@thi.ng/vectors

[!NOTE] This is one of 199 standalone projects, maintained as part of the @thi.ng/umbrella monorepo and anti-framework.

🚀 Please help me to work full-time on these projects by sponsoring me on GitHub. Thank you! ❤️

• About
  • Features
• Status
  • Breaking changes in v6.0.0
  • Breaking changes in v3.0.0
• Related packages
• Installation
• Dependencies
• Usage examples
• API
  • Basic usage
  • Naming conventions
  • Constants
  • Component setters & copying
  • Component swizzling
  • Vector creation
  • Basic vector math
    • Vector / vector
    • Vector / scalar
  • Combined operations
  • Constraints
  • Cross product
  • Dot product
  • Interpolation
  • Normalization / magnitude
  • Distances
  • Orientation
  • Rotations
  • Polar / cartesian conversion
  • Randomness
  • Unary vector math ops
  • Vector array batch processing
  • Comparison / equality
  • Bitwise operations (int / uint vec)
  • Vector conversions / coercions
  • Boolean vector logic
  • Componentwise comparisons
  • Hashing
  • Code generator
• Authors
• License

About

Optimized 2d/3d/4d and arbitrary length vector operations, support for memory mapping/layouts.

Likely the most comprehensive vector library for TypeScript / JavaScript currently available.

This package provides over 875(!) largely code generated functions and supporting types to perform vector operations on fixed and arbitrary-length vectors, both packed and strided (i.e. where individual vector components are not successive array elements, for example in SOA memory layouts).

Includes componentwise logic operations for boolean vectors, componentwise comparisons for numeric vectors and componentwise binary ops for signed & unsigned integer vectors.

Features

• Small & fast: The vast majority of functions are code generated with fixed-sized versions not using any loops. Minified + gzipped, the entire package is ~11.8KB (though you'll hardly ever use all functions).
• Unified API: Any ArrayLike type can be used as vector containers (e.g. JS arrays, typed arrays, custom impls). Most functions are implemented as multi-methods, dispatching to any potentially optimized versions based on given vector arguments.
• Highly modular: Each function is defined in its own submodule / file. In addition to each generic multi-method base function, all fixed-length optimized versions are exported too. E.g. If add performs vector addition on arbitrary-length vectors, add2, add3, add4 are the optimized version for fixed-length vectors...
• Pluggable interface: The VecAPI interface defines objects of the ~70 most common vector operations implemented for specific vector sizes. Using this interface simplifies performance-critical use cases & algorithms which target different dimensions (e.g. 2d/3d), but should use the avaiable size-optimized vector ops. See VEC2, VEC3 and VEC4
• Extensible: Custom vector ops can be defined in a similar manner using the provided code generation helpers (see vop.ts and emit.ts for details).
• Immutable by default: Each operation producing a vector result takes an output vector as first argument. If null, the vector given as 2nd argument will (usually) be used as output (i.e. for mutation).
• Strided vector support is handled via the lightweight Vec2/3/4 class wrappers and the gvec() proxy (for generic, arbitrary-length vectors). These types behave like normal arrays (for read/write operations) and are also iterable. A subset of functions (suffixed with S, e.g. addS vs. add) also support striding without the need for extra class wrappers. This is handled via additional index and stride arguments for each input/output vector. These functions are only available for sizes 2 / 3 / 4, though.
• Random vector functions support the IRandom interface defined by @thi.ng/random to work with custom (P)RNGs. If omitted, the built-in Math.random() will be used.

Partially ported from thi.ng/geom-clj (Clojure) and c.thi.ng (C11).

Status

STABLE - used in production

Search or submit any issues for this package

Breaking changes in v6.0.0

The introduction of seveveral standard libc math functions to the @thi.ng/math package caused a behavior change of existing fmod() function. For symmetry reasons the same changes have been applied to this package...

