@thi.ng/vectors

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

• About
  • Features
  • Related packages
• Installation
• Dependencies
• Usage examples
• API
  • Breaking changes in v3.0.0
  • Naming conventions
  • Constants
  • Component setters & copying
  • Component swizzling
  • Vector creation
  • Basic vector math
  • 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)
  • Boolean vector logic
  • Componentwise comparisons
  • Hashing
  • Code generator
• Authors
• License

About

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

This package provides ~720 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 ~10.1KB (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...
• 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.

Related packages

• @thi.ng/color - vector based color operations / conversions
• @thi.ng/geom - 2D/3D geometry types & operations
• @thi.ng/imgui - immediate mode GUI
• @thi.ng/matrices - 2x2, 2x3, 3x3, 4x4 matrix & quaternion ops
• @thi.ng/shader-ast - Shader DSL & cross-compilation
• @thi.ng/shader-ast-js - JS code generator for shader-ast
• @thi.ng/vector-pools - operations on memory mapped data

Installation

yarn add @thi.ng/vectors

Dependencies

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

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 (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

API

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

Naming conventions

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

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:

// 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:

Combined operations

Constraints

Cross product

Dot product

Interpolation

Normalization / magnitude

Distances

Orientation

Rotations

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

Polar / cartesian conversion

Randomness

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

Unary vector math ops

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

Bitwise operations (int / uint vec)

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

Boolean vector logic

Componentwise comparisons

All resulting in boolean vectors:

Hashing

• hash

Code generator

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

For more information about the code generator see:

• codegen.ts
• templates.ts
• vop.ts

Authors

• Karsten Schmidt

License

© 2018 Karsten Schmidt // Apache Software License 2.0