NPM Package

Fast 3d math library for webgpu

Why another 3d math library?

  • Most other 3D math libraries are designed for WebGL, not WebGPU
    • WebGPU uses clip space Z 0 to 1, vs WebGL -1 to 1. So ortho, perspective, frustum are different
    • WebGPU mat3s are 12 floats (padded), WebGL they're 9.
  • Many other 3D math libraries are overly verbose
    • compare

      // wgpu-matrix
      const t = mat4.translation([x, y, z]);
      const p = mat4.perspective(fov, aspect, near, far);
      const r = mat4.rotationX(rad);
      // gl-matrix
      const t = mat4.create();
      mat4.fromTranslation(t, [x, y, z]);

      const p = mat4.create();
      mat4.perspective(p, fov, aspect, near, far);

      const r = mat4.create();
      mat4.fromXRotation(r, rad);

      note that if you want to pre-create matrices you can still do this in wgpu-matrix

      const t = mat4.create();
      mat4.translation([x, y, z], t);

      const p = mat4.create();
      mat4.perspective(fov, aspect, near, far, p);

      const r = mat4.create();
      mat4.rotationX(rad, r);


import {
} from 'https://wgpu-matrix.org/dist/2.x/wgpu-matrix.module.js';

const fov = 60 * Math.PI / 180
const aspect = width / height;
const near = 0.1;
const far = 1000;
const perspective = mat4.perspective(fov, aspect, near, far);

const eye = [3, 5, 10];
const target = [0, 4, 0];
const up = [0, 1, 0];
const view = mat4.lookAt(eye, target, up);

Note: for translation, rotation, and scaling there are 2 versions of each function. One generates a translation, rotation, or scaling matrix. The other translates, rotates, or scales a matrix.

const t = mat4.translation([1, 2, 3]);    // a translation matrix
const r = mat4.rotationX(Math.PI * 0.5); // a rotation matrix
const s = mat4.scaling([1, 2, 3]); // a scaling matrix
const m = mat4.identity();
const t = mat4.translate(m, [1, 2, 3]); // m * translation([1, 2, 3])
const r = mat4.rotateX(m, Math.PI * 0.5); // m * rotationX(Math.PI * 0.5)
const s = mat4.scale(m, [1, 2, 3]); // m * scaling([1, 2, 3])

Functions take an optional destination to hold the result.

const m = mat4.create();            // m = new mat4
mat4.identity(m); // m = identity
mat4.translate(m, [1, 2, 3], m); // m *= translation([1, 2, 3])
mat4.rotateX(m, Math.PI * 0.5, m); // m *= rotationX(Math.PI * 0.5)
mat4.scale(m, [1, 2, 3], m); // m *= scaling([1, 2, 3])

There is also the minified version

import {
} from 'https://wgpu-matrix.org/dist/2.x/wgpu-matrix.module.js';

// ... etc ...

or via npm

npm install --save wgpu-matrix

then using a build process

import {vec3, mat3} from 'wgpu-matrix';

// ... etc ...




mat4.perspective, mat4.ortho, and mat4.frustum all return matrices with Z clip space from 0 to 1 (unlike most WebGL matrix libraries which return -1 to 1)

mat4.create makes an all zero matrix if passed no parameters. If you want an identity matrix call mat4.identity


mat3 uses the space of 12 elements

// a mat3
xx, xy, xz, ?
yx, yy, yz, ?
zx, zy, zz, ?

This is because WebGPU requires mat3s to be in this format and since this library is for WebGPU it makes sense to match so you can manipulate mat3s in TypeArrays directly.

vec3 in this library uses 3 floats per but be aware that an array of vec3 in a Uniform Block or other structure in WGSL, each vec3 is padded to 4 floats! In other words, if you declare

struct Foo {
bar: vec3<f32>[3];

then bar[0] is at byte offset 0, bar[1] at byte offset 16, bar[2] at byte offset 32.

See the WGSL spec on alignment and size.

Columns vs Rows

WebGPU follows the same conventions as OpenGL, Vulkan, Metal for matrices. Some people call this "column major". The issue is the columns of a traditional "math" matrix are stored as rows when declaring a matrix in code.

x1, x2, x3, x4, // <- column 0
y1, y2, y3, y4, // <- column 1
z1, z2, z3, z4, // <- column 2
w1, w2, w3, w4, // <- column 3

To put it another way, the translation vector is in elements 12, 13, 14

xx, xy, xz, 0, // <- x-axis
yx, yy, yz, 0, // <- y-axis
zx, zy, zz, 0, // <- z-axis
tx, ty, tz, 1, // <- translation

This issue has confused programmers since at least the early 90s 😌

Performance vs Convenience

Most functions take an optional destination as the last argument. If you don't supply it, a new one (vector, matrix) will be created for you.

// convenient usage

const persp = mat4.perspective(fov, aspect, near, far);
const camera = mat4.lookAt(eye, target, up);
const view = mat4.inverse(camera);
// performant usage

// at init time
const persp = mat4.create();
const camera = mat4.create();
const view = mat4.create();

// at usage time
mat4.perspective(fov, aspect, near, far, persp);
mat4.lookAt(eye, target, up, camera);
mat4.inverse(camera, view);

For me, most of the stuff I do in WebGPU, the supposed performance I might lose from using the convenient style is so small as to be unmeasurable. I'd prefer to stay convenient and then, if and only if I find a performance issue, then I might bother to switch to the performant style.

As the saying goes premature optimization is the root of all evil. 😉


1.x -> 2.x

  • mat4.lookAt changed from a "camera matrix" to a "view matrix" (same as gluLookAt). If you want a matrix that orients an something in world space see mat4.aim. Sorry about this change but people are used to lookAt making a a view matrix and it seemed prudent to make this change now and save more people from frustration going forward.


git clone https://github.com/greggman/wgpu-matrix.git
cd wgpu-matrix
npm i
npm run build
npm test

You can run tests in the browser by starting a local server

npx servez

Now go to wherever your server serves pages. In the case of servez that's probably http://localhost:8080/test/.

By default the tests test the minified version. To test the source use src=true as in http://localhost:8080/test/?src=true.

To limit which tests are run use grep=<regex>. For example http://localhost:8080/test/?src=true&grep=mat3.*?translate runs only tests with mat3 followed by translate in the name of test.