• swap fmod() ⇄ mod(), to align the latter with its GLSL counterpart
• the new fmod() has standard libc behavior (same as JS % operator)
• add remainder() with standard libc behavior

Breaking changes in v3.0.0

• to avoid confusion, the arg order of madd and maddN functions have been updated to be compatible with the OpenCL mad function and to generally follow the expanded name, i.e. multiply-add:
  • madd([], a, b, c): before a + b * c, now: a * b + c
  • maddN([], a, b, n) => maddN([], a, n, b) (i.e. a * n + b)
• rename perpendicularLeft2 => perpendicularCCW
• rename perpendicularRight2 => perpendicularCW
• rename normalLeft2/ normalRight2 => normalCCW / normalCW

Related packages

• @thi.ng/color - Array-based color types, CSS parsing, conversions, transformations, declarative theme generation, gradients, presets
• @thi.ng/distance - N-dimensional distance metrics & K-nearest neighborhoods for point queries
• @thi.ng/ecs - Entity Component System based around typed arrays & sparse sets
• @thi.ng/geom - Functional, polymorphic API for 2D geometry types & SVG generation
• @thi.ng/hdom-canvas - @thi.ng/hdom component wrapper for declarative canvas scenegraphs
• @thi.ng/imgui - Immediate mode GUI with flexible state handling & data only shape output
• @thi.ng/matrices - Matrix & quaternion operations for 2D/3D geometry processing
• @thi.ng/simd - WASM based SIMD vector operations for batch processing
• @thi.ng/soa - SOA & AOS memory mapped structured views with optional & extensible serialization
• @thi.ng/shader-ast-js - Customizable JS codegen, compiler & runtime for @thi.ng/shader-ast
• @thi.ng/vector-pools - Data structures for managing & working with strided, memory mapped vectors
• @thi.ng/webgl - WebGL & GLSL abstraction layer

Installation

yarn add @thi.ng/vectors

ESM import:

import * as vec from "@thi.ng/vectors";

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/vectors"></script>

JSDelivr documentation

For Node.js REPL:

const vec = await import("@thi.ng/vectors");

Package sizes (brotli'd, pre-treeshake): ESM: 14.01 KB

Dependencies

• @thi.ng/api
• @thi.ng/binary
• @thi.ng/checks
• @thi.ng/equiv
• @thi.ng/errors
• @thi.ng/math
• @thi.ng/memoize
• @thi.ng/random
• @thi.ng/strings
• @thi.ng/transducers

Note: @thi.ng/api is in most cases a type-only import (not used at runtime)

Usage examples

35 projects in this repo's /examples directory are using this package:

Screenshot	Description	Live demo	Source
	ASCII art raymarching with thi.ng/shader-ast & thi.ng/text-canvas	Demo	Source
	Basic 2D boid simulation and spatial indexing neighbor lookups	Demo	Source
	Canvas based dial widget	Demo	Source
	Self-modifying, animated typographic grid with emergent complex patterns	Demo	Source
	Interactive visualization of closest points on ellipses	Demo	Source
	Piechart visualization of CSV data	Demo	Source
	Doodle w/ K-nearest neighbor search result visualization	Demo	Source
	K-nearest neighbor search in an hash grid	Demo	Source
	SVG path to SDF, applying deformation and converting back to SVG	Demo	Source
	Mouse gesture / stroke analysis, simplification, corner detection	Demo	Source
	Realtime analog clock demo	Demo	Source
	Interactive pattern drawing demo using transducers	Demo	Source
	2D Bezier curve-guided particle system	Demo	Source
	Various hdom-canvas shape drawing examples & SVG conversion / export	Demo	Source
	Canvas based Immediate Mode GUI components	Demo	Source
	Animated sine plasma effect visualized using contour lines	Demo	Source
	k-means clustering visualization	Demo	Source
	Animated, iterative polygon subdivisions & visualization	Demo	Source
	Quasi-random lattice generator	Demo	Source
	Unison wavetable synth with waveform editor	Demo	Source
	Steering behavior drawing with alpha-blended shapes	Demo	Source
	Minimal rdom-canvas animation	Demo	Source
	Animated Voronoi diagram, cubic splines & SVG download	Demo	Source
	2D scenegraph & shape picking	Demo	Source
	2D scenegraph & image map based geometry manipulation	Demo	Source
	Minimal shader graph developed during livestream #2	Demo	Source
	Fitting, transforming & plotting 10k data points per frame using SIMD	Demo	Source
	Entity Component System w/ 100k 3D particles	Demo	Source
	Compute cubic spline position & tangent using Dual Numbers	Demo	Source
	3D wireframe textmode demo	Demo	Source
	Visual comparison of biased vs. unbiased normal vectors projected on the surface of a sphere	Demo	Source
	WebGL multi-colored cube mesh	Demo	Source
	Drawing to floating point offscreen / multi-pass shader pipeline	Demo	Source
	WebGL instancing, animated grid	Demo	Source
	WebGL MSDF text rendering & particle system	Demo	Source

