/// <reference path="../../../globals.d.ts" />
/// <reference path="./vec.d.ts" />

declare module goog.vec.Matrix4 {

    /**
     * @typedef {goog.vec.ArrayType}
     */
    type Type = goog.vec.ArrayType;

    /**
     * Creates the array representation of a 4x4 matrix. The use of the array
     * directly eliminates any overhead associated with the class representation
     * defined above. The returned matrix is cleared to all zeros.
     *
     * @return {goog.vec.Matrix4.Type} The new, sixteen element array.
     */
    function create(): goog.vec.Matrix4.Type;

    /**
     * Creates the array representation of a 4x4 matrix. The use of the array
     * directly eliminates any overhead associated with the class representation
     * defined above. The returned matrix is initialized with the identity
     *
     * @return {goog.vec.Matrix4.Type} The new, sixteen element array.
     */
    function createIdentity(): goog.vec.Matrix4.Type;

    /**
     * Creates a 4x4 matrix initialized from the given array.
     *
     * @param {goog.vec.ArrayType} matrix The array containing the
     *     matrix values in column major order.
     * @return {goog.vec.Matrix4.Type} The new, 16 element array.
     */
    function createFromArray(matrix: goog.vec.ArrayType): goog.vec.Matrix4.Type;

    /**
     * Creates a 4x4 matrix initialized from the given values.
     *
     * @param {number} v00 The values at (0, 0).
     * @param {number} v10 The values at (1, 0).
     * @param {number} v20 The values at (2, 0).
     * @param {number} v30 The values at (3, 0).
     * @param {number} v01 The values at (0, 1).
     * @param {number} v11 The values at (1, 1).
     * @param {number} v21 The values at (2, 1).
     * @param {number} v31 The values at (3, 1).
     * @param {number} v02 The values at (0, 2).
     * @param {number} v12 The values at (1, 2).
     * @param {number} v22 The values at (2, 2).
     * @param {number} v32 The values at (3, 2).
     * @param {number} v03 The values at (0, 3).
     * @param {number} v13 The values at (1, 3).
     * @param {number} v23 The values at (2, 3).
     * @param {number} v33 The values at (3, 3).
     * @return {goog.vec.Matrix4.Type} The new, 16 element array.
     */
    function createFromValues(v00: number, v10: number, v20: number, v30: number, v01: number, v11: number, v21: number, v31: number, v02: number, v12: number, v22: number, v32: number, v03: number, v13: number, v23: number, v33: number): goog.vec.Matrix4.Type;

    /**
     * Creates a clone of a 4x4 matrix.
     *
     * @param {goog.vec.Matrix4.Type} matrix The source 4x4 matrix.
     * @return {goog.vec.Matrix4.Type} The new, 16 element matrix.
     */
    function clone(matrix: goog.vec.Matrix4.Type): goog.vec.Matrix4.Type;

    /**
     * Retrieves the element at the requested row and column.
     *
     * @param {goog.vec.ArrayType} mat The matrix containing the
     *     value to retrieve.
     * @param {number} row The row index.
     * @param {number} column The column index.
     * @return {number} The element value at the requested row, column indices.
     */
    function getElement(mat: goog.vec.ArrayType, row: number, column: number): number;

    /**
     * Sets the element at the requested row and column.
     *
     * @param {goog.vec.ArrayType} mat The matrix containing the
     *     value to retrieve.
     * @param {number} row The row index.
     * @param {number} column The column index.
     * @param {number} value The value to set at the requested row, column.
     */
    function setElement(mat: goog.vec.ArrayType, row: number, column: number, value: number): void;

    /**
     * Initializes the matrix from the set of values. Note the values supplied are
     * in column major order.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {number} v00 The values at (0, 0).
     * @param {number} v10 The values at (1, 0).
     * @param {number} v20 The values at (2, 0).
     * @param {number} v30 The values at (3, 0).
     * @param {number} v01 The values at (0, 1).
     * @param {number} v11 The values at (1, 1).
     * @param {number} v21 The values at (2, 1).
     * @param {number} v31 The values at (3, 1).
     * @param {number} v02 The values at (0, 2).
     * @param {number} v12 The values at (1, 2).
     * @param {number} v22 The values at (2, 2).
     * @param {number} v32 The values at (3, 2).
     * @param {number} v03 The values at (0, 3).
     * @param {number} v13 The values at (1, 3).
     * @param {number} v23 The values at (2, 3).
     * @param {number} v33 The values at (3, 3).
     */
    function setFromValues(mat: goog.vec.ArrayType, v00: number, v10: number, v20: number, v30: number, v01: number, v11: number, v21: number, v31: number, v02: number, v12: number, v22: number, v32: number, v03: number, v13: number, v23: number, v33: number): void;

