Radiance Caching
Radiance Caching Radiance Caching
Practical Global Illumination With Irradiance Caching (SIGRAPH 2008 Class) J. Křivánek Course #16: Practical global illumination with irradiance caching - Caching on glossy surfaces Incoming Radiance Representation • Spherical harmonics • Basis functions on the sphere • Intro to Spherical harmonics [Green 2003] For various reasons that will become clearer later, we use spherical harmonics to represent the incoming radiance at a point. Spherical harmonics are basis functions defined on the unit sphere. August 2008
Practical Global Illumination With Irradiance Caching (SIGRAPH 2008 Class) J. Křivánek Course #16: Practical global illumination with irradiance caching - Caching on glossy surfaces Incoming Radiance Representation • Linear combination of basis functions L i (ω) = −1 λ × λ × × 0 λ −2 2 2 × 0 λ 0 + 0 λ × × 1 λ × + + λ + −1 1 1 + + + × 1 2 − n 1 m= l ∑∑ m m L ( ω) = λ H ( ω) i l= 0 m= −l l l λ × 2 λ Incoming radiance, as well as any other function defined on the hemisphere, can be represented as a linear combination of the basis functions. The coefficients in this linear combination make up the representation of our function. For spherical harmonics, the coefficients are indexed by two indices, l (lower index) and m (upper index). The l-index runs from 0 to n-1, where n is the order of the spherical harmonics representation. The higher the order, the better (more accurate) representation. Spherical harmonics with the same l-index form a band (a row on the slide above). Within one band, the m index goes from –l to +l. So there is one harmonic in the first band, three harmonics in the second band, five in the third band etc. There are n2 coefficients in total for an order-n representation. The double sum in the formula on the slide simply stands for summing over all harmonics up to order n. It could also be expressed as a single sum for i from 0 to n2-1, with i given by : i = l(l+1) + m. To summarize, an order-n representation of a function consists of n2 coefficients, which is what we to store in the cache. (Actually, we store one coefficient vector for each color component, R, G, and B). Typically, we use order up to 10 in radiance caching, corresponding to 100 coefficients. 2 1 + 2 August 2008
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Practical Global Illumination With Irradiance <strong>Caching</strong><br />
(SIGRAPH 2008 Class)<br />
J. Křivánek<br />
Course #16: Practical global illumination with irradiance caching - <strong>Caching</strong> on glossy surfaces<br />
Incoming <strong>Radiance</strong> Representation<br />
• Spherical<br />
harmonics<br />
• Basis functions<br />
on the sphere<br />
• Intro to Spherical harmonics [Green 2003]<br />
For various reasons that will become clearer later, we use spherical harmonics to<br />
represent the incoming radiance at a point. Spherical harmonics are basis functions<br />
defined on the unit sphere.<br />
August 2008
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