Math

Source (.js)Source (.d.ts)

Introduction

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++).

Methods

LUFactor3x3

LU Factorization of a 3x3 matrix.

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes
index_3	Vector3	Yes

LUSolve3x3

LU back substitution for a 3x3 matrix.

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes
index_3	Vector3	Yes
x_3	Vector3	Yes

Pi

Get the number π.

add

Add two 3-vectors.

Argument	Type	Required	Description
a	Vector3	Yes	The first 3D vector.
b	Vector3	Yes	The second 3D vector.
out	Vector3	Yes	The output 3D vector.

angleBetweenVectors

Angle between 3D vectors.

Argument	Type	Required	Description
v1	Vector3	Yes	The first 3D vector.
v2	Vector3	Yes	The second 3D vector.

areBoundsInitialized

Argument	Type	Required	Description
bounds	Bounds	Yes	The bounds to check.

areEquals

Returns true if elements of both arrays are equals.

Argument	Type	Required	Description
a	Array[Number]	Yes	An array of numbers (vector, point, matrix...)
b	Array[Number]	Yes	An array of numbers (vector, point, matrix...)
eps	Number	No	The tolerance value.

arrayMax

Get the maximum of the array.

Argument	Type	Required	Description
arr	Array[Number]	Yes	The array.
offset	Number	Yes	The offset.
stride	Number	Yes	The stride.

arrayMin

Get the minimum of the array.

Argument	Type	Required	Description
arr	Array[Number]	Yes	The array.
offset	Number	Yes	The offset.
stride	Number	Yes	The stride.

arrayRange

Argument	Type	Required	Description
arr	Array[Number]	Yes	The array.
offset	Number	Yes	The offset.
stride	Number	Yes	The stride.

beginCombination

Start iterating over "m choose n" objects.

Argument	Type	Required	Description
m	Number	No	The first numeric expression.
n	Number	No	The second numeric expression.

binomial

The number of combinations of n objects from a pool of m objects (m>n).

Argument	Type	Required	Description
m	Number	Yes	The first numeric expression.
n	Number	Yes	The second numeric expression.

boundsIsWithinOtherBounds

Check if first 3D bounds is within the second 3D bounds.

Argument	Type	Required	Description
bounds1_6	Bounds	Yes	The first bounds.
bounds2_6	Bounds	Yes	The second bounds.
delta_3	Vector3	Yes	The error margin along each axis.

ceil

Same as Math.ceil().

Argument	Type	Required	Description
param1	Number	Yes	A numeric expression.

ceilLog2

Gives the exponent of the lowest power of two not less than x.

clampAndNormalizeValue

Argument	Type	Required	Description
value	Number	Yes
range	Range	Yes

clampValue

Clamp some value against a range.

Argument	Type	Required	Description
value	Number	Yes	The value to clamp.
minValue	Number	Yes	The minimum value.
maxValue	Number	Yes	The maximum value.

clampVector

Clamp some vector against a range.

Argument	Type	Required	Description
vector	Vector3	Yes	The vector to clamp.
minVector	Vector3	Yes	The minimum vector.
maxVector	Vector3	Yes	The maximum vector.
out	Vector3	Yes	The output vector.

columnsToMat3

Fill a 3x3 matrix with the given column vectors

Argument	Type	Required	Description
column0	Vector3	Yes
column1	Vector3	Yes
column2	Vector3	Yes
mat	Matrix	Yes

columnsToMat4

Fill a 4x4 matrix with the given column vectors

Argument	Type	Required	Description
column0	Vector4	Yes
column1	Vector4	Yes
column2	Vector4	Yes
column3	Vector4	Yes
mat	Matrix	Yes

createArray

Argument	Type	Required	Description
size	Number	Yes	The size of the array.

createUninitializedBounds

cross

Computes cross product of 3D vectors x and y.

Argument	Type	Required	Description
x	Vector3	Yes	The first 3D vector.
y	Vector3	Yes	The second 3D vector.
out	Vector3	Yes	The output 3D vector.

degreesFromRadians

Convert radians to degrees.