    /**
     * Sets the matrix from the array of values stored in column major order.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {goog.vec.ArrayType} values The column major ordered
     *     array of values to store in the matrix.
     */
    function setFromArray(mat: goog.vec.ArrayType, values: goog.vec.ArrayType): void;

    /**
     * Sets the matrix from the array of values stored in row major order.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {goog.vec.ArrayType} values The row major ordered array of
     *     values to store in the matrix.
     */
    function setFromRowMajorArray(mat: goog.vec.ArrayType, values: goog.vec.ArrayType): void;

    /**
     * Sets the diagonal values of the matrix from the given values.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {number} v00 The values for (0, 0).
     * @param {number} v11 The values for (1, 1).
     * @param {number} v22 The values for (2, 2).
     * @param {number} v33 The values for (3, 3).
     */
    function setDiagonalValues(mat: goog.vec.ArrayType, v00: number, v11: number, v22: number, v33: number): void;

    /**
     * Sets the diagonal values of the matrix from the given vector.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {goog.vec.ArrayType} vec The vector containing the
     *     values.
     */
    function setDiagonal(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType): void;

    /**
     * Sets the specified column with the supplied values.
     *
     * @param {goog.vec.ArrayType} mat The matrix to recieve the
     *     values.
     * @param {number} column The column index to set the values on.
     * @param {number} v0 The value for row 0.
     * @param {number} v1 The value for row 1.
     * @param {number} v2 The value for row 2.
     * @param {number} v3 The value for row 3.
     */
    function setColumnValues(mat: goog.vec.ArrayType, column: number, v0: number, v1: number, v2: number, v3: number): void;

    /**
     * Sets the specified column with the value from the supplied array.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {number} column The column index to set the values on.
     * @param {goog.vec.ArrayType} vec The vector of elements for the
     *     column.
     */
    function setColumn(mat: goog.vec.ArrayType, column: number, vec: goog.vec.ArrayType): void;

    /**
     * Retrieves the specified column from the matrix into the given vector
     * array.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     values.
     * @param {number} column The column to get the values from.
     * @param {goog.vec.ArrayType} vec The vector of elements to
     *     receive the column.
     */
    function getColumn(mat: goog.vec.ArrayType, column: number, vec: goog.vec.ArrayType): void;

    /**
     * Sets the columns of the matrix from the set of vector elements.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {goog.vec.ArrayType} vec0 The values for column 0.
     * @param {goog.vec.ArrayType} vec1 The values for column 1.
     * @param {goog.vec.ArrayType} vec2 The values for column 2.
     * @param {goog.vec.ArrayType} vec3 The values for column 3.
     */
    function setColumns(mat: goog.vec.ArrayType, vec0: goog.vec.ArrayType, vec1: goog.vec.ArrayType, vec2: goog.vec.ArrayType, vec3: goog.vec.ArrayType): void;

    /**
     * Retrieves the column values from the given matrix into the given vector
     * elements.
     *
     * @param {goog.vec.ArrayType} mat The matrix containing the
     *     columns to retrieve.
     * @param {goog.vec.ArrayType} vec0 The vector elements to receive
     *     column 0.
     * @param {goog.vec.ArrayType} vec1 The vector elements to receive
     *     column 1.
     * @param {goog.vec.ArrayType} vec2 The vector elements to receive
     *     column 2.
     * @param {goog.vec.ArrayType} vec3 The vector elements to receive
     *     column 3.
     */
    function getColumns(mat: goog.vec.ArrayType, vec0: goog.vec.ArrayType, vec1: goog.vec.ArrayType, vec2: goog.vec.ArrayType, vec3: goog.vec.ArrayType): void;