API

Generated API docs

Basic usage

import * as v from "@thi.ng/vectors";

// immutable vector addition (1st arg is result)
v.add([], [1, 2, 3, 4], [10, 20, 30, 40]);
// [11, 22, 33, 44]

// mutable addition
// (if first arg (output) is null writes result to 2nd arg)
a = [1, 2, 3];
v.add(null, a, a);
// [2, 4, 6]

// multiply-add (o = a * b + c)
v.madd([], [10, 20], [0.5, 0.25], [1, 2]);
// [6, 7]

// multiply-add w/ scalar (o = a * n + b)
v.maddN([], [10, 20], 0.5, [1, 2]);
// [6, 12]

// scalar addition w/ arbitrary length & strided vector
v.addN([], gvec([0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0], 3, 1, 4), 10);
// [11, 12, 13]

// or operate on raw arrays directly...
// here the last 4 args define:
// out index, src index, out stride, src stride
v.addNS3(null, [0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0], 10, 1, 1, 4, 4)
// [0, 11, 0, 0, 0, 12, 0, 0, 0, 13, 0, 0, 0]

v.dist([1, 2], [100, 200]);
// 221.37072977247917

v.distManhattan([1, 2], [100, 200]);
// 297

v.distChebyshev([1, 2], [100, 200]);
// 198

v.mixN([], [1, 2], [10, 20], 0.5);
// [5.5, 11]

v.fromHomogeneous([], [100, 200, 0.5]);
// [200, 400]

v.swizzle4([], [1, 2], 1, 1, 0, 0);
// [ 2, 2, 1, 1 ]

v.hash([1, 2, 3])
// 2383338936

Using the VecAPI implementation objects to use size-optimized vector ops in a pluggable manner (this is in addition/alternative to using the standard set of polymorphic functions for similar results).

import { VEC2, VEC3, type Vec, type VecAPI } from "@thi.ng/vectors";

interface Particle {
    pos: Vec;
    dir: Vec;
    targetDir: Vec;
    speed: number;
    turnSpeed: number;
}

const updateParticle = (p: Particle, { maddN, mixN, normalize }: VecAPI) => {
    // interpolate current direction toward target dir
    mixN(null, p.dir, p.targetDir, p.turnSpeed);
    // normalize direction
    normalize(null, p.dir);
    // add scaled direction to position (and store as new position)
    return maddN(p.pos, p.dir, p.speed, p.pos);
};

// 2d version
let p2d: Particle = {
    pos: [10, 20], dir: [0, 1], targetDir: [1, 0], speed: 5, turnSpeed: 0.1,
};

updateParticle(p2d, VEC2);
// [ 10.552, 24.969 ]

// 3d version
let p3d: Particle = {
    pos: [10, 20, 30], dir: [0, 1, 0], targetDir: [0, 0, 1], speed: 5, turnSpeed: 0.1,
};

updateParticle(p3d, VEC3);
// [ 10, 24.969, 30.552 ]

Naming conventions

Wherever possible, each operation comes in different variations. All fixed size versions use optimized, loop-free implementations.

