@kitware/vtk.js/Common/Core/Math.d.ts

Visualization Toolkit for the Web

import {
  Bounds,
  Extent,
  HSVColor,
  RGBAColor,
  RGBColor,
  Matrix,
  Matrix3x3,
  Range,
  Vector2,
  Vector3,
  Vector4,
} from './../../types';

/**
 *
 * @param {Number} size The size of the array.
 */
export function createArray(size?: number): number[];

/**
 * Given two rows indices, swap the two rows of a nxn matrix
 * @param {Number[]} matrix The n by n matrix in wich we want to swap the vectors.
 * @param {Number} n size of the matrix.
 * @param {Number} row1 index of first row to swap with the other.
 * @param {Number} row2 index of second row to swap with the other.
 */
export function swapRowsMatrix_nxn(
  matrix: number[],
  n: number,
  row1: number,
  row2: number
): void;

/**
 * Given two columns indices, swap the two columns of a nxn matrix
 * @param {Number[]} matrix The n by n matrix in wich we want to swap the vectors.
 * @param {Number} n size of the matrix.
 * @param {Number} column1 index of first col to swap with the other.
 * @param {Number} column2 index of second col to swap with the other.
 */
export function swapColumnsMatrix_nxn(
  matrix: number[],
  n: number,
  column1: number,
  column2: number
): void;

/**
 * Get the number π.
 */
export function Pi(): number;

/**
 * Calculates x times (2 to the power of exponent).
 */
export function ldexp(x: number, exponent: number): number;

/**
 * Convert degrees to radians.
 * @param {Number} deg The value in degrees.
 */
export function radiansFromDegrees(deg: number): number;

/**
 * Convert radians to degrees.
 * @param {Number} rad The value in radians.
 */
export function degreesFromRadians(rad: number): number;

/**
 * Same as Math.round().
 * @param {Number} param1 The value to be rounded to the nearest integer.
 */
export function round(param1: number): number;

/**
 * Same as Math.floor().
 * @param {Number} param1 A numeric expression.
 */
export function floor(param1: number): number;

/**
 * Same as Math.ceil().
 * @param {Number} param1 A numeric expression.
 */
export function ceil(param1: number): number;

/**
 * Get the minimum of the two arguments provided. If either argument is NaN,
 * the first argument will always be returned.
 * @param {Number} param1 The first numeric expression.
 * @param {Number} param2 The second numeric expression.
 */
export function min(param1: number, param2: number): number;

/**
 * Get the maximum of the two arguments provided. If either argument is NaN,
 * the first argument will always be returned.
 * @param {Number} param1 The first numeric expression.
 * @param {Number} param2 The second numeric expression.
 */
export function max(param1: number, param2: number): number;

/**
 * Get the minimum of the array.
 * @param {Number[]} arr The array.
 * @param {Number} offset The offset.
 * @param {Number} stride The stride.
 */
export function arrayMin(arr: number[], offset: number, stride: number): number;

/**
 * Get the maximum of the array.
 * @param {Number[]} arr The array.
 * @param {Number} offset The offset.
 * @param {Number} stride The stride.
 */
export function arrayMax(arr: number[], offset: number, stride: number): number;

/**
 *
 * @param {Number[]} arr The array.
 * @param {Number} offset The offset.
 * @param {Number} stride The stride.
 */
export function arrayRange(
  arr: number[],
  offset: number,
  stride: number
): number[];

/**
 * Gives the exponent of the lowest power of two not less than x.
 *
 */
export function ceilLog2(): void;

/**
 * Compute N factorial, N! = N*(N-1) * (N-2)...*3*2*1.
 */
export function factorial(): void;

/**
 * Generate pseudo-random numbers distributed according to the standard normal
 * distribution.
 */
export function gaussian(): void;

/**
 * Compute the nearest power of two that is not less than x.
 * @param {Number} xi A numeric expression.
 */
export function nearestPowerOfTwo(xi: number): number;

/**
 * Returns true if integer is a power of two.
 * @param {Number} x A numeric expression.
 */
export function isPowerOfTwo(x: number): boolean;

/**
 * The number of combinations of n objects from a pool of m objects (m>n).
 * @param {Number} m The first numeric expression.
 * @param {Number} n The second numeric expression.
 */
export function binomial(m: number, n: number): number;

/**
 * Start iterating over "m choose n" objects.
 * @param {Number} [m] The first numeric expression.
 * @param {Number} [n] The second numeric expression.
 */
export function beginCombination(m?: number, n?: number): number;

/**
 * Given m, n, and a valid combination of n integers in the range [0,m[, this
 * function alters the integers into the next combination in a sequence of all
 * combinations of n items from a pool of m.
 * @param {Number} m The first numeric expression.
 * @param {Number} n The second numeric expression.
 * @param {Number[]} r
 */
export function nextCombination(m: number, n: number, r: number[]): number;