Argument	Type	Required	Description
rad	Number	Yes	The value in radians.

determinant2x2

Argument	Type	Required	Description
args	Array[Number]	Yes

determinant3x3

Calculate the determinant of a 3x3 matrix.

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes	The input 3x3 matrix.

diagonalize3x3

Argument	Type	Required	Description
a_3x3	Matrix3x3	Yes
w_3	Vector3	Yes
v_3x3	Matrix3x3	Yes

distance2BetweenPoints

Compute distance squared between two points p1 and p2.

Argument	Type	Required	Description
x	Vector3	Yes	The first 3D vector.
y	Vector3	Yes	The second 3D vector.

dot

Dot product of two 3-vectors.

Argument	Type	Required	Description
x	Vector3	Yes
y	Vector3	Yes

dot2D

Compute the dot product of two 2D vectors.

Argument	Type	Required	Description
x	Vector2	Yes
y	Vector2	Yes

estimateMatrixCondition

Argument	Type	Required	Description
A	Matrix	Yes
size	Number	Yes

extentIsWithinOtherExtent

Check if first 3D extent is within second 3D extent.

Argument	Type	Required	Description
extent1	Extent	Yes	The first extent.
extent2	Extent	Yes	The second extent.

factorial

Compute N factorial, N! = N*(N-1) * (N-2)...32*1.

float2CssRGBA

Convert RGB or RGBA color array to CSS representation

Argument	Type	Required	Description
rgbArray	RGBColor or RGBAColor	Yes	The color array.

floatRGB2HexCode

Argument	Type	Required	Description
rgbArray	RGBColor	Yes
prefix	string	No

floatToHex2

Argument	Type	Required	Description
value	Number	Yes	The value to convert.

floor

Same as Math.floor().

Argument	Type	Required	Description
param1	Number	Yes	A numeric expression.

gaussian

Generate pseudo-random numbers distributed according to the standard normal distribution.

gaussianAmplitude

Compute the amplitude of a Gaussian function with mean=0 and specified variance.

Argument	Type	Required	Description
mean	Number	Yes	The mean value.
variance	Number	Yes	The variance value.
position	Number	Yes	The position value.

gaussianWeight

Compute the amplitude of an unnormalized Gaussian function with mean=0 and specified variance.

Argument	Type	Required	Description
mean	Number	Yes	The mean value.
variance	Number	Yes	The variance value.
position	Number	Yes	The position value.

getAdjustedScalarRange

getMajorAxisIndex

Argument	Type	Required	Description
vector	Array[Number]	Yes

getScalarTypeFittingRange

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

getSeed

Return the current seed used by the random number generator.

getSparseOrthogonalMatrix

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

Argument	Type	Required	Description
matrix	Array[Number]	Yes	The matrix of size nxn
n	Array[Number]	Yes	The size of the square matrix, defaults to 3

hex2float

Argument	Type	Required	Description
hexStr	String	Yes
outFloatArray	Array[Number]	No

hsv2rgb

Argument	Type	Required	Description
hsv	HSVColor	Yes	An Array of the HSV color.
rgb	RGBColor	Yes	An Array of the RGB color.

identity

Set mat to the identity matrix.

Argument	Type	Required	Description
n	Number	Yes	The size of the matrix.
mat	Array[Number]	Yes	The output matrix.

identity3x3

Set mat_3x3 to the identity matrix.

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes	The input 3x3 matrix.

invert3x3

Invert a 3x3 matrix.

Argument	Type	Required	Description
in_3x3	Matrix3x3	Yes	The input 3x3 matrix.
outI_3x3	Matrix3x3	Yes	The output 3x3 matrix.

invertMatrix

Argument	Type	Required	Description
A	Matrix	Yes	The input matrix. It is modified during the inversion.
AI	Matrix	Yes	The output inverse matrix. Can be the same as input matrix.
size	Number	No	The square size of the matrix to invert : 4 for a 4x4
index	Array[Number]	No
column	Array[Number]	No

Returns

Type	Description
	AI on success, null otherwise

isFinite

Determines whether the passed value is a finite number.

