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WebGL Fundamentals

This is a series of lessons or tutorials about WebGL.

Unlike most WebGL lessons these are not based off of OpenGL. OpenGL is 20 years old. The lessons of OpenGL don't match well with WebGL. The APIs have changed too much. The ideas of OpenGL and OpenGL tutorials are out of date with WebGL, OpenGL ES 2.0 and the land of shaders.

I would argue that WebGL is actually a very simple API. What makes it appear complicated is the way in which it's used. The complications are added by the programmer. WebGL itself is simple.

These lessons try to show that simplicity and well as teach the fundamentals of 2D math and 3D math so readers can hopefully have an easier time writing their own WebGL programs and understanding the complexity that other programmers pile on top of simple WebGL.

This is work in progress. Feel free to contribute.


Of course bug fixes are always welcome.

If you'd like to write a new article please try to always take one step at a time. Don't do 2 or more things in a single step. Explain any new math in the simplest terms possible. Ideally with diagrams where possible.


Each translation goes in a folder under webgl/lessons/<country-code>.

Required files are



Defines various language specific options. Hanson is a JSON like format but allows comments.

Current fields are

  // The language (will show up in the language selection menu)
  language: 'English',

  // Phrase that appears under examples
  defaultExampleCaption: "click here to open in a separate window",

  // Title that appears on each page
  title: 'WebGL Fundamentals',

  // Basic description that appears on each page
  description: 'Learn WebGL from the ground up. No magic',

  // Link to the language root.
  link: '',  // replace `ja` with country code

  // html that appears after the article and before the comments
  commentSectionHeader: '<div>Questions? <a href="">Ask on stackoverflow</a>.</div>\n        <div>Issue/Bug? <a href="">Create an issue on github</a>.</div>',

  // markdown that appears for untranslated articles
  missing: "Sorry this article has not been translated yet. [Translations Welcome](! 😄\n\n[Here's the original English article for now]({{{origLink}}}).",

  // the phrase "Table of Contents"
  toc: "Table of Contents",

  // translation of categories for table of contents
  categoryMapping: {
    'fundamentals': "Fundamentals",
    'image-processing': "Image Processing",
    'matrices': "2D translation, rotation, scale, matrix math",
    '3d': "3D",
    'lighting': "Lighting",
    'organization': "Structure and Organization",
    'geometry': "Geometry",
    'textures': "Textures",
    'rendertargets': "Rendering To A Texture",
    '2d': "2D",
    'text': "Text",
    'misc': "Misc",
    'reference': "Reference",


This is the template for the main page for each language


This is template for the table of contents for the language. It is included on both the index and on each article. The only parts not auto-generated are the links ending links which you can translate if you want to. The build system will create a placeholder for every English article for which there is no corresponding article in that langauge. It will be filled the missing message from above.

Translation notes

The build process will make a placeholder html file for each article has an english .md file in webgl/lessons but no corresponding .md file for the language. This is to make it easy to include links in one article that links to another article but that other article has not yet been translated. This way you don't have to go back and fix already translated articles. Just translate one article at a time and leave the links as is. They'll link to placeholders until someone translates the missing articles.

Articles have front matter at the top

Title: Localized Title of article
Description: Localized description of article (used in RSS and social media tags)
TOC: Localized text for Table of Contents

DO NOT CHANGE LINKS : For example a link to a local resources might look like



<img src="somelink">

While you can add query parameters (see below) do not add "../" to try to make the link relative to the .md file. Links should stay as though the article exists at the same location as the original English.

UI localization

Some of the diagrams allow passing translations for the UI and other text.

For example if there is a slider named "rotation" you can add "?ui-rotation=girar" at the end of the URL for the diagram. For 2 or more translations separate them with a &. Certain characters are disallowed in URLs like =, #, & etc. For those use their uri encoding.

For diagram labels you'll have to look inside the code. For example for the directional lighting diagram near the start of the code it looks like this

const lang = {
  lightDir: opt.lightDir || "light direction",
  dot: || "dot(reverseLightDirection,surfaceDirection) = ",
  surface1: opt.surface1 || "surface",
  surface2: opt.surface2 || "direction",

Which means you can localize the labels like this

{{{diagram url="resources/directional-lighting.html?lightDir=光線方向&surface1=オブジェクト&surface2=表面方向&dot=dot(光線反対方向,表面方向)%20%3D%20&ui-rotation=角度" caption="方向を回転してみて" width="500" height="400"}}}

For testing reference the sample directly in your browser. For example


To build

The site is built into the out folder


git clone
npm install
npm run build
npm start

now open your browser to http://localhost:8080

Continuous build

You can run npm run watch after you've built to get continuous building. Only the article .md files and files that are normally copied are supported.

Build options

This is mostly for debugging build.js. Since it takes a while to process all the files you can set ARTICLE_FILTER to a substring of the filenames to process. For example

ARTICLE_FILTER=rotation npm run build

Will build the site as though only articles with rotation in their filename exist.


A list of articles I'd like to write or see written

  • lighting
    • normal maps
    • shadow maps
  • geometry
    • plane, cube, sphere, cone, disc, torus
      • lines vs triangles
      • indexed vs non
      • vertex colors
    • .obj
    • other
    • pre-process (don't load .obj, .dae, .fbx etc at runtime)
    • pre-optimize (texture atlas, sizes, combine meshes, etc...)
  • animation
    • blendshapes
    • hierarchical animation
  • debugging
    • debugging JS WebGL
      • example (
        • actually read the error message
        • understand it.
          • INVALID_ENUM means one of your gl.XXX values is not valid period
          • INVALID_VALUE means one of the int or float values is probably off
          • INVALID_OPERATION means something you tried to do won't work for the given state
          • texture not renderable
          • attribute out of range
          • check your framebuffers
          • check your extensions
      • make shorter samples (MCVE) See
        • remove any code you don't need
        • get rid of CSS
        • get rid of HTML
        • consider using a POINT (no attributes needed)
        • don't use images if they are not relevant. Use a canvas or a single and double pixel texture
        • While creating this MCVE you'll often find the bug
    • debugging a shader
      • set fragment shader to solid color.
      • render normals
      • render texcoords
      • render cube/sphere/plane
  • text
    • glyph cache
  • post processing
    • DOF
    • glow
    • light rays
    • RGB glitch, CRT distortion, scanlines
    • color mapping/tone mapping
  • Creative coding
  • code organization
    • scene graph
      • putting lights and camera in scene graph
  • Engine Creation
    • culling
      • frustum culling
      • grid culling
      • quad tree / oct tree
      • portals (is this still a thing?)
      • PVS
    • materials
    • lighting DB
  • Physically based rendering
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