    /**
     * Sets the row values from the supplied values.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {number} row The index of the row to receive the values.
     * @param {number} v0 The value for column 0.
     * @param {number} v1 The value for column 1.
     * @param {number} v2 The value for column 2.
     * @param {number} v3 The value for column 3.
     */
    function setRowValues(mat: goog.vec.ArrayType, row: number, v0: number, v1: number, v2: number, v3: number): void;

    /**
     * Sets the row values from the supplied vector.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     row values.
     * @param {number} row The index of the row.
     * @param {goog.vec.ArrayType} vec The vector containing the
     *     values.
     */
    function setRow(mat: goog.vec.ArrayType, row: number, vec: goog.vec.ArrayType): void;

    /**
     * Retrieves the row values into the given vector.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     values.
     * @param {number} row The index of the row supplying the values.
     * @param {goog.vec.ArrayType} vec The vector to receive the
     *     row.
     */
    function getRow(mat: goog.vec.ArrayType, row: number, vec: goog.vec.ArrayType): void;

    /**
     * Sets the rows of the matrix from the supplied vectors.
     *
     * @param {goog.vec.ArrayType} mat The matrix to receive the
     *     values.
     * @param {goog.vec.ArrayType} vec0 The values for row 0.
     * @param {goog.vec.ArrayType} vec1 The values for row 1.
     * @param {goog.vec.ArrayType} vec2 The values for row 2.
     * @param {goog.vec.ArrayType} vec3 The values for row 3.
     */
    function setRows(mat: goog.vec.ArrayType, vec0: goog.vec.ArrayType, vec1: goog.vec.ArrayType, vec2: goog.vec.ArrayType, vec3: goog.vec.ArrayType): void;

    /**
     * Retrieves the rows of the matrix into the supplied vectors.
     *
     * @param {goog.vec.ArrayType} mat The matrix to supply the
     *     values.
     * @param {goog.vec.ArrayType} vec0 The vector to receive row 0.
     * @param {goog.vec.ArrayType} vec1 The vector to receive row 1.
     * @param {goog.vec.ArrayType} vec2 The vector to receive row 2.
     * @param {goog.vec.ArrayType} vec3 The vector to receive row 3.
     */
    function getRows(mat: goog.vec.ArrayType, vec0: goog.vec.ArrayType, vec1: goog.vec.ArrayType, vec2: goog.vec.ArrayType, vec3: goog.vec.ArrayType): void;

    /**
     * Clears the given matrix to zero.
     *
     * @param {goog.vec.ArrayType} mat The matrix to clear.
     */
    function setZero(mat: goog.vec.ArrayType): void;

    /**
     * Sets the given matrix to the identity matrix.
     *
     * @param {goog.vec.ArrayType} mat The matrix to set.
     */
    function setIdentity(mat: goog.vec.ArrayType): void;

    /**
     * Performs a per-component addition of the matrix mat0 and mat1, storing
     * the result into resultMat.
     *
     * @param {goog.vec.ArrayType} mat0 The first addend.
     * @param {goog.vec.ArrayType} mat1 The second addend.
     * @param {goog.vec.ArrayType} resultMat The matrix to
     *     receive the results (may be either mat0 or mat1).
     * @return {goog.vec.ArrayType} return resultMat so that operations can be
     *     chained together.
     */
    function add(mat0: goog.vec.ArrayType, mat1: goog.vec.ArrayType, resultMat: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Performs a per-component subtraction of the matrix mat0 and mat1,
     * storing the result into resultMat.
     *
     * @param {goog.vec.ArrayType} mat0 The minuend.
     * @param {goog.vec.ArrayType} mat1 The subtrahend.
     * @param {goog.vec.ArrayType} resultMat The matrix to receive
     *     the results (may be either mat0 or mat1).
     * @return {goog.vec.ArrayType} return resultMat so that operations can be
     *     chained together.
     */
    function subtract(mat0: goog.vec.ArrayType, mat1: goog.vec.ArrayType, resultMat: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Performs a component-wise multiplication of mat0 with the given scalar
     * storing the result into resultMat.
     *
     * @param {goog.vec.ArrayType} mat0 The matrix to scale.
     * @param {number} scalar The scalar value to multiple to each element of mat0.
     * @param {goog.vec.ArrayType} resultMat The matrix to receive
     *     the results (may be mat0).
     * @return {goog.vec.ArrayType} return resultMat so that operations can be
     *     chained together.
     */
    function scale(mat0: goog.vec.ArrayType, scalar: number, resultMat: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Multiplies the two matrices mat0 and mat1 using matrix multiplication,
     * storing the result into resultMat.
     *
     * @param {goog.vec.ArrayType} mat0 The first (left hand) matrix.
     * @param {goog.vec.ArrayType} mat1 The second (right hand)
     *     matrix.
     * @param {goog.vec.ArrayType} resultMat The matrix to receive
     *     the results (may be either mat0 or mat1).
     * @return {goog.vec.ArrayType} return resultMat so that operations can be
     *     chained together.
     */
    function multMat(mat0: goog.vec.ArrayType, mat1: goog.vec.ArrayType, resultMat: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Transposes the given matrix mat storing the result into resultMat.
     * @param {goog.vec.ArrayType} mat The matrix to transpose.
     * @param {goog.vec.ArrayType} resultMat The matrix to receive
     *     the results (may be mat).
     * @return {goog.vec.ArrayType} return resultMat so that operations can be
     *     chained together.
     */
    function transpose(mat: goog.vec.ArrayType, resultMat: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Computes the determinant of the matrix.
     *
     * @param {goog.vec.ArrayType} mat The matrix to compute the
     *     matrix for.
     * @return {number} The determinant of the matrix.
     */
    function determinant(mat: goog.vec.ArrayType): number;