Argument	Type	Required	Description
value		Yes	The value to check.

isIdentity

Returns true if provided matrix is the identity matrix.

Argument	Type	Required	Description
mat	Array[Number]	Yes	The 3x3 matrix to check
eps	Number	No	The tolerance value.

isIdentity3x3

Returns true if provided 3x3 matrix is the identity matrix.

Argument	Type	Required	Description
mat	Matrix3x3	Yes	The 3x3 matrix to check
eps	Number	No	The tolerance value.

isInf

Determines whether the passed value is a infinite number.

Argument	Type	Required	Description
value	Number	Yes	The value to check.

isNaN

Determines whether the passed value is a NaN.

Argument	Type	Required	Description
value	Number	Yes	The value to check.

isNan

Determines whether the passed value is a NaN.

Argument	Type	Required	Description
value	Number	Yes	The value to check.

isPowerOfTwo

Returns true if integer is a power of two.

Argument	Type	Required	Description
x	Number	Yes	A numeric expression.

jacobi

Argument	Type	Required	Description
a_3x3	Matrix3x3	Yes
w	Array[Number]	Yes
v	Array[Number]	Yes

jacobiN

Jacobi iteration for the solution of eigenvectors/eigenvalues. Input matrix a is modified (the upper triangle is filled with zeros)

Argument	Type	Required	Description
a	Matrix	Yes	real symetric nxn matrix
n	Number	Yes	matrix size
w	Array[Number]	Yes	vector of size n to store eigenvalues (stored in decreasing order)
v	Array[Number]	Yes	matrix of size nxn to store eigenvectors (stored in decreasing order, normalized)

lab2rgb

Argument	Type	Required	Description
lab	Vector3	Yes
rgb	RGBColor	Yes	An Array of the RGB color.

lab2xyz

Argument	Type	Required	Description
lab	Vector3	Yes
xyz	Vector3	Yes

ldexp

Calculates x times (2 to the power of exponent).

linearSolve3x3

Solve mat_3x3y_3 = x_3 for y and place the result in y.

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes
x_3	Vector3	Yes
y_3	Vector3	Yes

luFactorLinearSystem

Argument	Type	Required	Description
A	Matrix	Yes
index	Array[Number]	Yes
size	Number	Yes

luSolveLinearSystem

Argument	Type	Required	Description
A	Matrix	Yes
index	Array[Number]	Yes
x	Array[Number]	Yes
size	Number	Yes

matrix3x3ToQuaternion

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes
quat_4	Vector4	Yes

max

Get the maximum of the two arguments provided. If either argument is NaN, the first argument will always be returned.

Argument	Type	Required	Description
param1	Number	Yes	The first numeric expression.
param2	Number	Yes	The second numeric expression.

min

Get the minimum of the two arguments provided. If either argument is NaN, the first argument will always be returned.

Argument	Type	Required	Description
param1	Number	Yes	The first numeric expression.
param2	Number	Yes	The second numeric expression.

multiply3x3_mat3

Argument	Type	Required	Description
a_3x3	Matrix3x3	Yes
b_3x3	Matrix3x3	Yes
out_3x3	Matrix3x3	Yes

multiply3x3_vect3

Argument	Type	Required	Description
mat_3x3	Matrix3x3	Yes
in_3	Vector3	Yes
out_3	Vector3	Yes

multiplyAccumulate

Multiply two 3-vectors.

Argument	Type	Required	Description
a	Vector3	Yes
b	Vector3	Yes
scalar	Number	Yes
out	Vector3	Yes

multiplyAccumulate2D

Multiply two 2-vectors.

Argument	Type	Required	Description
a	Vector2	Yes
b	Vector2	Yes
scalar	Number	Yes
out	Vector2	Yes

multiplyMatrix

Multiply two matrices.

Argument	Type	Required	Description
a	Matrix	Yes
b	Matrix	Yes
rowA	Number	Yes
colA	Number	Yes
rowB	Number	Yes
colB	Number	Yes
outRowAColB	Matrix	Yes

multiplyQuaternion

Argument	Type	Required	Description
quat_1	Vector4	Yes
quat_2	Vector4	Yes
quat_out	Vector4	Yes

multiplyScalar

Multiply a 3-vector by a scalar.

