I Built a Mini 3D Rendering Engine Using Just Canvas & Math

I didn’t.

Instead, I decided to reinvent the wheel — and honestly, it was one of the most fun and eye-opening things I’ve done.

In this article, I’ll walk you through how I built a fully interactive 3D cube using just the HTML Canvas and math — no 3D frameworks at all.

Live Demo: click here
Source Code: GitHub repo

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🎯 Why I Did This

I wanted to understand:

• How 3D actually works behind the scenes

• How objects are rotated in space

• How 3D coordinates become 2D pixels

And the best way to learn that?

👉 Build it yourself.

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🧊 Step 1: Representing a Cube in 3D

A cube is just 8 points in 3D space.

In my code, I defined them like this conceptually:

• Each vertex has (x, y, z)

• Values go from -25 to 25 to center the cube

So imagine something like:

• Front face → z = +25

• Back face → z = -25

This gives us a cube centered around the origin.

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🔗 Step 2: Connecting the Dots (Edges)

Points alone don’t make a cube — we need lines.

So I defined connections between vertices like:

• Top square

• Bottom square

• Vertical edges

This creates a wireframe cube.

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🔄 Step 3: Rotating the Vector

This is where things get interesting.

To rotate a point in 3D, we use rotation formulas.

For example, rotating around one axis:

• Mixes two coordinates

• Keeps one unchanged

In my implementation, I rotated points step by step:

1. Rotate in one plane

2. Then another

So each vertex gets transformed like:

👉 original → rotated → moved → projected

This is handled by a transformation pipeline in my code.

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📏 Step 4: Converting 3D → 2D (Projection)

This is the most important part.

We can’t display 3D directly on a screen — we need to project it into 2D.

The magical formula:

• x' = x / z

• y' = y / z

This creates a perspective effect:

• Far objects look smaller

• Near objects look bigger

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🖥️ Step 5: Mapping to Screen Coordinates

After projection, values are between -1 and 1.

But the canvas needs pixel values.

So I mapped them like:

• Center → middle of canvas

• Scale → fit entire cube

This step converts math into actual pixels.

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🎨 Step 6: Drawing on Canvas

Now comes the fun part — rendering.

I built small helper functions:

• Draw a point

• Draw a line

• Fill a face

Then for each frame:

1. Transform all vertices

2. Project them

3. Draw them

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🟦 Step 7: Adding Colors (Faces)

A cube has 6 faces.

To make it look solid:

• I grouped vertices into faces

• Assigned each face a color

• Drew them in order

But there’s a catch 👇

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🧠 Step 8: Depth Sorting (Painter’s Algorithm)

If you draw faces randomly, they overlap incorrectly.

So I:

1. Calculated average depth (z) of each face

2. Sorted them from far → near

3. Drew them in that order

This creates a proper 3D illusion.

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🖱️ Step 9: Interaction (Drag to Rotate)

I added mouse + touch support:

• Drag left/right → rotate horizontally

• Drag up/down → rotate vertically

When not dragging:

• Cube slowly auto-rotates

This makes it feel alive.

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⚙️ Step 10: Customization Panel

One of the coolest parts I built:

👉 A UI to edit the cube itself

You can:

• Add/remove vertices

• Change coordinates

• Define edges manually

This turns the cube into a mini 3D editor.

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🔁 Step 11: The Render Loop

Everything runs inside a loop:

• Clear canvas

• Transform vertices

• Draw cube

• Repeat

This creates smooth animation (~60 FPS).

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💡 What I Learned

This project taught me:

• 3D is just math (vectors + transformations)

• Perspective is just division

• Rendering = drawing in the right order

• Libraries like Three.js hide a LOT of complexity

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🚀 Final Thoughts

Reinventing the wheel is often discouraged…

But sometimes, it’s the best way to truly understand things.

If you’re learning graphics, I highly recommend trying this.

Not for production.

But for clarity.