Introduction to Spherical Harmonics for Graphics Programmers

2 days ago

Spherical harmonics approximate functions on a sphere using polynomial coefficients, useful for modeling lighting in computer graphics.
They form an orthonormal basis, allowing any continuous function on a sphere to be expressed as an infinite weighted sum.
SH functions are organized by degree (ℓ) and order (m), where lower degrees capture low-frequency details and higher degrees capture high-frequency details.
Practical applications include projecting cubemaps to SH coefficients for lighting approximation and using SH for irradiance in lightmaps to react to normal maps.
Artifacts like ringing (negative values) can occur when projecting discontinuous functions; deringing via windowing functions (e.g., sinc) helps mitigate this.
Convolution with SH simplifies irradiance calculations, enabling efficient storage and evaluation for diffuse lighting.

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