wgpu-matrix

wgpu-matrix

Fast 3d math library for webgpu

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Usage

import {
  vec3,
  mat4,
} from 'https://wgpu-matrix.org/dist/0.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 camera = mat4.lookAt(eye, target, up);

const view = mat4.inverse(camera);

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]);    // generates a translation matrix
const r = mat4.rotationX(Math.PI * 0.5);  // generates a rotation matrix
const s = mat4.scaling([1, 2, 3]);        // generates a scaling matrix

const m = mat4.create();
const t = mat4.translate(m, [1, 2, 3]);    // generates m translated
const r = mat4.rotateX(m, Math.PI * 0.5);  // generates m rotated
const s = mat4.scale(m, [1, 2, 3]);        // generates m scaled

Functions take an optional destination to hold the result.

const m = mat4.create();
mat4.translate(m, [1, 2, 3], m);    // translates m
mat4.rotateX(m, Math.PI * 0.5, m);  // rotates m
mat4.scale(m, [1, 2, 3], m);        // scales m

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Notes

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.lookAt returns a matrix that makes an object look down the -Z axis. If you want a view matrix take its inverse.

Important!

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 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,  // <- xaxis
  yx, yy, yz, 0,  // <- yaxis
  zx, zy, zz, 0,  // <- zaxis
  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.target(eye, target, up);
const view = mat4.inverse(camera);

// performant usage

const persp = mat4.create();
const camera = mat4.create();
const view = mat4.create();

mat4.perspective(fov, aspect, near, far, persp);
mat4.target(eye, target, up, camera);
mat4.inverse(camera, view);

For me, most of the stuff I do in WebGPU, the supposed performance I might loss from using the convenient style is so small as to be unmeasurable. I'd prefer to be 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. 😉