    /**
     * Computes the inverse of mat storing the result into resultMat. If the
     * inverse is defined, this function returns true, false otherwise.
     *
     * @param {goog.vec.ArrayType} mat The matrix to invert.
     * @param {goog.vec.ArrayType} resultMat The matrix to receive
     *     the result (may be mat).
     * @return {boolean} True if the inverse is defined. If false is returned,
     *     resultMat is not modified.
     */
    function invert(mat: goog.vec.ArrayType, resultMat: goog.vec.ArrayType): boolean;

    /**
     * Returns true if the components of mat0 are equal to the components of mat1.
     *
     * @param {goog.vec.ArrayType} mat0 The first matrix.
     * @param {goog.vec.ArrayType} mat1 The second matrix.
     * @return {boolean} True if the the two matrices are equivalent.
     */
    function equals(mat0: goog.vec.ArrayType, mat1: goog.vec.ArrayType): boolean;

    /**
     * Transforms the given vector with the given matrix storing the resulting,
     * transformed vector into resultVec. The input vector is multiplied against the
     * upper 3x4 matrix omitting the projective component.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     transformation.
     * @param {goog.vec.ArrayType} vec The 3 element vector to
     *     transform.
     * @param {goog.vec.ArrayType} resultVec The 3 element vector to
     *     receive the results (may be vec).
     * @return {goog.vec.ArrayType} return resultVec so that operations can be
     *     chained together.
     */
    function multVec3(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType, resultVec: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Transforms the given vector with the given matrix storing the resulting,
     * transformed vector into resultVec. The input vector is multiplied against the
     * upper 3x3 matrix omitting the projective component and translation
     * components.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     transformation.
     * @param {goog.vec.ArrayType} vec The 3 element vector to
     *     transform.
     * @param {goog.vec.ArrayType} resultVec The 3 element vector to
     *     receive the results (may be vec).
     * @return {goog.vec.ArrayType} return resultVec so that operations can be
     *     chained together.
     */
    function multVec3NoTranslate(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType, resultVec: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Transforms the given vector with the given matrix storing the resulting,
     * transformed vector into resultVec. The input vector is multiplied against the
     * full 4x4 matrix with the homogeneous divide applied to reduce the 4 element
     * vector to a 3 element vector.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     transformation.
     * @param {goog.vec.ArrayType} vec The 3 element vector to
     *     transform.
     * @param {goog.vec.ArrayType} resultVec The 3 element vector
     *     to receive the results (may be vec).
     * @return {goog.vec.ArrayType} return resultVec so that operations can be
     *     chained together.
     */
    function multVec3Projective(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType, resultVec: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Transforms the given vector with the given matrix storing the resulting,
     * transformed vector into resultVec.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     transformation.
     * @param {goog.vec.ArrayType} vec The vector to transform.
     * @param {goog.vec.ArrayType} resultVec The vector to
     *     receive the results (may be vec).
     * @return {goog.vec.ArrayType} return resultVec so that operations can be
     *     chained together.
     */
    function multVec4(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType, resultVec: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Transforms the given vector with the given matrix storing the resulting,
     * transformed vector into resultVec. The input matrix is multiplied against the
     * upper 3x4 matrix omitting the projective component.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     transformation.
     * @param {goog.vec.ArrayType} vec The 3 element vector to
     *     transform.
     * @param {goog.vec.ArrayType} resultVec The 3 element vector to
     *     receive the results (may be vec).
     * @return {goog.vec.ArrayType} return resultVec so that operations can be
     *     chained together.
     */
    function multVec3ToArray(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType, resultVec: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Transforms the given vector with the given matrix storing the resulting,
     * transformed vector into resultVec.
     *
     * @param {goog.vec.ArrayType} mat The matrix supplying the
     *     transformation.
     * @param {goog.vec.ArrayType} vec The vector to transform.
     * @param {goog.vec.ArrayType} resultVec The vector to
     *     receive the results (may be vec).
     * @return {goog.vec.ArrayType} return resultVec so that operations can be
     *     chained together.
     */
    function multVec4ToArray(mat: goog.vec.ArrayType, vec: goog.vec.ArrayType, resultVec: goog.vec.ArrayType): goog.vec.ArrayType;