Argument	Type	Required	Description
vec	Vector3	Yes
scalar	Number	Yes

multiplyScalar2D

Multiply a 3-vector by a scalar.

Argument	Type	Required	Description
vec	Vector2	Yes
scalar	Number	Yes

nearestPowerOfTwo

Compute the nearest power of two that is not less than x.

Argument	Type	Required	Description
xi	Number	Yes	A numeric expression.

nextCombination

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.

Argument	Type	Required	Description
m	Number	Yes	The first numeric expression.
n	Number	Yes	The second numeric expression.
r	Array[Number]	Yes

norm

Compute the norm of a vector.

Argument	Type	Required	Description
x	Array[Number]	Yes	The vector to compute the norm of.
n	Number	No	The number of components to consider (default is 3).

norm2D

Compute the norm of a 2-vector.

Argument	Type	Required	Description
x2D	Vector2	Yes	x The 2D vector.

normalize

Normalize in place. Returns norm.

Argument	Type	Required	Description
x	Array[Number]	Yes	The vector to normalize.

normalize2D

Normalize (in place) a 2-vector.

Argument	Type	Required	Description
x	Vector2	Yes	The 2D vector.

normalize4D

Normalize in place. Returns norm.

Argument	Type	Required	Description
x	Array[Number]	Yes	The vector to normalize.

orthogonalize3x3

Argument	Type	Required	Description
a_3x3	Matrix3x3	Yes
out_3x3	Matrix3x3	Yes

outer

Outer product of two 3-vectors.

Argument	Type	Required	Description
x	Vector3	Yes	The first 3D vector.
y	Vector3	Yes	The second 3D vector.
out_3x3	Matrix3x3	Yes	The output 3x3 matrix.

outer2D

Outer product of two 2-vectors.

Argument	Type	Required	Description
x	Vector2	Yes	The first 2D vector.
y	Vector2	Yes	The second 2D vector.
out_2x2	Matrix	Yes	The output 2x2 matrix.

perpendiculars

Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3

Argument	Type	Required	Description
x	Vector3	Yes	The first vector.
y	Vector3	Yes	The second vector.
z	Vector3	Yes	The third vector.
theta	Number	Yes

pointIsWithinBounds

Check if point is within the given 3D bounds.

Argument	Type	Required	Description
point_3	Vector3	Yes	The coordinate of the point.
bounds_6	Bounds	Yes	The bounds.
delta_3	Vector3	Yes	The error margin along each axis.

projectVector

Project vector a onto vector b and returns the result in projection vector.

Argument	Type	Required	Description
a	Vector3	Yes	The first 3D vector.
b	Vector3	Yes	The second 3D vector.
projection	Vector3	Yes	The projection 3D vector.

projectVector2D

Compute the projection of 2D vector a on 2D vector b and returns the result in projection vector.

Argument	Type	Required	Description
a	Vector2	Yes	The first 2D vector.
b	Vector2	Yes	The second 2D vector.
projection	Vector2	Yes	The projection 2D vector.

quaternionToMatrix3x3

Argument	Type	Required	Description
quat_4	Vector4	Yes
mat_3x3	Matrix3x3	Yes

radiansFromDegrees

Convert degrees to radians.

Argument	Type	Required	Description
deg	Number	Yes	The value in degrees.

random

Generate pseudo-random numbers distributed according to the uniform distribution between min and max.

Argument	Type	Required	Description
minValue	Number	Yes
maxValue	Number	Yes

randomSeed

Initialize seed value.

Argument	Type	Required	Description
seed	Number	Yes

rgb2hsv

Argument	Type	Required	Description
rgb	RGBColor	Yes	An Array of the RGB color.
hsv	HSVColor	Yes	An Array of the HSV color.

rgb2lab

Argument	Type	Required	Description
rgb	RGBColor	Yes
lab	Vector3	Yes

rgb2xyz

Argument	Type	Required	Description
rgb	RGBColor	Yes	An Array of the RGB color.
xyz	Vector3	Yes

round

Same as Math.round().