Suffix	Description
none	arbitrary length vector arg(s)
2	2d vector arg(s)
3	3d vector arg(s)
4	4d vector arg(s)
N2	2d vector(s) & scalar
N3	3d vector(s) & scalar
N4	4d vector(s) & scalar
I	arbitrary len, signed int vec
U	arbitrary len, unsigned int vec
I2 / I3 / I4	fixed size signed int vec
U2 / U3 / U4	fixed size signed int vec
NI / NU	arbitrary len, signed int vec & scalar
NI2 / NI3 / NI4	fixed size signed int vec & scalar
NU2 / NU3 / NU4	fixed size unsigned int vec & scalar
S2 / S3 / S4	fixed size strided vec
NS2 / NS3 / NS4	fixed size strided vec & scalar
C	arbitrary len vec, component wise args
C2 / C3 / C4	fixed size vec, component wise args
CS2 / CS3 / CS4	fixed size strided vec, component args

Constants

• MAX2 / MAX3 / MAX4 - each component +Infinity
• MIN2 / MIN3 / MIN4 - each component -Infinity
• ONE2 / ONE3 / ONE4 - each component 1
• ZERO2 / ZERO3 / ZERO4 - each component 0
• X2 / X3 / X4 - positive X axis
• Y2 / Y3 / Y4 - positive Y axis
• Z3 / Z4 - positive Z axis
• W4 - positive W axis

Component setters & copying

• set / set2 / set3 / set4
• setC / setC2 / setC3 / setC4 / setC6
• setN / setN2 / setN3 / setN4
• setS / setS2 / setS3 / setS4
• setCS2 / setCS3 / setCS4
• setNS2 / setNS3 / setNS4
• copy
• empty
• one
• zero

Component swizzling

• swizzle2 / swizzle3 / swizzle4
• setSwizzle1 / setSwizzle2 / setSwizzle3 / setSwizzle4
• swapXY / swapXZ / swapYZ

Vector creation

Functions to create wrapped (strided) vector instances:

• vec2 / vec2n
• vec3 / vec3n
• vec4 / vec4n
• gvec

Wrap existing vanilla vectors:

• asVec2 / asVec3 / asVec4

Vanilla vector (array) factories:

• ones
• zeroes
• vecOf
• setVN3 / setVN4
• setVV4 / setVV6 / setVV9 / setVV16

Basic vector math

Vector / vector

Component wise op with 2 input vectors:

Function	Generic	Fixed	Strided	Int	Comments
add	✓	2-4	S2-S4	I2-I4, U2-U4
div	✓	2-4	S2-S4	I2-I4, U2-U4
mul	✓	2-4	S2-S4	I2-I4, U2-U4
sub	✓	2-4	S2-S4	I2-I4, U2-U4
fmod	✓	2-4			(C/JS behavior)
mod	✓	2-4			(GLSL behavior)
pow	✓	2-4
remainder	✓	2-4			(C behavior)

import { add, add2, addU2, addS2 } from "@thi.ng/vectors";

// generic
add([], [1, 2, 3, 4, 5], [10, 20, 30, 40, 50]);
// [11, 22, 33, 44, 55]

// fixed size & packed
add2([], [1, 2], [10, 20])
// [11, 22]

// unsigned int
addU2([], [1, -2], [-10, 20])
// [4294967287, 18]

// strided
addS2([], [1,0,2,0], [0,10,0,0,0,20], 0, 0, 1, 1, 2, 4)
// [11, 22]

Vector / scalar

Component wise op with one input vector and single scalar:

