vec

A small vector and matrix library

Usage

Node:

const { vec, mat } = require('@basementuniverse/vec');

Browser:

<script src="vec.js"></script>

Typescript:

import { vec, mat } from '@basementuniverse/vec';

Functions

vec([x], [y]) ⇒ vec: Create a new vector
mat([m], [n], [entries]) ⇒ mat: Create a new matrix

Typedefs

vec : Object: A 2d vector
vectorMapCallback ⇒ number: A function to call on each component of a vector
mat : Object: A matrix
matrixMapCallback ⇒ number: A function to call on each entry of a matrix

vec([x], [y]) ⇒ `vec`

Create a new vector

Kind: global function
Returns: vec - A new vector

Param	Type	Description
[x]	`number` \| `vec`	The x component of the vector, or a vector to copy
[y]	`number`	The y component of the vector

Example (Various ways to initialise a vector)

let a = vec(3, 2);  // (3, 2)
let b = vec(4);     // (4, 4)
let c = vec(a);     // (3, 2)
let d = vec();      // (0, 0)

vec([x], [y]) ⇒ vec
- .components(a) ⇒ Array.<number>
- .ux() ⇒ vec
- .uy() ⇒ vec
- .add(a, b) ⇒ vec
- .mul(a, b) ⇒ vec
- .sub(a, b) ⇒ vec
- .len(a) ⇒ number
- .manhattan(a) ⇒ number
- .nor(a) ⇒ vec
- .dot(a, b) ⇒ number
- .rot(a, r) ⇒ vec
- .eq(a, b) ⇒ boolean
- .rad(a) ⇒ number
- .cpy(a) ⇒ vec
- .map(a, f) ⇒ vec
- .str(a, [s]) ⇒ string

vec.components(a) ⇒ `Array.<number>`

Get the components of a vector as an array

Kind: static method of vec
Returns: Array.<number> - The vector components as an array

Param	Type	Description
a	`vec`	The vector to get components from

vec.ux() ⇒ `vec`

Return a unit vector (1, 0)

Kind: static method of vec
Returns: vec - A unit vector (1, 0)

vec.uy() ⇒ `vec`

Return a unit vector (0, 1)

Kind: static method of vec
Returns: vec - A unit vector (0, 1)

vec.add(a, b) ⇒ `vec`

Add vectors

Kind: static method of vec
Returns: vec - a + b

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.mul(a, b) ⇒ `vec`

Scale a vector

Kind: static method of vec
Returns: vec - a * b

Param	Type	Description
a	`vec`	Vector a
b	`number`	Scalar b

vec.sub(a, b) ⇒ `vec`

Subtract vectors

Kind: static method of vec
Returns: vec - a - b

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.len(a) ⇒ `number`

Get the length of a vector

Kind: static method of vec
Returns: number - |a|

Param	Type	Description
a	`vec`	Vector a

vec.manhattan(a) ⇒ `number`

Get the length of a vector using taxicab geometry

Kind: static method of vec
Returns: number - |a|

Param	Type	Description
a	`vec`	Vector a

vec.nor(a) ⇒ `vec`

Normalise a vector

Kind: static method of vec
Returns: vec - ^a

Param	Type	Description
a	`vec`	The vector to normalise

vec.dot(a, b) ⇒ `number`

Get a dot product of vectors

Kind: static method of vec
Returns: number - a ∙ b

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.rot(a, r) ⇒ `vec`

Rotate a vector by r radians

Kind: static method of vec
Returns: vec - A rotated vector

Param	Type	Description
a	`vec`	The vector to rotate
r	`number`	The angle to rotate by, measured in radians

vec.eq(a, b) ⇒ `boolean`

Check if two vectors are equal

Kind: static method of vec
Returns: boolean - True if vectors a and b are equal, false otherwise

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.rad(a) ⇒ `number`

Get the angle of a vector

Kind: static method of vec
Returns: number - The angle of vector a in radians

Param	Type	Description
a	`vec`	Vector a

vec.cpy(a) ⇒ `vec`

Copy a vector

Kind: static method of vec
Returns: vec - A copy of vector a

Param	Type	Description
a	`vec`	The vector to copy

vec.map(a, f) ⇒ `vec`

Call a function on each component of a vector and build a new vector from the results