/**
 * Initialize seed value.
 * @param {Number} seed
 */
export function randomSeed(seed: number): void;

/**
 * Return the current seed used by the random number generator.
 */
export function getSeed(): number;

/**
 * Generate pseudo-random numbers distributed according to the uniform
 * distribution between min and max.
 * @param {Number} minValue
 * @param {Number} maxValue
 */
export function random(minValue: number, maxValue: number): number;

/**
 * Add two 3-vectors.
 * @param {Vector3} a The first 3D vector.
 * @param {Vector3} b The second 3D vector.
 * @param {Vector3} out The output 3D vector.
 * @example
 * ```js
 * a[3] + b[3] => out[3]
 * ```
 */
export function add(a: Vector3, b: Vector3, out: Vector3): Vector3;

/**
 * Substract two 3-vectors.
 * @param {Vector3} a The first 3D vector.
 * @param {Vector3} b The second 3D vector.
 * @param {Vector3} out The output 3D vector.
 * @example
 * ```js
 * a[3] - b[3] => out[3]
 * ```
 */
export function subtract(a: Vector3, b: Vector3, out: Vector3): Vector3;

/**
 * Multiply a 3-vector by a scalar.
 * @param {Vector3} vec
 * @param {Number} scalar
 * @example
 * ```js
 * vec[3] * scalar => vec[3]
 * ```
 */
export function multiplyScalar(vec: Vector3, scalar: number): Vector3;

/**
 * Multiply a 3-vector by a scalar.
 * @param {Vector2} vec
 * @param {Number} scalar
 * @example
 * ```js
 * vec[3] * scalar => vec[3]
 * ```
 */
export function multiplyScalar2D(vec: Vector2, scalar: number): Vector2;

/**
 * Multiply two 3-vectors.
 * @param {Vector3} a
 * @param {Vector3} b
 * @param {Number} scalar
 * @param {Vector3} out
 * @example
 * ```js
 * a[3] +  b[3] * scalar => out[3]
 * ```
 */
export function multiplyAccumulate(
  a: Vector3,
  b: Vector3,
  scalar: number,
  out: Vector3
): Vector3;

/**
 * Multiply two 2-vectors.
 * @param {Vector2} a
 * @param {Vector2} b
 * @param {Number} scalar
 * @param {Vector2} out
 * @example
 * ```js
 * a[2] + b[2] * scalar => out[2]
 * ```
 */
export function multiplyAccumulate2D(
  a: Vector2,
  b: Vector2,
  scalar: number,
  out: Vector2
): Vector2;

/**
 * Dot product of two 3-vectors.
 * @param {Vector3} x
 * @param {Vector3} y
 * @example
 * ```js
 * a[2] + b[2] * scalar => out[2]
 * ```
 */
export function dot(x: Vector3, y: Vector3): number;

/**
 * Outer product of two 3-vectors.
 * @param {Vector3} x The first 3D vector.
 * @param {Vector3} y The second 3D vector.
 * @param {Matrix3x3} out_3x3 The output 3x3 matrix.
 */
export function outer(x: Vector3, y: Vector3, out_3x3: Matrix3x3): void;

/**
 * Computes cross product of 3D vectors x and y.
 * @param {Vector3} x The first 3D vector.
 * @param {Vector3} y The second 3D vector.
 * @param {Vector3} out The output 3D vector.
 */
export function cross(x: Vector3, y: Vector3, out: Vector3): Vector3;

/**
 * Compute the norm of a vector.
 * @param {Number[]} x The vector to compute the norm of.
 * @param {Number} [n] The number of components to consider (default is 3).
 */
export function norm(x: number[], n?: number): number;

/**
 * Normalize in place. Returns norm.
 * @param {Number[]} x The vector to normalize.
 */
export function normalize(x: number[]): number;

/**
 * Normalize in place. Returns norm.
 * @param {Number[]} x The vector to normalize.
 */
export function normalize4D(x: number[]): number;

/**
 * Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3
 * @param {Vector3} x The first vector.
 * @param {Vector3} y The second vector.
 * @param {Vector3} z The third vector.
 * @param {Number} theta
 */
export function perpendiculars(
  x: Vector3,
  y: Vector3,
  z: Vector3,
  theta: number
): void;

/**
 * Project vector `a` onto vector `b` and returns the result in projection vector.
 * @param {Vector3} a The first 3D vector.
 * @param {Vector3} b The second 3D vector.
 * @param {Vector3} projection The projection 3D vector.
 */
export function projectVector(
  a: Vector3,
  b: Vector3,
  projection: Vector3
): boolean;

/**
 * Compute the dot product of two 2D vectors.
 * @param {Vector2} x
 * @param {Vector2} y
 */
export function dot2D(x: Vector2, y: Vector2): number;