    /**
     * Initializes the given 4x4 matrix as a translation matrix with x, y and z
     * translation factors.
     * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix
     *     array to receive the new translation matrix.
     * @param {number} x The translation along the x axis.
     * @param {number} y The translation along the y axis.
     * @param {number} z The translation along the z axis.
     */
    function makeTranslate(mat: goog.vec.ArrayType, x: number, y: number, z: number): void;

    /**
     * Initializes the given 4x4 matrix as a scale matrix with x, y and z scale
     * factors.
     * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix
     *     array to receive the new translation matrix.
     * @param {number} x The scale along the x axis.
     * @param {number} y The scale along the y axis.
     * @param {number} z The scale along the z axis.
     */
    function makeScale(mat: goog.vec.ArrayType, x: number, y: number, z: number): void;

    /**
     * Initializes the given 4x4 matrix as a rotation matrix with the given rotation
     * angle about the axis defined by the vector (ax, ay, az).
     * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix
     *     array to receive the new translation matrix.
     * @param {number} angle The rotation angle in radians.
     * @param {number} ax The x component of the rotation axis.
     * @param {number} ay The y component of the rotation axis.
     * @param {number} az The z component of the rotation axis.
     */
    function makeAxisAngleRotate(mat: goog.vec.ArrayType, angle: number, ax: number, ay: number, az: number): void;

    /**
     * Initializes the given 4x4 matrix as a perspective projection matrix.
     * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix
     *     array to receive the new translation matrix.
     * @param {number} left The coordinate of the left clipping plane.
     * @param {number} right The coordinate of the right clipping plane.
     * @param {number} bottom The coordinate of the bottom clipping plane.
     * @param {number} top The coordinate of the top clipping plane.
     * @param {number} near The distance to the near clipping plane.
     * @param {number} far The distance to the far clipping plane.
     */
    function makeFrustum(mat: goog.vec.ArrayType, left: number, right: number, bottom: number, top: number, near: number, far: number): void;

    /**
     * Initializes the given 4x4 matrix as a perspective projection matrix given a
     * field of view and aspect ratio.
     * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix
     *     array to receive the new translation matrix.
     * @param {number} fovy The field of view along the y (vertical) axis in
     *     radians.
     * @param {number} aspect The x (width) to y (height) aspect ratio.
     * @param {number} near The distance to the near clipping plane.
     * @param {number} far The distance to the far clipping plane.
     */
    function makePerspective(mat: goog.vec.ArrayType, fovy: number, aspect: number, near: number, far: number): void;

    /**
     * Initializes the given 4x4 matrix as an orthographic projection matrix.
     * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix
     *     array to receive the new translation matrix.
     * @param {number} left The coordinate of the left clipping plane.
     * @param {number} right The coordinate of the right clipping plane.
     * @param {number} bottom The coordinate of the bottom clipping plane.
     * @param {number} top The coordinate of the top clipping plane.
     * @param {number} near The distance to the near clipping plane.
     * @param {number} far The distance to the far clipping plane.
     */
    function makeOrtho(mat: goog.vec.ArrayType, left: number, right: number, bottom: number, top: number, near: number, far: number): void;