Kind: static method of vec
Returns: vec - Vector a mapped through f

Param	Type	Description
a	`vec`	Vector a
f	`vectorMapCallback`	The function to call on each component of the vector

vec.str(a, [s]) ⇒ `string`

Convert a vector into a string

Kind: static method of vec
Returns: string - A string representation of the vector

Param	Type	Default	Description
a	`vec`		The vector to convert
[s]	`string`	`"', '"`	The separator string

mat([m], [n], [entries]) ⇒ `mat`

Create a new matrix

Kind: global function
Returns: mat - A new matrix

Param	Type	Default	Description
[m]	`number`	`4`	The number of rows
[n]	`number`	`4`	The number of columns
[entries]	`Array.<number>`	`[]`	Matrix values in reading order

mat([m], [n], [entries]) ⇒ mat
- .identity(n) ⇒ mat
- .get(a, i, j) ⇒ number
- .set(a, i, j, v)
- .row(a, m) ⇒ Array.<number>
- .col(a, n) ⇒ Array.<number>
- .add(a, b) ⇒ mat
- .sub(a, b) ⇒ mat
- .mul(a, b) ⇒ mat | boolean
- .scale(a, b) ⇒ mat
- .trans(a) ⇒ mat
- .minor(a, i, j) ⇒ mat | boolean
- .det(a) ⇒ number | boolean
- .nor(a) ⇒ mat | boolean
- .adj(a) ⇒ mat
- .inv(a) ⇒ mat | boolean
- .eq(a, b) ⇒ boolean
- .cpy(a) ⇒ mat
- .map(a, f) ⇒ mat
- .str(a, [ms], [ns]) ⇒ string

mat.identity(n) ⇒ `mat`

Get an identity matrix of size n

Kind: static method of mat
Returns: mat - An identity matrix

Param	Type	Description
n	`number`	The size of the matrix

mat.get(a, i, j) ⇒ `number`

Get an entry from a matrix

Kind: static method of mat
Returns: number - The value at position (i, j) in matrix a

Param	Type	Description
a	`mat`	Matrix a
i	`number`	The row offset
j	`number`	The column offset

mat.set(a, i, j, v)

Set an entry of a matrix

Kind: static method of mat

Param	Type	Description
a	`mat`	Matrix a
i	`number`	The row offset
j	`number`	The column offset
v	`number`	The value to set in matrix a

mat.row(a, m) ⇒ `Array.<number>`

Get a row from a matrix as an array

Kind: static method of mat
Returns: Array.<number> - Row m from matrix a

Param	Type	Description
a	`mat`	Matrix a
m	`number`	The row offset

mat.col(a, n) ⇒ `Array.<number>`

Get a column from a matrix as an array

Kind: static method of mat
Returns: Array.<number> - Column n from matrix a

Param	Type	Description
a	`mat`	Matrix a
n	`number`	The column offset

mat.add(a, b) ⇒ `mat`

Add matrices

Kind: static method of mat
Returns: mat - a + b

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.sub(a, b) ⇒ `mat`

Subtract matrices

Kind: static method of mat
Returns: mat - a - b

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.mul(a, b) ⇒ `mat` | `boolean`

Multiply matrices

Kind: static method of mat
Returns: mat | boolean - ab or false if the matrices cannot be multiplied

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.scale(a, b) ⇒ `mat`

Scale a matrix

Kind: static method of mat
Returns: mat - a * b

Param	Type	Description
a	`mat`	Matrix a
b	`number`	Scalar b

mat.trans(a) ⇒ `mat`

Transpose a matrix

Kind: static method of mat
Returns: mat - A transposed matrix

Param	Type	Description
a	`mat`	The matrix to transpose

mat.minor(a, i, j) ⇒ `mat` | `boolean`

Get the minor of a matrix

Kind: static method of mat
Returns: mat | boolean - The (i, j) minor of matrix a or false if the matrix is not square

Param	Type	Description
a	`mat`	Matrix a
i	`number`	The row offset
j	`number`	The column offset

mat.det(a) ⇒ `number` | `boolean`

Get the determinant of a matrix

Kind: static method of mat
Returns: number | boolean - |a| or false if the matrix is not square