/**
 * Compute the projection of 2D vector `a` on 2D vector `b` and returns the
 * result in projection vector.
 * @param {Vector2} a The first 2D vector.
 * @param {Vector2} b The second 2D vector.
 * @param {Vector2} projection The projection 2D vector.
 */
export function projectVector2D(
  a: Vector2,
  b: Vector2,
  projection: Vector2
): boolean;

/**
 * Compute distance squared between two points p1 and p2.
 * @param {Vector3} x The first 3D vector.
 * @param {Vector3} y The second 3D vector.
 */
export function distance2BetweenPoints(x: Vector3, y: Vector3): number;

/**
 * Angle between 3D vectors.
 * @param {Vector3} v1 The first 3D vector.
 * @param {Vector3} v2 The second 3D vector.
 */
export function angleBetweenVectors(v1: Vector3, v2: Vector3): number;

/**
 * Signed angle between v1 and v2 with regards to plane defined by normal vN.
 * angle between v1 and v2 with regards to plane defined by normal vN.Signed
 * angle between v1 and v2 with regards to plane defined by normal
 * vN.t3(mat_3x3, in_3, out_3)
 * @param {Vector3} v1 The first 3D vector.
 * @param {Vector3} v2 The second 3D vector.
 * @param {Vector3} vN
 */
export function signedAngleBetweenVectors(
  v1: Vector3,
  v2: Vector3,
  vN: Vector3
): number;

/**
 * Compute the amplitude of a Gaussian function with mean=0 and specified variance.
 * @param {Number} mean The mean value.
 * @param {Number} variance The variance value.
 * @param {Number} position The position value.
 */
export function gaussianAmplitude(
  mean: number,
  variance: number,
  position: number
): number;

/**
 * Compute the amplitude of an unnormalized Gaussian function with mean=0 and
 * specified variance.
 * @param {Number} mean The mean value.
 * @param {Number} variance The variance value.
 * @param {Number} position The position value.
 */
export function gaussianWeight(
  mean: number,
  variance: number,
  position: number
): number;

/**
 * Outer product of two 2-vectors.
 * @param {Vector2} x The first 2D vector.
 * @param {Vector2} y The second 2D vector.
 * @param {Matrix} out_2x2 The output 2x2 matrix.
 */
export function outer2D(x: Vector2, y: Vector2, out_2x2: Matrix): void;

/**
 * Compute the norm of a 2-vector.
 * @param {Vector2} x2D x The 2D vector.
 */
export function norm2D(x2D: Vector2): number;

/**
 * Normalize (in place) a 2-vector.
 * @param {Vector2} x The 2D vector.
 */
export function normalize2D(x: Vector2): number;

/**
 *
 * @param {Number[]} args
 */
export function determinant2x2(args: number[]): number;

/**
 * Fill a 4x4 matrix with the given row vectors
 * @param {Vector4} row0
 * @param {Vector4} row1
 * @param {Vector4} row2
 * @param {Vector4} row3
 * @param {Matrix} mat
 */
export function rowsToMat4(
  row0: Vector4,
  row1: Vector4,
  row2: Vector4,
  row3: Vector4,
  mat: Matrix
): Matrix;

/**
 * Fill a 4x4 matrix with the given column vectors
 * @param {Vector4} column0
 * @param {Vector4} column1
 * @param {Vector4} column2
 * @param {Vector4} column3
 * @param {Matrix} mat
 */
export function columnsToMat4(
  column0: Vector4,
  column1: Vector4,
  column2: Vector4,
  column3: Vector4,
  mat: Matrix
): Matrix;

/**
 * Fill a 3x3 matrix with the given row vectors
 * @param {Vector3} row0
 * @param {Vector3} row1
 * @param {Vector3} row2
 * @param {Matrix} mat
 */
export function rowsToMat3(
  row0: Vector3,
  row1: Vector3,
  row2: Vector3,
  mat: Matrix
): Matrix;

/**
 * Fill a 3x3 matrix with the given column vectors
 * @param {Vector3} column0
 * @param {Vector3} column1
 * @param {Vector3} column2
 * @param {Matrix} mat
 */
export function columnsToMat3(
  column0: Vector3,
  column1: Vector3,
  column2: Vector3,
  mat: Matrix
): Matrix;

/**
 * LU Factorization of a 3x3 matrix.
 * @param {Matrix3x3} mat_3x3
 * @param {Vector3} index_3
 */
export function LUFactor3x3(mat_3x3: Matrix3x3, index_3: Vector3): void;

/**
 * LU back substitution for a 3x3 matrix.
 * @param {Matrix3x3} mat_3x3
 * @param {Vector3} index_3
 * @param {Vector3} x_3
 */
export function LUSolve3x3(
  mat_3x3: Matrix3x3,
  index_3: Vector3,
  x_3: Vector3
): void;