    /**
     * Updates a matrix representing the modelview matrix of a camera so that
     * the camera is 'looking at' the given center point.
     * @param {goog.vec.ArrayType} viewMatrix The matrix.
     * @param {goog.vec.ArrayType} eyePt The position of the eye point
     *     (camera origin).
     * @param {goog.vec.ArrayType} centerPt The point to aim the camera
     *     at.
     * @param {goog.vec.ArrayType} worldUpVec The vector that
     *     identifies the up direction for the camera.
     */
    function lookAt(viewMatrix: goog.vec.ArrayType, eyePt: goog.vec.ArrayType, centerPt: goog.vec.ArrayType, worldUpVec: goog.vec.ArrayType): void;

    /**
     * Decomposes a matrix into the lookAt vectors eyePt, fwdVec and worldUpVec.
     * The matrix represents the modelview matrix of a camera. It is the inverse
     * of lookAt except for the output of the fwdVec instead of centerPt.
     * The centerPt itself cannot be recovered from a modelview matrix.
     * @param {goog.vec.ArrayType} viewMatrix The matrix.
     * @param {goog.vec.ArrayType} eyePt The position of the eye point
     *     (camera origin).
     * @param {goog.vec.ArrayType} fwdVec The vector describing where
     *     the camera points to.
     * @param {goog.vec.ArrayType} worldUpVec The vector that
     *     identifies the up direction for the camera.
     * @return {boolean} True if the method succeeds, false otherwise.
     *     The method can only fail if the inverse of viewMatrix is not defined.
     */
    function toLookAt(viewMatrix: goog.vec.ArrayType, eyePt: goog.vec.ArrayType, fwdVec: goog.vec.ArrayType, worldUpVec: goog.vec.ArrayType): boolean;

    /**
     * Constructs a rotation matrix from its Euler angles using the ZXZ convention.
     * Given the euler angles [theta1, theta2, theta3], the rotation is defined as
     * rotation = rotation_z(theta1) * rotation_x(theta2) * rotation_z(theta3),
     * where rotation_x(theta) means rotation around the X axis of theta radians.
     * @param {goog.vec.ArrayType} matrix The rotation matrix.
     * @param {number} theta1 The angle of rotation around the Z axis in radians.
     * @param {number} theta2 The angle of rotation around the X axis in radians.
     * @param {number} theta3 The angle of rotation around the Z axis in radians.
     */
    function fromEulerZXZ(matrix: goog.vec.ArrayType, theta1: number, theta2: number, theta3: number): void;

    /**
     * Decomposes a rotation matrix into Euler angles using the ZXZ convention.
     * @param {goog.vec.ArrayType} matrix The rotation matrix.
     * @param {goog.vec.ArrayType} euler The ZXZ Euler angles in
     *     radians. euler = [roll, tilt, pan].
     */
    function toEulerZXZ(matrix: goog.vec.ArrayType, euler: goog.vec.ArrayType): void;

    /**
     * Applies a translation by x,y,z to the given matrix.
     *
     * @param {goog.vec.ArrayType} mat The matrix.
     * @param {number} x The translation along the x axis.
     * @param {number} y The translation along the y axis.
     * @param {number} z The translation along the z axis.
     */
    function applyTranslate(mat: goog.vec.ArrayType, x: number, y: number, z: number): void;

    /**
     * Applies an x,y,z scale to the given matrix.
     *
     * @param {goog.vec.ArrayType} mat The matrix.
     * @param {number} x The x scale factor.
     * @param {number} y The y scale factor.
     * @param {number} z The z scale factor.
     */
    function applyScale(mat: goog.vec.ArrayType, x: number, y: number, z: number): void;

    /**
     * Applies a rotation by angle about the x,y,z axis to the given matrix.
     *
     * @param {goog.vec.ArrayType} mat The matrix.
     * @param {number} angle The angle in radians.
     * @param {number} x The x component of the rotation axis.
     * @param {number} y The y component of the rotation axis.
     * @param {number} z The z component of the rotation axis.
     */
    function applyRotate(mat: goog.vec.ArrayType, angle: number, x: number, y: number, z: number): void;
}