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@thi.ng/vectors

@thi.ng/vectors

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This project is part of the @thi.ng/umbrella monorepo.

About

This package provides 350+ largely code generated functions & 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 layouts).

Features

  • Small & fast: The vast majority of these functions are code generated with fixed-sized versions not using any loops. Minified + gzipped, the entire package is ~7.6KB.
  • 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...
  • Extensible: Custom vector ops can be defined in a similar manner using the provided code generation helpers (see vop.ts and codegen.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 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.

Installation

yarn add @thi.ng/vectors

Dependencies

Usage examples

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 is null)
a = [1, 2, 3];
v.add(null, a, a);
// [2, 4, 6]

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

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

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 ]

API

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
  • setSN2 / setSN3 / setSN4
  • copy
  • empty
  • one
  • zero

Component swizzling

  • swizzle2 / swizzle3 / swizzle4
  • swapXY / swapXZ / swapYZ

Vector creation

Functions to create wrapped vector instances:

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

Wrap existing vanilla vectors:

  • asVec2 / asVec3 / asVec4

Vanilla vector (array) factories:

  • ones
  • zeroes

Basic vector math

Vector / vector

Component wise op with 2 input vectors:

  • add / add2 / add3 / add4
  • div / div2 / div3 / div4
  • mul / mul2 / mul3 / mul4
  • sub / sub2 / sub3 / sub4
  • mod / mod2 / mod3 / mod4
  • pow / pow2 / pow3 / pow4

Vector / scalar

Component wise op with one input vector and single scalar:

  • addN / addN2 / addN3 / addN4
  • divN / divN2 / divN3 / divN4
  • mulN / mulN2 / mulN3 / mulN4
  • subN / subN2 / subN3 / subN4
  • neg - same as mulN(out, v, -1)
  • modN / modN2 / modN3 / modN4
  • powN / powN2 / powN3 / powN4

Strided vectors

Functions for memory mapped, strided vectors (without requiring wrappers):

  • addS2 / addS3 / addS4
  • divS2 / divS3 / divS4
  • mulS2 / mulS3 / mulS4
  • subS2 / subS3 / subS4

Multiply-add

  • addm / addm2 / addm3 / addm4
  • addmN / addmN2 / addmN3 / addmN4
  • addW2 / addW3 / addW4 / addW5
  • madd / madd2 / madd3 / madd4
  • maddN / maddN2 / maddN3 / maddN4
  • subm / subm2 / subm3 / subm4
  • submN / submN2 / submN3 / submN4

Constraints

  • clamp
  • clamp2 / clamp3 / clamp4
  • clampN / clampN2 / clampN3 / clampN4
  • clamp01 / clamp01_2 / clamp01_3 / clamp01_4
  • clamp11 / clamp11_2 / clamp11_3 / clamp11_4
  • max / max2 / max3 / max4
  • min / min2 / min3 / min4

Cross product

  • cross2
  • cross3
  • orthoNormal3
  • signedArea2

Dot product

  • dot
  • dot2 / dot3 / dot4
  • dotC4 / dotC6 / dotC8
  • dotS2 / dotS3 / dotS4

Interpolation

  • fit / fit2 / fit3 / fit4
  • fit01 / fit01_2 / fit01_3 / fit01_4
  • fit11 / fit11_2 / fit11_3 / fit11_4
  • mix / mix2 / mix3 / mix4
  • mixN / mixN2 / mixN3 / mixN4
  • mixBilinear / mixBilinear2 / mixBilinear3 / mixBilinear4
  • mixCubic
  • mixQuadratic
  • smoothStep / smoothStep2 / smoothStep3 / smoothStep4
  • step / step2 / step3 / step4

Normalization / magnitude

  • limit
  • mag
  • magSq / magSq2 / magSq3 / magSq4
  • normalize

Distances

  • dist
  • distSq / distSq2 / distSq3 / distSq4
  • distChebyshev / distChebyshev2 / distChebyshev3 / distChebyshev4
  • distManhattan / distManhattan2 / distManhattan3 / distManhattan4

Orientation

  • angleBetween2 / angleBetween3
  • angleRatio
  • bisect2
  • direction
  • faceForward
  • heading / headingXY / headingXZ / headingYZ
  • headingSegment / headingSegmentXY / headingSegmentXZ / headingSegmentYZ
  • normalLeft2 / normalRight2
  • perpendicularLeft2 / perpendicularRight2
  • project
  • reflect
  • refract

Rotations

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

  • rotateAroundAxis3
  • rotateAroundPoint2
  • rotateX \ rotateY \ rotateZ

Polar / cartesian conversion

  • cartesian / cartesian2 / cartesian3
  • polar / polar2 / polar3

Randomness

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

  • jitter
  • randMinMax / randMinMax2 / randMinMax3 / randMinMax4
  • randNorm
  • random / random2 / random3 / random4

Unary vector math ops

  • abs / abs2 / abs3 / abs4
  • acos / acos2 / acos3 / acos4
  • asin / asin2 / asin3 / asin4
  • ceil / ceil2 / ceil3 / ceil4
  • cos / cos2 / cos3 / cos4
  • cosh / cosh2 / cosh3 / cosh4
  • exp / exp2 / exp3 / exp4
  • floor / floor2 / floor3 / floor4
  • fract / fract2 / fract3 / fract4
  • fromHomogeneous / fromHomogeneous3 / fromHomogeneous4
  • invert / invert2 / invert3 / invert4
  • invSqrt / invSqrt2 / invSqrt3 / invSqrt4
  • log / log2 / log3 / log4
  • major / major2 / major3 / major4
  • minor / minor2 / minor3 / minor4
  • round / round2 / round3 / round4
  • sign / sign2 / sign3 / sign4
  • sin / sin2 / sin3 / sin4
  • sinh / sinh2 / sinh3 / sinh4
  • sqrt / sqrt2 / sqrt3 / sqrt4
  • sum / sum2 / sum3 / sum4
  • tan / tan2 / tan3 / tan4
  • tanh / tanh2 / tanh3 / tanh4
  • trunc / trunc2 / trunc3 / trunc4
  • wrap / wrap2 / wrap3 / wrap4

Vector array batch processing

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

  • mapV / mapVN / mapVV / mapVVN / mapVVV

Comparison / equality

  • comparator2 / comparator3 / comparator4
  • eqDelta / eqDelta2 / eqDelta3 / eqDelta4
  • eqDeltaS
  • eqDeltaArray

Code generator

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

For more information about the code generator see:

Authors

  • Karsten Schmidt

License

© 2018 Karsten Schmidt // Apache Software License 2.0

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