Shader Story

Lighting Models : Banded

Banded lighting (also known as cel lighting) quantizes smooth lighting into discrete brightness bands. Instead of a continuous gradient from light to dark, you are able to get the distinct “steps”. Its a common technique in e.g. comic rendering.

It’s one of the simplest yet most effective ways to give 3D objects a hand-painted, non-photorealistic feel.

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Visual demo

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// Pseudo-code (Complete implementation, with detailed comments, is available in the related Patreon post)
// Link: https://www.patreon.com/posts/shader-story-141647294

// Regular Lambertian diffuse term
float NdotL = max(0.0, dot(normal, lightDir));

// Optional offset for better visual balance
float additive = numSteps * (useHalfStep ? 1.0 : 0.5);

// Quantize smooth lighting into discrete bands
float banded = floor((NdotL stepSize + additive) / numSteps) (numSteps / stepSize);
banded = saturate(banded);

// Combine with diffuse term and light color
return banded * diffuseIntensity * lightColor;

Complete implementation, with detailed comments, is available on Patreon.

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Basic idea

Banded lighting takes smooth shading (like Lambert) and breaks it into a few flat tones. Commonly applied technique, just like in cartoon or cel-shaded art.

It starts with regular lighting:

• Calculate how much the surface faces the light using the dot product (N · L). This gives a smooth gradient from bright to dark.

Then, gradient should be turned into bands:

• Instead of keeping it smooth, the brightness is "quantized" - rounding it down into a few fixed levels.

Control the smoothness:

• TDedicated properties define how many bands appear and how wide each one is. More steps = smoother look. Fewer steps = bold, stylized shading.

(Optionally) Bands offset applied:

• The half-step factor shifts the light bands slightly, helping to center them and avoid harsh transitions.

Equation

L_banded = floor((max(0, N · L) × s + a) / n) × (n / s)

Where:

• N · L - Lambertian diffuse
• s - lighting step size (smoothness)
• a - additive offset (half-step factor toggle)
• n - number of light bands

This quantized diffuse factor replaces the smooth falloff used in traditional Lambert or Blinn-Phong lighting.

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🔗 Related Functions

Max • Floor • Saturate

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