, column0Row1, column1Row1, column2Row1, column3Row1, column0Row2, column1Row2, column2Row2, column3Row2, column0Row3, column1Row3, column2Row3, column3Row3)

  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.fromTranslationQuaternionRotationScale
  - Matrix4.fromTranslation
  - Matrix4.fromScale
  - Matrix4.fromUniformScale
  - Matrix4.fromCamera
  - Matrix4.computePerspectiveFieldOfView
  - Matrix4.computeOrthographicOffCenter
  - Matrix4.computePerspectiveOffCenter
  - Matrix4.computeInfinitePerspectiveOffCenter
  - Matrix4.computeViewportTransformation
  - Matrix2
  - Matrix3
  - Packable
  Source: Core/Matrix4.js, line 64

### Members

#### staticconstantMatrix4.COLUMN0ROW0 :Number

  The index into Matrix4 for column 0, row 0.
  Source: Core/Matrix4.js, line 2564

#### staticconstantMatrix4.COLUMN0ROW1 :Number

  The index into Matrix4 for column 0, row 1.
  Source: Core/Matrix4.js, line 2572

#### staticconstantMatrix4.COLUMN0ROW2 :Number

  The index into Matrix4 for column 0, row 2.
  Source: Core/Matrix4.js, line 2580

#### staticconstantMatrix4.COLUMN0ROW3 :Number

  The index into Matrix4 for column 0, row 3.
  Source: Core/Matrix4.js, line 2588

#### staticconstantMatrix4.COLUMN1ROW0 :Number

  The index into Matrix4 for column 1, row 0.
  Source: Core/Matrix4.js, line 2596

#### staticconstantMatrix4.COLUMN1ROW1 :Number

  The index into Matrix4 for column 1, row 1.
  Source: Core/Matrix4.js, line 2604

#### staticconstantMatrix4.COLUMN1ROW2 :Number

  The index into Matrix4 for column 1, row 2.
  Source: Core/Matrix4.js, line 2612

#### staticconstantMatrix4.COLUMN1ROW3 :Number

  The index into Matrix4 for column 1, row 3.
  Source: Core/Matrix4.js, line 2620

#### staticconstantMatrix4.COLUMN2ROW0 :Number

  The index into Matrix4 for column 2, row 0.
  Source: Core/Matrix4.js, line 2628

#### staticconstantMatrix4.COLUMN2ROW1 :Number

  The index into Matrix4 for column 2, row 1.
  Source: Core/Matrix4.js, line 2636

#### staticconstantMatrix4.COLUMN2ROW2 :Number

  The index into Matrix4 for column 2, row 2.
  Source: Core/Matrix4.js, line 2644

#### staticconstantMatrix4.COLUMN2ROW3 :Number

  The index into Matrix4 for column 2, row 3.
  Source: Core/Matrix4.js, line 2652

#### staticconstantMatrix4.COLUMN3ROW0 :Number

  The index into Matrix4 for column 3, row 0.
  Source: Core/Matrix4.js, line 2660

#### staticconstantMatrix4.COLUMN3ROW1 :Number

  The index into Matrix4 for column 3, row 1.
  Source: Core/Matrix4.js, line 2668

#### staticconstantMatrix4.COLUMN3ROW2 :Number

  The index into Matrix4 for column 3, row 2.
  Source: Core/Matrix4.js, line 2676

#### staticconstantMatrix4.COLUMN3ROW3 :Number

  The index into Matrix4 for column 3, row 3.
  Source: Core/Matrix4.js, line 2684

#### staticconstantMatrix4.IDENTITY :Matrix4

  An immutable Matrix4 instance initialized to the identity matrix.
  Source: Core/Matrix4.js, line 2542

#### staticMatrix4.packedLength :Number

  The number of elements used to pack the object into an array.
  Source: Core/Matrix4.js, line 90

#### staticconstantMatrix4.ZERO :Matrix4

  An immutable Matrix4 instance initialized to the zero matrix.
  Source: Core/Matrix4.js, line 2553

### Methods

#### clone(result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 2692

#### equals(right) → Boolean

  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.
  Source: Core/Matrix4.js, line 2703

#### equalsEpsilon(right, epsilon) → Boolean

  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.
  Source: Core/Matrix4.js, line 2738

#### toString() → String

  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)'.
  Source: Core/Matrix4.js, line 2748

#### staticMatrix4.abs(matrix, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 2105

#### staticMatrix4.add(left, right, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 1415

#### staticMatrix4.clone(matrix, result) → Matrix4

  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)
  Source: Core/Matrix4.js, line 176

#### staticMatrix4.computeInfinitePerspectiveOffCenter(left, right, bottom, top, near, far, result)

  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.
  Source: Core/Matrix4.js, line 827

#### staticMatrix4.computeOrthographicOffCenter(left, right, bottom, top, near, far, result)

  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.
  Source: Core/Matrix4.js, line 696

#### staticMatrix4.computePerspectiveFieldOfView(fovY, aspectRatio, near, far, result)

  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.
  Source: Core/Matrix4.js, line 639

#### staticMatrix4.computePerspectiveOffCenter(left, right, bottom, top, near, far, result)

  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.
  Source: Core/Matrix4.js, line 763