/**
 * Solve mat_3x3y_3 = x_3 for y and place the result in y.
 * @param {Matrix3x3} mat_3x3
 * @param {Vector3} x_3
 * @param {Vector3} y_3
 */
export function linearSolve3x3(
  mat_3x3: Matrix3x3,
  x_3: Vector3,
  y_3: Vector3
): void;

/**
 *
 * @param {Matrix3x3} mat_3x3
 * @param {Vector3} in_3
 * @param {Vector3} out_3
 */
export function multiply3x3_vect3(
  mat_3x3: Matrix3x3,
  in_3: Vector3,
  out_3: Vector3
): void;

/**
 *
 * @param {Matrix3x3} a_3x3
 * @param {Matrix3x3} b_3x3
 * @param {Matrix3x3} out_3x3
 */
export function multiply3x3_mat3(
  a_3x3: Matrix3x3,
  b_3x3: Matrix3x3,
  out_3x3: Matrix3x3
): void;

/**
 * Multiply two matrices.
 * @param {Matrix} a
 * @param {Matrix} b
 * @param {Number} rowA
 * @param {Number} colA
 * @param {Number} rowB
 * @param {Number} colB
 * @param {Matrix} outRowAColB
 */
export function multiplyMatrix(
  a: Matrix,
  b: Matrix,
  rowA: number,
  colA: number,
  rowB: number,
  colB: number,
  outRowAColB: Matrix
): void;

/**
 * Transpose a 3x3 matrix.
 * @param {Matrix3x3} in_3x3 The input 3x3 matrix.
 * @param {Matrix3x3} outT_3x3 The output 3x3 matrix.
 */
export function transpose3x3(in_3x3: Matrix3x3, outT_3x3: Matrix3x3): void;

/**
 * Invert a 3x3 matrix.
 * @param {Matrix3x3} in_3x3 The input 3x3 matrix.
 * @param {Matrix3x3} outI_3x3 The output 3x3 matrix.
 */
export function invert3x3(in_3x3: Matrix3x3, outI_3x3: Matrix3x3): void;

/**
 * Set mat to the identity matrix.
 * @param {Number} n The size of the matrix.
 * @param {Number[]} mat The output matrix.
 * @see isIdentity()
 * @see identity3x3()
 */
export function identity(n: number, mat: number[]): void;

/**
 * Set mat_3x3 to the identity matrix.
 * @param {Matrix3x3} mat_3x3 The input 3x3 matrix.
 * @see isIdentity3x3()
 * @see identity()
 */
export function identity3x3(mat_3x3: Matrix3x3): void;

/**
 * Returns true if provided matrix is the identity matrix.
 * @param {Number[]} mat The 3x3 matrix to check
 * @param {Number} [eps] The tolerance value.
 * @see isIdentity()
 * @see identity()
 */
export function isIdentity(mat: Matrix3x3, eps?: number): boolean;

/**
 * Returns true if provided 3x3 matrix is the identity matrix.
 * @param {Matrix3x3} mat The 3x3 matrix to check
 * @param {Number} [eps] The tolerance value.
 * @see isIdentity()
 * @see identity3x3()
 */
export function isIdentity3x3(mat: Matrix3x3, eps?: number): boolean;

/**
 * Calculate the determinant of a 3x3 matrix.
 * @param {Matrix3x3} mat_3x3 The input 3x3 matrix.
 */
export function determinant3x3(mat_3x3: Matrix3x3): number;

/**
 *
 * @param {Vector4} quat_4
 * @param {Matrix3x3} mat_3x3
 */
export function quaternionToMatrix3x3(
  quat_4: Vector4,
  mat_3x3: Matrix3x3
): void;

/**
 * Returns true if elements of both arrays are equals.
 * @param {Number[]} a An array of numbers (vector, point, matrix...)
 * @param {Number[]} b An array of numbers (vector, point, matrix...)
 * @param {Number} [eps] The tolerance value.
 */
export function areEquals(a: number[], b: number[], eps?: number): boolean;

/**
 *
 * @param {Number} num
 * @param {Number} [digits]
 */
export function roundNumber(num: number, digits?: number): number;

/**
 *
 * @param {Vector3} vector
 * @param {Vector3} [out]
 * @param {Number} [digits]
 */
export function roundVector(
  vector: Vector3,
  out?: Vector3,
  digits?: number
): Vector3;

/**
 * Jacobi iteration for the solution of eigenvectors/eigenvalues. Input matrix a is modified (the upper triangle is filled with zeros)
 * @param {Matrix} a real symetric nxn matrix
 * @param {Number} n matrix size
 * @param {Number[]} w vector of size n to store eigenvalues (stored in decreasing order)
 * @param {Number[]} v matrix of size nxn to store eigenvectors (stored in decreasing order, normalized)
 */
export function jacobiN(a: Matrix, n: number, w: number[], v: number[]): number;