Param	Type	Description
a	`mat`	Matrix a

mat.nor(a) ⇒ `mat` | `boolean`

Normalise a matrix

Kind: static method of mat
Returns: mat | boolean - ^a or false if the matrix is not square

Param	Type	Description
a	`mat`	The matrix to normalise

mat.adj(a) ⇒ `mat`

Get the adjugate of a matrix

Kind: static method of mat
Returns: mat - The adjugate of a

Param	Type	Description
a	`mat`	The matrix from which to get the adjugate

mat.inv(a) ⇒ `mat` | `boolean`

Get the inverse of a matrix

Kind: static method of mat
Returns: mat | boolean - a^-1 or false if the matrix has no inverse

Param	Type	Description
a	`mat`	The matrix to invert

mat.eq(a, b) ⇒ `boolean`

Check if two matrices are equal

Kind: static method of mat
Returns: boolean - True if matrices a and b are identical, false otherwise

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.cpy(a) ⇒ `mat`

Copy a matrix

Kind: static method of mat
Returns: mat - A copy of matrix a

Param	Type	Description
a	`mat`	The matrix to copy

mat.map(a, f) ⇒ `mat`

Call a function on each entry of a matrix and build a new matrix from the results

Kind: static method of mat
Returns: mat - Matrix a mapped through f

Param	Type	Description
a	`mat`	Matrix a
f	`matrixMapCallback`	The function to call on each entry of the matrix

mat.str(a, [ms], [ns]) ⇒ `string`

Convert a matrix into a string

Kind: static method of mat
Returns: string - A string representation of the matrix

Param	Type	Default	Description
a	`mat`		The matrix to convert
[ms]	`string`	`"', '"`	The separator string for columns
[ns]	`string`	`"'\n'"`	The separator string for rows

vec : `Object`

A 2d vector

Kind: global typedef
Properties

Name	Type	Description
x	`number`	The x component of the vector
y	`number`	The y component of the vector

vec : Object
- .components(a) ⇒ Array.<number>
- .ux() ⇒ vec
- .uy() ⇒ vec
- .add(a, b) ⇒ vec
- .mul(a, b) ⇒ vec
- .sub(a, b) ⇒ vec
- .len(a) ⇒ number
- .manhattan(a) ⇒ number
- .nor(a) ⇒ vec
- .dot(a, b) ⇒ number
- .rot(a, r) ⇒ vec
- .eq(a, b) ⇒ boolean
- .rad(a) ⇒ number
- .cpy(a) ⇒ vec
- .map(a, f) ⇒ vec
- .str(a, [s]) ⇒ string

vec.components(a) ⇒ `Array.<number>`

Get the components of a vector as an array

Kind: static method of vec
Returns: Array.<number> - The vector components as an array

Param	Type	Description
a	`vec`	The vector to get components from

vec.ux() ⇒ `vec`

Return a unit vector (1, 0)

Kind: static method of vec
Returns: vec - A unit vector (1, 0)

vec.uy() ⇒ `vec`

Return a unit vector (0, 1)

Kind: static method of vec
Returns: vec - A unit vector (0, 1)

vec.add(a, b) ⇒ `vec`

Add vectors

Kind: static method of vec
Returns: vec - a + b

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.mul(a, b) ⇒ `vec`

Scale a vector

Kind: static method of vec
Returns: vec - a * b

Param	Type	Description
a	`vec`	Vector a
b	`number`	Scalar b

vec.sub(a, b) ⇒ `vec`

Subtract vectors

Kind: static method of vec
Returns: vec - a - b

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.len(a) ⇒ `number`

Get the length of a vector

Kind: static method of vec
Returns: number - |a|

Param	Type	Description
a	`vec`	Vector a

vec.manhattan(a) ⇒ `number`

Get the length of a vector using taxicab geometry

Kind: static method of vec
Returns: number - |a|

Param	Type	Description
a	`vec`	Vector a

vec.nor(a) ⇒ `vec`

Normalise a vector

Kind: static method of vec
Returns: vec - ^a

Param	Type	Description
a	`vec`	The vector to normalise

vec.dot(a, b) ⇒ `number`

Get a dot product of vectors

Kind: static method of vec
Returns: number - a ∙ b

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.rot(a, r) ⇒ `vec`

Rotate a vector by r radians

Kind: static method of vec
Returns: vec - A rotated vector

Param	Type	Description
a	`vec`	The vector to rotate
r	`number`	The angle to rotate by, measured in radians

vec.eq(a, b) ⇒ `boolean`

Check if two vectors are equal

Kind: static method of vec
Returns: boolean - True if vectors a and b are equal, false otherwise