Function	Generic	Fixed	Strided	Int	Comments
addN	✓	2-4	S2-S4	I2-I4, U2-U4
divN	✓	2-4	S2-S4	I2-I4, U2-U4
mulN	✓	2-4	S2-S4	I2-I4, U2-U4
subN	✓	2-4	S2-S4	I2-I4, U2-U4
neg	✓				same as mulN(out, v, -1)
fmodN	✓	2-4			(C/JS behavior)
modN	✓	2-4			(GLSL behavior)
powN	✓	2-4
remainderN	✓	2-4			(C behavior)
roundN	✓	2-4

Combined operations

Function	Generic	Fixed	Strided	Int	Comments
addm	✓	2-4	S2-S4		(a + b) * c
addmN	✓	2-4	S2-S4		(a + b) * n
madd	✓	2-4	S2-S4		a * n + c
maddN	✓	2-4	S2-S4		a * n + b
msub	✓	2-4	S2-S4		a * n - c
msubN	✓	2-4	S2-S4		a * n - b
subm	✓	2-4	S2-S4		(a - b) * c
submN	✓	2-4	S2-S4		(a - b) * n

Constraints

Function	Generic	Fixed	Strided	Int	Comments
clamp	✓	2-4			min(max(a, b), c)
clampN	✓	2-4			min(max(a, n), m)
clamp01	✓	_2 - _4			min(max(a, 0), 1)
clamp11	✓	_2 - _4			min(max(a, -1), 1)
max	✓	2-4			max(a, b)
min	✓	2-4			min(a, b)

Cross product

Function	Generic	Fixed	Strided	Int	Comments
cross		2, 3	S2, S3		2D version returns scalar
orthoNormal		3
signedArea		2

Dot product

Function	Generic	Fixed	Strided	Cwise	Comments
dot	✓	2-4	S2-S4	C4, C6, C8

Interpolation

Function	Generic	Fixed	Strided	Int	Comments
fit	✓	2-4
fit01	✓	_2 - _4
fit11	✓	_2 - _4
mix	✓	2-4	S2 - S4
mixN	✓	2-4	S2 - S4
mixBilinear	✓	2-4
mixCubic	✓
mixQuadratic	✓
smoothStep	✓	2-4
step	✓	2-4

Normalization / magnitude

Function	Generic	Fixed	Strided	Int	Comments
limit	✓
mag	✓		S2-S4
magSq	✓	2-4	S2-S4
normalize	✓		S2-S4		w/ opt target length

Distances

Function	Generic	Fixed	Strided	Int	Comments
dist	✓
distSq	✓	2-4
distBrayCurtis	✓
distCanberra	✓
distChebyshev	✓	2-4
distCosine	✓
distHamming	✓
distHaversineLatLon		2			lat/lon coordinates
distHaversineLonLat		2			lon/lat coordinates
distJaccard	✓
distManhattan	✓	2-4
distMinkowski	✓
distSorensenDice	✓
distWeighted	✓
pointOnRay	✓	2-3			point at distance

Orientation

Function	Generic	Fixed	Strided	Int	Comments
angleBetween		2, 3
angleRatio	✓
atan_2	✓	2-4			Math.atan2(y, x)
bisect		2
cornerBisector	✓
degrees	✓	2-4
direction	✓				normalize(b - a)
faceForward	✓
heading	✓				alias headingXY
headingXY	✓
headingXZ	✓
headingYZ	✓
headingSegment	✓				alias headingSegmentXY
headingSegmentXY	✓
headingSegmentXZ	✓
headingSegmentYZ	✓
normalCCW					2D only
normalCW					2D only
perpendicularCCW					2D only
perpendicularCW					2D only
project	✓
radians	✓	2-4
reflect	✓
refract	✓

Rotations

(Also see rotation matrices provided by @thi.ng/matrices)

Function	Generic	Fixed	Strided	Int	Comments
rotationAroundAxis		3
rotationAroundPoint		2
rotate			S2		alias for rotateZ
rotateX			S3
rotateY			S3
rotateZ			S3

Polar / cartesian conversion

Function	Generic	Fixed	Strided	Int	Comments
cartesian	✓	2, 3			2D/3D only
polar	✓	2, 3			2D/3D only