/**
 *
 * @param {Matrix3x3} mat_3x3
 * @param {Vector4} quat_4
 */
export function matrix3x3ToQuaternion(
  mat_3x3: Matrix3x3,
  quat_4: Vector4
): void;

/**
 *
 * @param {Vector4} quat_1
 * @param {Vector4} quat_2
 * @param {Vector4} quat_out
 */
export function multiplyQuaternion(
  quat_1: Vector4,
  quat_2: Vector4,
  quat_out: Vector4
): void;

/**
 *
 * @param {Matrix3x3} a_3x3
 * @param {Matrix3x3} out_3x3
 */
export function orthogonalize3x3(a_3x3: Matrix3x3, out_3x3: Matrix3x3): void;

/**
 *
 * @param {Matrix3x3} a_3x3
 * @param {Vector3} w_3
 * @param {Matrix3x3} v_3x3
 */
export function diagonalize3x3(
  a_3x3: Matrix3x3,
  w_3: Vector3,
  v_3x3: Matrix3x3
): void;

/**
 *
 * @param {Matrix3x3} a_3x3
 * @param {Matrix3x3} u_3x3
 * @param {Vector3} w_3
 * @param {Matrix3x3} vT_3x3
 */
export function singularValueDecomposition3x3(
  a_3x3: Matrix3x3,
  u_3x3: Matrix3x3,
  w_3: Vector3,
  vT_3x3: Matrix3x3
): void;

/**
 *
 * @param {Matrix} A
 * @param {Number[]} index
 * @param {Number} size
 */
export function luFactorLinearSystem(
  A: Matrix,
  index: number[],
  size: number
): number;

/**
 *
 * @param {Matrix} A
 * @param {Number[]} index
 * @param {Number[]} x
 * @param {Number} size
 */
export function luSolveLinearSystem(
  A: Matrix,
  index: number[],
  x: number[],
  size: number
): void;

/**
 *
 * @param {Matrix} A
 * @param {Number[]} x
 * @param {Number} size
 */
export function solveLinearSystem(A: Matrix, x: number[], size: number): number;

/**
 *
 * @param {Matrix} A The input matrix. It is modified during the inversion.
 * @param {Matrix} AI The output inverse matrix. Can be the same as input matrix.
 * @param {Number} [size] The square size of the matrix to invert : 4 for a 4x4
 * @param {Number[]} [index]
 * @param {Number[]} [column]
 * @returns AI on success, null otherwise
 */
export function invertMatrix(
  A: Matrix,
  AI: Matrix,
  size?: number,
  index?: number[],
  column?: number[]
): Matrix | null;

/**
 *
 * @param {Matrix} A
 * @param {Number} size
 */
export function estimateMatrixCondition(A: Matrix, size: number): number;

/**
 *
 * @param {Matrix3x3} a_3x3
 * @param {Number[]} w
 * @param {Number[]} v
 */
export function jacobi(a_3x3: Matrix3x3, w: number[], v: number[]): number;

/**
 * Solves for the least squares best fit matrix for the homogeneous equation
 * X'M' = 0'. Uses the method described on pages 40-41 of Computer Vision by
 * Forsyth and Ponce, which is that the solution is the eigenvector associated
 * with the minimum eigenvalue of T(X)X, where T(X) is the transpose of X. The
 * inputs and output are transposed matrices. Dimensions: X' is numberOfSamples
 * by xOrder, M' dimension is xOrder by yOrder. M' should be pre-allocated. All
 * matrices are row major. The resultant matrix M' should be pre-multiplied to
 * X' to get 0', or transposed and then post multiplied to X to get 0
 * @param {Number} numberOfSamples
 * @param {Matrix} xt
 * @param {Number} xOrder
 * @param {Matrix} mt
 */
export function solveHomogeneousLeastSquares(
  numberOfSamples: number,
  xt: Matrix,
  xOrder: number,
  mt: Matrix
): number;

/**
 * Solves for the least squares best fit matrix for the equation X'M' = Y'. Uses
 * pseudoinverse to get the ordinary least squares. The inputs and output are
 * transposed matrices. Dimensions: X' is numberOfSamples by xOrder, Y' is
 * numberOfSamples by yOrder, M' dimension is xOrder by yOrder. M' should be
 * pre-allocated. All matrices are row major. The resultant matrix M' should be
 * pre-multiplied to X' to get Y', or transposed and then post multiplied to X
 * to get Y By default, this method checks for the homogeneous condition where
 * Y==0, and if so, invokes SolveHomogeneousLeastSquares. For better performance
 * when the system is known not to be homogeneous, invoke with
 * checkHomogeneous=0.
 * @param {Number} numberOfSamples
 * @param {Matrix} xt
 * @param {Number} xOrder
 * @param {Matrix} yt
 * @param {Number} yOrder
 * @param {Matrix} mt
 * @param {Boolean} [checkHomogeneous]
 */
export function solveLeastSquares(
  numberOfSamples: number,
  xt: Matrix,
  xOrder: number,
  yt: Matrix,
  yOrder: number,
  mt: Matrix,
  checkHomogeneous?: boolean
): number;

