MathBox is a library for rendering presentation-quality math diagrams in a browser using WebGL. Built on top of Three.js and ShaderGraph it provides a clean API to visualize mathematical relationships and animate them declaratively.

For background, see the article series on Acko.net.

Presentations:

• The Pixel Factory

Demos:

• Audio Visualizer (code)
• Cylindrical Stream (code)
• Data/Shape Mapping (code)
• LaTeX/HTML/GL Labels (code)
• Quaternion Hypersphere (code)
• Render-to-Texture History (code)
• Vertex Warping (code)
• Volumetric Vectors (code)

And many more at https://mathbox.org.

You can install MathBox via npm for use with a bundler like Webpack, or include a global MathBox object onto your page by including the library via CDN.

• Run the following in your project's directory to install MathBox and Three.js via npm:

npm install mathbox three

Import THREE and MathBox (library and stylesheet), along with a controls instance that you'll pass to the MathBox.mathBox constructor:

import "mathbox/mathbox.css"

import * as THREE from "three"
import { OrbitControls } from "three/examples/jsm/controls/OrbitControls.js"
import * as MathBox from "mathbox"

Include the following in your HTML header to load all required libraries and styles:

<!-- Install your choice of three.js version from CDN: -->
<script
  type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/[email protected]/build/three.min.js"
></script>

<!-- Load a Controls instance, making sure that the version matches the Three.js version above: -->
<script
  type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/[email protected]/examples/js/controls/OrbitControls.js"
></script>

<!-- Install the latest MathBox, either mathbox.js or mathbos.min.js -->
<script
  type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathbox@latest/build/bundle/mathbox.js"
></script>

<!-- Include the MathBox CSS: -->
<link
  rel="stylesheet"
  href="https://cdn.jsdelivr.net/npm/mathbox@latest/build/mathbox.css"
/>

Construct a MathBox instance by passing initialization options to the mathBox() constructor:

const options = {
  controls: {
    // Orbit controls, i.e. Euler angles, with gimbal lock
    klass: THREE.OrbitControls
  },
};
const root = MathBox.mathBox(options);

Note See threestrap for all available options.

To spawn inside a specific element, pass an HTMLElement with the element option:

const element = document.querySelector("#my-thing");

const options = {
  element: element,
  controls: {
    klass: THREE.OrbitControls
  },
};
const root = MathBox.mathBox(options);

On initialization, mathBox returns a MathBox API object, wrapping the MathBox <root/>. Insert new MathBox nodes into the component tree by calling the method associated with the primitive you'd like to add.

Note See the Primitives doc for a description of all primitives and their properties.

The following code will set up a 3D Cartesian coordinate system with the specified range and scale for its x, y and z axes, and then insert an x and y axis into the scene:

const view = root
  .cartesian({
    range: [
      [-2, 2],
      [-1, 1],
      [-1, 1],
    ],
    scale: [2, 1, 1],
  })
  .axis({
    axis: 1,
  })
  .axis({
    axis: 2,
  });

Use your mouse to click and drag the camera's orientation, and zoom in and out:

Each primitive call:

• creates a new element
• inserts it into the tree
• returns a version of the API object with its selection focused on the new element.

Calling print() on some selection will print a representation to the console of the selection and any children. For example, view.print() prints the following:

<cartesian
  range={[
    [-2, 2],
    [-1, 1],
    [-1, 1],
  ]}
  scale={[2, 1, 1]}
>
  <axis axis={1} />
  <axis axis={2} />
</cartesian>

Select objects using .select() and a CSS-like selector to get a jQuery-like selection:

root.select("cartesian > axis");

Next, visit the Quick Start page for a more involved example that builds up an animating, interactive mathematical graph with labeled axes.

For help, see the following resources:

• Glossary of terms to help get familiar with MathBox and WebGL.
• MathBox API for typical usage.
• List of Primitives for a full element reference.
• Writing Custom Shaders for info on custom shaders and GPU-side processing.
• Context API for advanced usage.

For more involved questions, or just to say hi, please join us in the MathBox Google Group.

• threestrap - Three.js bootstrapper
• shadergraph - Functional GLSL linker
• MathBox-react - React bindings for MathBox
• MathBox.cljs - ClojureScript bindings for MathBox via MathBox-react

• Math3D online graphing calculator
• KineticGraphs JS Engine (code)
• Textbook: "Interactive Linear Algebra"" (code)
• Many visualizations at Sam Zhang's homepage
• Jesse Bettencourt's Torus Knot Fibration Master's project (code)
• Interactive knot visualizations

And the many demos listed on this thread of the MathBox Google group.

MIT License.

MathBox and ShaderGraph (c) Steven Wittens 2013-2023.

Libraries and 3rd party shaders (c) their respective authors.