Argument	Type	Required	Description
param1	Number	Yes	The value to be rounded to the nearest integer.

roundNumber

Argument	Type	Required	Description
num	Number	Yes
digits	Number	No

roundVector

Argument	Type	Required	Description
vector	Vector3	Yes
out	Vector3	Yes

roundVector

Argument	Type	Required	Description
vector	Vector3	Yes
out	Vector3	No
digits	Number	No

rowsToMat3

Fill a 3x3 matrix with the given row vectors

Argument	Type	Required	Description
row0	Vector3	Yes
row1	Vector3	Yes
row2	Vector3	Yes
mat	Matrix	Yes

rowsToMat4

Fill a 4x4 matrix with the given row vectors

Argument	Type	Required	Description
row0	Vector4	Yes
row1	Vector4	Yes
row2	Vector4	Yes
row3	Vector4	Yes
mat	Matrix	Yes

signedAngleBetweenVectors

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)

Argument	Type	Required	Description
v1	Vector3	Yes	The first 3D vector.
v2	Vector3	Yes	The second 3D vector.
vN	Vector3	Yes

singularValueDecomposition3x3

Argument	Type	Required	Description
a_3x3	Matrix3x3	Yes
u_3x3	Matrix3x3	Yes
w_3	Vector3	Yes
vT_3x3	Matrix3x3	Yes

solve3PointCircle

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

Argument	Type	Required	Description
p1	Vector3	Yes	The coordinate of the first point.
p2	Vector3	Yes	The coordinate of the second point.
p3	Vector3	Yes	The coordinate of the third point.
center	Vector3	Yes	The coordinate of the center point.

solveHomogeneousLeastSquares

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

Argument	Type	Required	Description
numberOfSamples	Number	Yes
xt	Matrix	Yes
xOrder	Number	Yes
mt	Matrix	Yes

solveLeastSquares

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.

Argument	Type	Required	Description
numberOfSamples	Number	Yes
xt	Matrix	Yes
xOrder	Number	Yes
yt	Matrix	Yes
yOrder	Number	Yes
mt	Matrix	Yes
checkHomogeneous	Boolean	No

solveLinearSystem

Argument	Type	Required	Description
A	Matrix	Yes
x	Array[Number]	Yes
size	Number	Yes

subtract

Substract two 3-vectors.

Argument	Type	Required	Description
a	Vector3	Yes	The first 3D vector.
b	Vector3	Yes	The second 3D vector.
out	Vector3	Yes	The output 3D vector.

swapColumnsMatrix_nxn

Given two columns indices, swap the two columns of a nxn matrix

Argument	Type	Required	Description
matrix	Array[Number]	Yes	The n by n matrix in wich we want to swap the vectors.
n	Number	Yes	size of the matrix.
column1	Number	Yes	index of first col to swap with the other.
column2	Number	Yes	index of second col to swap with the other.

swapRowsMatrix_nxn

Given two rows indices, swap the two rows of a nxn matrix

Argument	Type	Required	Description
matrix	Array[Number]	Yes	The n by n matrix in wich we want to swap the vectors.
n	Number	Yes	size of the matrix.
row1	Number	Yes	index of first row to swap with the other.
row2	Number	Yes	index of second row to swap with the other.

transpose3x3

Transpose a 3x3 matrix.

Argument	Type	Required	Description
in_3x3	Matrix3x3	Yes	The input 3x3 matrix.
outT_3x3	Matrix3x3	Yes	The output 3x3 matrix.

uninitializeBounds

Returns bounds.

Argument	Type	Required	Description
bounds	Bounds	Yes	Output array that hold bounds, optionally empty.

xyz2lab

Argument	Type	Required	Description
xyz	Vector3	Yes
lab	Vector3	Yes

xyz2rgb

Argument	Type	Required	Description
xyz	Vector3	Yes
rgb	RGBColor	Yes	An Array of the RGB color.