#### staticMatrix4.computeViewportTransformation(viewport, nearDepthRange, farDepthRange, result)

  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());

  Source: Core/Matrix4.js, line 894

#### staticMatrix4.equals(left, right) → Boolean

  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

  Source: Core/Matrix4.js, line 2164

#### staticMatrix4.equalsEpsilon(left, right, epsilon) → Boolean

  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

  Source: Core/Matrix4.js, line 2226

#### staticMatrix4.fromArray(array, startingIndex, result) → Matrix4

  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);

  Source: Core/Matrix4.js, line 228

#### staticMatrix4.fromCamera(camera, result)

  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.
  Source: Core/Matrix4.js, line 539

#### staticMatrix4.fromColumnMajorArray(values, result)

  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.
  Source: Core/Matrix4.js, line 237

#### staticMatrix4.fromRotationTranslation(rotation, translation, result)

  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.
  Source: Core/Matrix4.js, line 296

#### staticMatrix4.fromRowMajorArray(values, result)

  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.
  Source: Core/Matrix4.js, line 255

#### staticMatrix4.fromScale(scale, result)

  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));

  Source: Core/Matrix4.js, line 446

#### staticMatrix4.fromTranslation(translation, result)

  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
  Source: Core/Matrix4.js, line 421

#### staticMatrix4.fromTranslationQuaternionRotationScale(translation, rotation, scale, result)

  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);

  Source: Core/Matrix4.js, line 348

#### staticMatrix4.fromUniformScale(scale, result)

  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);

  Source: Core/Matrix4.js, line 495

#### staticMatrix4.getColumn(matrix, index, result) → Cartesian4

  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;

  Source: Core/Matrix4.js, line 1047

#### staticMatrix4.getElementIndex(row, column) → Number

  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;

  Source: Core/Matrix4.js, line 1007

#### staticMatrix4.getMaximumScale(matrix) → Number

  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.
  Source: Core/Matrix4.js, line 1308

#### staticMatrix4.getRotation(matrix, result) → Matrix3

  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]

  Source: Core/Matrix4.js, line 2299

#### staticMatrix4.getRow(matrix, index, result) → Cartesian4

  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;

  Source: Core/Matrix4.js, line 1197

#### staticMatrix4.getScale(matrix, result) → Cartesian3

  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
  Source: Core/Matrix4.js, line 1282

#### staticMatrix4.getTranslation(matrix, result) → Cartesian3

  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.
  Source: Core/Matrix4.js, line 2261

#### staticMatrix4.inverse(matrix, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 2338

#### staticMatrix4.inverseTransformation(matrix, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 2483

#### staticMatrix4.multiply(left, right, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 1321

#### staticMatrix4.multiplyByMatrix3(matrix, rotation, result) → Matrix4

  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);

  Source: Core/Matrix4.js, line 1594

#### staticMatrix4.multiplyByPoint(matrix, cartesian, result) → Cartesian3

  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());

  Source: Core/Matrix4.js, line 1906

#### staticMatrix4.multiplyByPointAsVector(matrix, cartesian, result) → Cartesian3

  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);

  Source: Core/Matrix4.js, line 1866

#### staticMatrix4.multiplyByScalar(matrix, scalar, result) → Matrix4

  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]

  Source: Core/Matrix4.js, line 1957

#### staticMatrix4.multiplyByScale(matrix, scale, result) → Matrix4

  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
  Source: Core/Matrix4.js, line 1771

#### staticMatrix4.multiplyByTranslation(matrix, translation, result) → Matrix4

  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);

  Source: Core/Matrix4.js, line 1672

#### staticMatrix4.multiplyByUniformScale(matrix, scale, result) → Matrix4

  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
  Source: Core/Matrix4.js, line 1733

#### staticMatrix4.multiplyByVector(matrix, cartesian, result) → Cartesian4

  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.
  Source: Core/Matrix4.js, line 1820

#### staticMatrix4.multiplyTransformation(left, right, result) → Matrix4

  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());

  Source: Core/Matrix4.js, line 1506

#### staticMatrix4.negate(matrix, result) → Matrix4

  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]

  Source: Core/Matrix4.js, line 2011

#### staticMatrix4.pack(value, array, startingIndex)

  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.

  Source: Core/Matrix4.js, line 99

#### staticMatrix4.setColumn(matrix, index, cartesian, result) → Matrix4

  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]

  Source: Core/Matrix4.js, line 1100

#### staticMatrix4.setRow(matrix, index, cartesian, result) → Matrix4

  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]

  Source: Core/Matrix4.js, line 1249

#### staticMatrix4.setTranslation(matrix, translation, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 1134

#### staticMatrix4.subtract(left, right, result) → Matrix4

  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.
  Source: Core/Matrix4.js, line 1455

#### staticMatrix4.toArray(matrix, result) → Array.<Number>

  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]

  Source: Core/Matrix4.js, line 959

#### staticMatrix4.transpose(matrix, result) → Matrix4

  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]

  Source: Core/Matrix4.js, line 2062

#### staticMatrix4.unpack(array, startingIndex, result)

  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.

  Source: Core/Matrix4.js, line 137