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Analytical Render · LTC

Replace many direct-light samples with a compact geometric integral. A linearly transformed cosine approximates the material lobe, turning a polygonal emitter into an integrable boundary; a material garage compares the result with Monte Carlo lighting.

A fitted lobe → a polygon integral
FitTransformIntegrate
Brochure →Open project ↗
  1. f

    Fit the lobe

    Approximate the directional material response with a transformed cosine.

  2. M

    Transform the light

    Move the emitter vertices into the fitted distribution's coordinates.

  3. ∫

    Integrate the edges

    Accumulate oriented contributions around the transformed spherical polygon.

  4. Δ

    Compare the image

    Inspect fitted-model error beside a sampled direct-light reference.

The polygon integral is deterministic; the material-lobe fit is where the approximation enters.

WASM diffuse-light study with a split integral/Monte Carlo view and emitter-geometry controls.
WASM diffuse-light study with a split integral/Monte Carlo view and emitter-geometry controls.
The working WebGPU material garage: fitted LTC and sampled direct lighting share the same material scene. The organic medium is a separate numerical effect.
The working WebGPU material garage: fitted LTC and sampled direct lighting share the same material scene. The organic medium is a separate numerical effect.