Param	Type	Description
a	`vec`	Vector a
b	`vec`	Vector b

vec.rad(a) ⇒ `number`

Get the angle of a vector

Kind: static method of vec
Returns: number - The angle of vector a in radians

Param	Type	Description
a	`vec`	Vector a

vec.cpy(a) ⇒ `vec`

Copy a vector

Kind: static method of vec
Returns: vec - A copy of vector a

Param	Type	Description
a	`vec`	The vector to copy

vec.map(a, f) ⇒ `vec`

Call a function on each component of a vector and build a new vector from the results

Kind: static method of vec
Returns: vec - Vector a mapped through f

Param	Type	Description
a	`vec`	Vector a
f	`vectorMapCallback`	The function to call on each component of the vector

vec.str(a, [s]) ⇒ `string`

Convert a vector into a string

Kind: static method of vec
Returns: string - A string representation of the vector

Param	Type	Default	Description
a	`vec`		The vector to convert
[s]	`string`	`"', '"`	The separator string

vectorMapCallback ⇒ `number`

A function to call on each component of a vector

Kind: global typedef
Returns: number - The mapped component

Param	Type	Description
value	`number`	The component value
label	`'x'` \| `'y'`	The component label (x or y)

mat : `Object`

A matrix

Kind: global typedef
Properties

Name	Type	Description
m	`number`	The number of rows in the matrix
n	`number`	The number of columns in the matrix
entries	`Array.<number>`	The matrix values

mat : Object
- .identity(n) ⇒ mat
- .get(a, i, j) ⇒ number
- .set(a, i, j, v)
- .row(a, m) ⇒ Array.<number>
- .col(a, n) ⇒ Array.<number>
- .add(a, b) ⇒ mat
- .sub(a, b) ⇒ mat
- .mul(a, b) ⇒ mat | boolean
- .scale(a, b) ⇒ mat
- .trans(a) ⇒ mat
- .minor(a, i, j) ⇒ mat | boolean
- .det(a) ⇒ number | boolean
- .nor(a) ⇒ mat | boolean
- .adj(a) ⇒ mat
- .inv(a) ⇒ mat | boolean
- .eq(a, b) ⇒ boolean
- .cpy(a) ⇒ mat
- .map(a, f) ⇒ mat
- .str(a, [ms], [ns]) ⇒ string

mat.identity(n) ⇒ `mat`

Get an identity matrix of size n

Kind: static method of mat
Returns: mat - An identity matrix

Param	Type	Description
n	`number`	The size of the matrix

mat.get(a, i, j) ⇒ `number`

Get an entry from a matrix

Kind: static method of mat
Returns: number - The value at position (i, j) in matrix a

Param	Type	Description
a	`mat`	Matrix a
i	`number`	The row offset
j	`number`	The column offset

mat.set(a, i, j, v)

Set an entry of a matrix

Kind: static method of mat

Param	Type	Description
a	`mat`	Matrix a
i	`number`	The row offset
j	`number`	The column offset
v	`number`	The value to set in matrix a

mat.row(a, m) ⇒ `Array.<number>`

Get a row from a matrix as an array

Kind: static method of mat
Returns: Array.<number> - Row m from matrix a

Param	Type	Description
a	`mat`	Matrix a
m	`number`	The row offset

mat.col(a, n) ⇒ `Array.<number>`

Get a column from a matrix as an array

Kind: static method of mat
Returns: Array.<number> - Column n from matrix a

Param	Type	Description
a	`mat`	Matrix a
n	`number`	The column offset

mat.add(a, b) ⇒ `mat`

Add matrices

Kind: static method of mat
Returns: mat - a + b

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.sub(a, b) ⇒ `mat`

Subtract matrices

Kind: static method of mat
Returns: mat - a - b

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.mul(a, b) ⇒ `mat` | `boolean`

Multiply matrices

Kind: static method of mat
Returns: mat | boolean - ab or false if the matrices cannot be multiplied

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.scale(a, b) ⇒ `mat`

Scale a matrix

Kind: static method of mat
Returns: mat - a * b

Param	Type	Description
a	`mat`	Matrix a
b	`number`	Scalar b

mat.trans(a) ⇒ `mat`

Transpose a matrix

Kind: static method of mat
Returns: mat - A transposed matrix

Param	Type	Description
a	`mat`	The matrix to transpose

mat.minor(a, i, j) ⇒ `mat` | `boolean`

Get the minor of a matrix

Kind: static method of mat
Returns: mat | boolean - The (i, j) minor of matrix a or false if the matrix is not square

Param	Type	Description
a	`mat`	Matrix a
i	`number`	The row offset
j	`number`	The column offset

mat.det(a) ⇒ `number` | `boolean`

Get the determinant of a matrix

Kind: static method of mat
Returns: number | boolean - |a| or false if the matrix is not square

Param	Type	Description
a	`mat`	Matrix a

mat.nor(a) ⇒ `mat` | `boolean`

Normalise a matrix

Kind: static method of mat
Returns: mat | boolean - ^a or false if the matrix is not square

Param	Type	Description
a	`mat`	The matrix to normalise

mat.adj(a) ⇒ `mat`

Get the adjugate of a matrix

Kind: static method of mat
Returns: mat - The adjugate of a

Param	Type	Description
a	`mat`	The matrix from which to get the adjugate

mat.inv(a) ⇒ `mat` | `boolean`

Get the inverse of a matrix

Kind: static method of mat
Returns: mat | boolean - a^-1 or false if the matrix has no inverse

Param	Type	Description
a	`mat`	The matrix to invert

mat.eq(a, b) ⇒ `boolean`

Check if two matrices are equal

Kind: static method of mat
Returns: boolean - True if matrices a and b are identical, false otherwise

Param	Type	Description
a	`mat`	Matrix a
b	`mat`	Matrix b

mat.cpy(a) ⇒ `mat`

Copy a matrix

Kind: static method of mat
Returns: mat - A copy of matrix a

Param	Type	Description
a	`mat`	The matrix to copy

mat.map(a, f) ⇒ `mat`

Call a function on each entry of a matrix and build a new matrix from the results

Kind: static method of mat
Returns: mat - Matrix a mapped through f

Param	Type	Description
a	`mat`	Matrix a
f	`matrixMapCallback`	The function to call on each entry of the matrix

mat.str(a, [ms], [ns]) ⇒ `string`

Convert a matrix into a string

Kind: static method of mat
Returns: string - A string representation of the matrix

Param	Type	Default	Description
a	`mat`		The matrix to convert
[ms]	`string`	`"', '"`	The separator string for columns
[ns]	`string`	`"'\n'"`	The separator string for rows

matrixMapCallback ⇒ `number`

A function to call on each entry of a matrix

Kind: global typedef
Returns: number - The mapped entry

Param	Type	Description
value	`number`	The entry value
index	`number`	The entry index
entries	`Array.<number>`	The array of matrix entries

@basementuniverse/vec

mat.mul(a, b) ⇒ mat | boolean

mat.minor(a, i, j) ⇒ mat | boolean

mat.nor(a) ⇒ mat | boolean

mat.inv(a) ⇒ mat | boolean

mat.mul(a, b) ⇒ mat | boolean

mat.minor(a, i, j) ⇒ mat | boolean

mat.nor(a) ⇒ mat | boolean

mat.inv(a) ⇒ mat | boolean

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mat.mul(a, b) ⇒ `mat` | `boolean`

mat.minor(a, i, j) ⇒ `mat` | `boolean`

mat.nor(a) ⇒ `mat` | `boolean`

mat.inv(a) ⇒ `mat` | `boolean`

mat.mul(a, b) ⇒ `mat` | `boolean`

mat.minor(a, i, j) ⇒ `mat` | `boolean`

mat.nor(a) ⇒ `mat` | `boolean`

mat.inv(a) ⇒ `mat` | `boolean`

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