Randomness

All ops support custom PRNG impls based on the @thi.ng/random IRandom interface and use Math.random by default:

Function	Generic	Fixed	Strided	Int	Comments
jitter	✓
randMinMax	✓	2-4	S2-S4
randNorm	✓	2-4	S2-S4
randNormDistrib	✓	2-4	S2-S4
random	✓	2-4	S2-S4
randomDistrib	✓	2-4	S2-S4

Unary vector math ops

Function	Generic	Fixed	Strided	Int	Comments
abs	✓	2-4
acos	✓	2-4
asin	✓	2-4
atan	✓	2-4			Math.atan(y / x)
ceil	✓	2-4
cos	✓	2-4
cosh	✓	2-4
exp	✓	2-4
floor	✓	2-4
fract	✓	2-4
fromHomogeneous	✓	3, 4			3D/4D only
invert	✓	2-4
invSqrt	✓	2-4
isInf	✓	2-4
isNaN	✓	2-4
log	✓	2-4
major	✓	2-4
minor	✓	2-4
round	✓	2-4
sign	✓	2-4
sin	✓	2-4
sinh	✓	2-4
sqrt	✓	2-4
sum	✓	2-4
tan	✓	2-4
trunc	✓	2-4
wrap	✓	2-4

Vector array batch processing

Functions to transform flat / strided buffers w/ vector operations:

• mapV / mapVN / mapVV / mapVVN / mapVVV
• mean / median
• minBounds / maxBounds

Comparison / equality

• comparator2 / comparator3 / comparator4
• equals / equals2 / equals3 / equals4
• eqDelta / eqDelta2 / eqDelta3 / eqDelta4
• eqDeltaS
• eqDeltaArray

Bitwise operations (int / uint vec)

Arguments are assumed to be signed / unsigned ints. Results will be forced accordingly.

Function	Generic	Fixed	Strided	Int	Comments
bitAnd	✓			I2-I4, U2-U4
bitAndN	✓			I2-I4, U2-U4
bitNot	✓			I2-I4, U2-U4
bitOr	✓			I2-I4, U2-U4
bitOrN	✓			I2-I4, U2-U4
bitXor	✓			I2-I4, U2-U4
bitXorN	✓			I2-I4, U2-U4
lshift	✓			I2-I4, U2-U4
rshift	✓			I2-I4, U2-U4
lshiftN	✓			I2-I4, U2-U4
rshiftN	✓			I2-I4, U2-U4

Vector conversions / coercions

• asIVec (2-4) - signed int vector
• asUVec (2-4) - unsigned int vector
• asBVec (2-4) - boolean vector
• fromBVec (2-4) - coerces each component to 0/1

Boolean vector logic

Function	Generic	Fixed	Strided	Int	Comments
logicAnd	✓	2-4
logicAndN	✓	2-4
logicOr	✓	2-4
logicOrN	✓	2-4
logicNot	✓	2-4
every	✓	2-4			returns boolean
some	✓	2-4			returns boolean
not	✓	2-4

Componentwise comparisons

All resulting in boolean vectors:

Function	Generic	Fixed	Strided	Int	Comments
eq	✓	2-4
lt	✓	2-4
lte	✓	2-4
gt	✓	2-4
gte	✓	2-4
neq	✓	2-4

Hashing

• hash

Code generator

• compile / compileG / compileGHOF / compileHOF
• defOp / defOpS / defFnOp / defHofOp
• defMathNOp / defMathOp
• vop

For more information about the code generator see:

• emit.ts
• templates.ts
• vop.ts

Authors

• Karsten Schmidt

If this project contributes to an academic publication, please cite it as:

@misc{thing-vectors,
  title = "@thi.ng/vectors",
  author = "Karsten Schmidt",
  note = "https://thi.ng/vectors",
  year = 2015
}

License

© 2015 - 2024 Karsten Schmidt // Apache License 2.0