/**
 *
 * @param {String} hexStr
 * @param {Number[]} [outFloatArray]
 */
export function hex2float(hexStr: string, outFloatArray?: number[]): number[];

/**
 *
 * @param {RGBColor} rgb An Array of the RGB color.
 * @param {HSVColor} hsv An Array of the HSV color.
 */
export function rgb2hsv(rgb: RGBColor, hsv: HSVColor): void;

/**
 *
 * @param {HSVColor} hsv An Array of the HSV color.
 * @param {RGBColor} rgb An Array of the RGB color.
 */
export function hsv2rgb(hsv: HSVColor, rgb: RGBColor): void;

/**
 *
 * @param {Vector3} lab
 * @param {Vector3} xyz
 */
export function lab2xyz(lab: Vector3, xyz: Vector3): void;

/**
 *
 * @param {Vector3} xyz
 * @param {Vector3} lab
 */
export function xyz2lab(xyz: Vector3, lab: Vector3): void;

/**
 *
 * @param {Vector3} xyz
 * @param {RGBColor} rgb An Array of the RGB color.
 */
export function xyz2rgb(xyz: Vector3, rgb: RGBColor): void;

/**
 *
 * @param {RGBColor} rgb An Array of the RGB color.
 * @param {Vector3} xyz
 */
export function rgb2xyz(rgb: RGBColor, xyz: Vector3): void;

/**
 *
 * @param {RGBColor} rgb
 * @param {Vector3} lab
 */
export function rgb2lab(rgb: RGBColor, lab: Vector3): void;

/**
 *
 * @param {Vector3} lab
 * @param {RGBColor} rgb An Array of the RGB color.
 */
export function lab2rgb(lab: Vector3, rgb: RGBColor): void;

/**
 * Returns bounds.
 * @param {Bounds} bounds Output array that hold bounds, optionally empty.
 */
export function uninitializeBounds(bounds: Bounds): Bounds;

/**
 *
 * @param {Bounds} bounds The bounds to check.
 */
export function areBoundsInitialized(bounds: Bounds): boolean;

/**
 * Compute the bounds from points.
 * @param {Vector3} point1 The coordinate of the first point.
 * @param {Vector3} point2 The coordinate of the second point.
 * @param {Bounds} bounds Output array that hold bounds, optionally empty.
 * @deprecated please use vtkBoundingBox.addPoints(vtkBoundingBox.reset([]), points)
 */
export function computeBoundsFromPoints(
  point1: Vector3,
  point2: Vector3,
  bounds: Bounds
): Bounds;

/**
 * Clamp some value against a range.
 * @param {Number} value The value to clamp.
 * @param {Number} minValue The minimum value.
 * @param {Number} maxValue The maximum value.
 */
export function clampValue(
  value: number,
  minValue: number,
  maxValue: number
): number;

/**
 * Clamp some vector against a range.
 * @param {Vector3} vector The vector to clamp.
 * @param {Vector3} minVector The minimum vector.
 * @param {Vector3} maxVector The maximum vector.
 * @param {Vector3} out The output vector.
 */
export function clampVector(
  vector: Vector3,
  minVector: Vector3,
  maxVector: Vector3,
  out: Vector3
): Vector3;

/**
 *
 * @param {Vector3} vector
 * @param {Vector3} out
 */
export function roundVector(vector: Vector3, out: Vector3): Vector3;

/**
 *
 * @param {Number} value
 * @param {Range} range
 */
export function clampAndNormalizeValue(value: number, range: Range): number;

/**
 * Get the scalar type that is most likely to have enough precision to store a
 * given range of data once it has been scaled and shifted
 */
export function getScalarTypeFittingRange(): void;

/**
 *
 */
export function getAdjustedScalarRange(): void;

/**
 * Check if first 3D extent is within second 3D extent.
 * @param {Extent} extent1 The first extent.
 * @param {Extent} extent2 The second extent.
 */
export function extentIsWithinOtherExtent(
  extent1: Extent,
  extent2: Extent
): number;

/**
 * Check if first 3D bounds is within the second 3D bounds.
 * @param {Bounds} bounds1_6 The first bounds.
 * @param {Bounds} bounds2_6 The second bounds.
 * @param {Vector3} delta_3 The error margin along each axis.
 */
export function boundsIsWithinOtherBounds(
  bounds1_6: Bounds,
  bounds2_6: Bounds,
  delta_3: Vector3
): number;

