matrix

Diagonal values

dim

dim(m: matrix,
)

Returns the dimension of the given matrix as (m, n)

m:

The matrix

column

column(mat: matrix,n: int,
)

Returns the n-th column of a matrix as a vector

mat:

Input matrix

n:

int

The column’s index

round

round(mat: matrix,precision: int,
)

Rounds each value in the matrix to a precision.

mat:

Input matrix

precision:

int

Default: 10

Rounding precision (digits)

mul-mat

mul-mat(..matrices: matrix,
)

Multiplies matrices on top of each other.

..matrices:

The matrices to multiply from left to right.

mul4x4-vec3

mul4x4-vec3(mat: matrix,vec: vector,w: float,
)

Multiplies a $4 \times 4$ matrix with a vector of size 3 or 4. The resulting is three dimensional

mat:

The matrix to multiply

vec:

The vector to multiply

w:

The default value for the fourth element of the vector if it is three dimensional.

mul-vec

mul-vec(mat: matrix,vec: vector,
)

Multiplies an $𝑚 \times 𝑛$ matrix with an $𝑚$ th dimensional vector where $𝑚 \leq 4$ . Prefer the use of mul4x4-vec3 when possible as it does not use loops.

mat:

The matrix to multiply

vec:

The vector to multiply

is-identity

is-identity(m: matrix,
)

Returns true if m is 1.

m:

Matrix to check

inverse

inverse(matrix: matrix,
)

Calculates the inverse matrix of any size.

matrix:

The matrix to inverse.

transform-translate

transform-translate(x: float,y: float,z: float,
)

Returns a $4 \times 4$ translation matrix

x:

The translation in the $𝑥$ direction.

y:

The translation in the $𝑦$ direction.

z:

The translation in the $𝑥$ direction.

transform-shear-x

transform-shear-x(factor: float,
)

Returns a $4 \times 4$ x-shear matrix

factor:

The shear in the $𝑥$ direction.

transform-shear-z

transform-shear-z(factor: float,
)

Returns a $4 \times 4$ z-shear matrix

factor:

The shear in the $𝑧$ direction.

transform-scale

transform-scale(f: floatarraydictionary,
)

Returns a $4 \times 4$ scale matrix

f:

float or array or dictionary

The scale factor(s) of the matrix. An array of at least 3 floats sets the x, y and z scale factors. A dictionary sets the scale in the direction of the corresponding x, y and z keys. A single float sets the scale for all directions.

transform-rotate-dir

transform-rotate-dir(dir: vector,up: vector,
)

Returns a $4 \times 4$ rotation xyz matrix for a direction and up vector

dir:

idk

up:

idk

transform-rotate-x

transform-rotate-x(angle: angle,
)

Returns a $4 \times 4$ $𝑥$ rotation matrix

angle:

The angle to rotate around the $𝑥$ axis

transform-rotate-y

transform-rotate-y(angle: angle,
)

Returns a $4 \times 4$ $𝑦$ rotation matrix

angle:

The angle to rotate around the $𝑦$ axis

transform-rotate-z

transform-rotate-z(angle: angle,
)

Returns a $4 \times 4$ $𝑧$ rotation matrix

angle:

The angle to rotate around the $𝑧$ axis

transform-rotate-aer

transform-rotate-aer(azimuth: angle,elevation: angle,roll: angle,
)

Returns a $4 \times 4$ rotation matrix from azimuth/elevation/roll. Assumes the viewing convention where $𝑧$ points up and $𝑥$ points toward the viewer.

azimuth:

Rotation around z.

elevation:

Tilt above the xy plane.

roll:

Rotation around the current viewing axis.

transform-rotate-xz

transform-rotate-xz(x: angle,z: angle,
)

Returns a $4 \times 4$ $𝑥 𝑧$ rotation matrix

x:

The angle to rotate around the $𝑥$ axis

z:

The angle to rotate around the $𝑧$ axis

transform-rotate-ypr

transform-rotate-ypr(a: angle,b: angle,c: angle,
)

Returns a $4 \times 4$ rotation matrix - yaw-pitch-roll

a:

Yaw

b:

Pitch

c:

Roll

transform-rotate-xyz

transform-rotate-xyz(x: angle,y: angle,z: angle,
)

Returns a $4 \times 4$ rotation matrix - euler angles

Calculates the product of the three rotation matrices $𝑅 = 𝑅_{𝑧 (𝑧)} 𝑅_{𝑦 (𝑦)} 𝑅_{𝑥 (𝑥)}$

x:

Rotation about x

y:

Rotation about y

z: