@basementuniverse/vec

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';

Contents

• vec
• mat

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