/**
 * Check if point is within the given 3D bounds.
 * @param {Vector3} point_3 The coordinate of the point.
 * @param {Bounds} bounds_6 The bounds.
 * @param {Vector3} delta_3 The error margin along each axis.
 */
export function pointIsWithinBounds(
  point_3: Vector3,
  bounds_6: Bounds,
  delta_3: Vector3
): number;

/**
 * In Euclidean space, there is a unique circle passing through any given three
 * non-collinear points P1, P2, and P3.
 *
 * Using Cartesian coordinates to represent these points as spatial vectors, it
 * is possible to use the dot product and cross product to calculate the radius
 * and center of the circle. See:
 * http://en.wikipedia.org/wiki/Circumscribed_circle and more specifically the
 * section Barycentric coordinates from cross- and dot-products
 * @param {Vector3} p1 The coordinate of the first point.
 * @param {Vector3} p2 The coordinate of the second point.
 * @param {Vector3} p3 The coordinate of the third point.
 * @param {Vector3} center The coordinate of the center point.
 */
export function solve3PointCircle(
  p1: Vector3,
  p2: Vector3,
  p3: Vector3,
  center: Vector3
): number;

/**
 * Determines whether the passed value is a infinite number.
 * @param {Number} value The value to check.
 */
export function isInf(value: number): boolean;

/**
 *
 */
export function createUninitializedBounds(): Bounds;

/**
 *
 * @param {Number[]} vector
 */
export function getMajorAxisIndex(vector: number[]): number;

/**
 * Return the index of the component with the smallest absolute value.
 * Returns -1 for empty arrays.
 * @param {Number[]} vector
 */
export function getMinorAxisIndex(vector: number[]): number;

/**
 * Return the closest orthogonal matrix of 1, -1 and 0
 * It works for both column major and row major matrices
 * This function iteratively associate a column with a row by choosing
 * the greatest absolute value from the remaining row and columns
 * For each association, a -1 or a 1 is set in the output, depending on
 * the sign of the value in the original matrix
 *
 * @param {Number[]} matrix The matrix of size nxn
 * @param {Number[]} n The size of the square matrix, defaults to 3
 */
export function getSparseOrthogonalMatrix(
  matrix: number[],
  n: number
): number[];

/**
 *
 * @param {Number} value The value to convert.
 */
export function floatToHex2(value: number): string;

/**
 *
 * @param {RGBColor} rgbArray
 * @param {string} [prefix]
 */
export function floatRGB2HexCode(
  rgbArray: RGBColor | RGBAColor,
  prefix?: string
): string;

/**
 * Convert RGB or RGBA color array to CSS representation
 * @param {RGBColor|RGBAColor} rgbArray The color array.
 */
export function float2CssRGBA(rgbArray: RGBColor | RGBAColor): string;

/**
 * Determines whether the passed value is a NaN.
 * @param {Number} value The value to check.
 */
export function isNan(value: number): boolean;

/**
 * Determines whether the passed value is a NaN.
 * @param {Number} value The value to check.
 */
export function isNaN(value: number): boolean;

/**
 * Determines whether the passed value is a finite number.
 * @param value The value to check.
 */
export function isFinite(value: any): boolean;

/**
 * vtkMath provides methods to perform common math operations. These include
 * providing constants such as Pi; conversion from degrees to radians; vector
 * operations such as dot and cross products and vector norm; matrix determinant
 * for 2x2 and 3x3 matrices; univariate polynomial solvers; and for random
 * number generation (for backward compatibility only).
 * **Contrary to the rest of vtk.js, vtkMath is in row-major format (similar to VTK C++).**
 */
export declare const vtkMath: {
  createArray: typeof createArray;
  swapRowsMatrix_nxn: typeof swapRowsMatrix_nxn;
  swapColumnsMatrix_nxn: typeof swapColumnsMatrix_nxn;
  Pi: typeof Pi;
  radiansFromDegrees: typeof radiansFromDegrees;
  degreesFromRadians: typeof degreesFromRadians;
  round: typeof round;
  floor: typeof floor;
  ceil: typeof ceil;
  min: typeof min;
  max: typeof max;
  arrayMin: typeof arrayMin;
  arrayMax: typeof arrayMax;
  arrayRange: typeof arrayRange;
  ceilLog2: typeof ceilLog2;
  factorial: typeof factorial;
  gaussian: typeof gaussian;
  nearestPowerOfTwo: typeof nearestPowerOfTwo;
  isPowerOfTwo: typeof isPowerOfTwo;
  binomial: typeof binomial;
  beginCombination: typeof beginCombination;
  nextCombination: typeof nextCombination;
  randomSeed: typeof randomSeed;
  getSeed: typeof getSeed;
  random: typeof random;
  add: typeof add;
  subtract: typeof subtract;
  multiplyScalar: typeof multiplyScalar;
  multiplyScalar2D: typeof multiplyScalar2D;
  multiplyAccumulate: typeof multiplyAccumulate;
  multiplyAccumulate2D: typeof multiplyAccumulate2D;
  dot: typeof dot;
  outer: typeof outer;
  cross: typeof cross;
  norm: typeof norm;
  normalize: typeof normalize;
  perpendiculars: typeof perpendiculars;
  projectVector: typeof projectVector;
  dot2D: typeof dot2D;
  projectVector2D: typeof projectVector2D;
  distance2BetweenPoints: typeof distance2BetweenPoints;
  angleBetweenVectors: typeof angleBetweenVectors;
  gaussianAmplitude: typeof gaussianAmplitude;
  gaussianWeight: typeof gaussianWeight;
  outer2D: typeof outer2D;
  norm2D: typeof norm2D;
  normalize2D: typeof normalize2D;
  determinant2x2: typeof determinant2x2;
  rowsToMat4: typeof rowsToMat4;
  columnsToMat4: typeof columnsToMat4;
  rowsToMat3: typeof rowsToMat3;
  columnsToMat3: typeof columnsToMat3;
  LUFactor3x3: typeof LUFactor3x3;
  LUSolve3x3: typeof LUSolve3x3;
  linearSolve3x3: typeof linearSolve3x3;
  multiply3x3_vect3: typeof multiply3x3_vect3;
  multiply3x3_mat3: typeof multiply3x3_mat3;
  multiplyMatrix: typeof multiplyMatrix;
  transpose3x3: typeof transpose3x3;
  invert3x3: typeof invert3x3;
  identity3x3: typeof identity3x3;
  determinant3x3: typeof determinant3x3;
  quaternionToMatrix3x3: typeof quaternionToMatrix3x3;
  areEquals: typeof areEquals;
  areMatricesEqual: typeof areEquals;
  roundNumber: typeof roundNumber;
  roundVector: typeof roundVector;
  jacobiN: typeof jacobiN;
  matrix3x3ToQuaternion: typeof matrix3x3ToQuaternion;
  multiplyQuaternion: typeof multiplyQuaternion;
  orthogonalize3x3: typeof orthogonalize3x3;
  diagonalize3x3: typeof diagonalize3x3;
  singularValueDecomposition3x3: typeof singularValueDecomposition3x3;
  luFactorLinearSystem: typeof luFactorLinearSystem;
  luSolveLinearSystem: typeof luSolveLinearSystem;
  solveLinearSystem: typeof solveLinearSystem;
  invertMatrix: typeof invertMatrix;
  estimateMatrixCondition: typeof estimateMatrixCondition;
  jacobi: typeof jacobi;
  solveHomogeneousLeastSquares: typeof solveHomogeneousLeastSquares;
  solveLeastSquares: typeof solveLeastSquares;
  hex2float: typeof hex2float;
  rgb2hsv: typeof rgb2hsv;
  hsv2rgb: typeof hsv2rgb;
  lab2xyz: typeof lab2xyz;
  xyz2lab: typeof xyz2lab;
  xyz2rgb: typeof xyz2rgb;
  rgb2xyz: typeof rgb2xyz;
  rgb2lab: typeof rgb2lab;
  lab2rgb: typeof lab2rgb;
  uninitializeBounds: typeof uninitializeBounds;
  areBoundsInitialized: typeof areBoundsInitialized;
  computeBoundsFromPoints: typeof computeBoundsFromPoints;
  clampValue: typeof clampValue;
  clampVector: typeof clampVector;
  clampAndNormalizeValue: typeof clampAndNormalizeValue;
  getScalarTypeFittingRange: typeof getScalarTypeFittingRange;
  getAdjustedScalarRange: typeof getAdjustedScalarRange;
  extentIsWithinOtherExtent: typeof extentIsWithinOtherExtent;
  boundsIsWithinOtherBounds: typeof boundsIsWithinOtherBounds;
  pointIsWithinBounds: typeof pointIsWithinBounds;
  solve3PointCircle: typeof solve3PointCircle;
  isInf: typeof isInf;
  createUninitializedBounds: typeof createUninitializedBounds;
  getMajorAxisIndex: typeof getMajorAxisIndex;
  getMinorAxisIndex: typeof getMinorAxisIndex;
  getSparseOrthogonalMatrix: typeof getSparseOrthogonalMatrix;
  floatToHex2: typeof floatToHex2;
  floatRGB2HexCode: typeof floatRGB2HexCode;
  float2CssRGBA: typeof float2CssRGBA;
  inf: number;
  negInf: number;
  isNan: typeof isNaN;
  isNaN: typeof isNaN;
  isFinite: typeof isFinite;
};
export default vtkMath;