4 ms·
Tristimulus values (X, Y, Z) are the dot product of the incoming spectral radiance (L) and the spectral sensitivity curves (x, y, z) of the three cone cell type
by meindnoch 3y ago
Tristimulus values (X, Y, Z) are the dot product of the incoming spectral radiance (L) and the spectral sensitivity curves (x, y, z) of the three cone cell types:
X = dot(L, x)
Y = dot(L, y)
Z = dot(L, z)
The spectrum of the light reflected from a surface (Lᵣ) is the pointwise product of the incoming spectral radiance (L) and the spectral reflectance curve of the surface (R):
Lᵣ = L * R
What RGB rendering does, is it replaces this equation (for x, y, z):
X = dot(Lᵣ, x) = dot(L * R, x) (eq I)
with this (for x, y, z):
X = dot(L, x) * dot(R, x) (eq II)
Which are not equal in the general case. On the other hand, they are equal up to a scaling factor if L is a constant function, since in that case:
dot(L * R, x) = C * dot(R, x) (from eq I)
dot(L, x) * dot(R, x) = D * dot(R, x) (from eq II)
where C and D are scaling factors that depend solely on L. The interpretation of this is that as long as the light source has a sufficiently flat spectrum (like sunlight!), the difference between spectral rendering and RGB rendering will be negligible.
- david-gpu 3y ago> as long as the light source has a sufficiently flat spectrum (like sunlight!), the difference between spectral rendering and RGB rendering will be negligible. (Great comment, nitpick ahead) ...to the human eye, that is. For industrial applications spectral rendering can still be useful.
- kevingadd 3y agoone caveat is that (AFAIK) if you are doing optical simulations in your rendering, like prisms or glass, the spectral rendering would produce more accurate caustics/reflections/refractions. But to be fair, most realtime rendering is not doing that. I could imagine it being important for stuff like CG films.
- kelsolaar 3y agoOP author here. This is correct, however, not everything is lit by sunlight, especially onset in the motion picture industry, where solid state lighting and its narrow band irradiance sources, e.g. led lights or led walls, are prevalent. Those emission sources induce a lot of unexpected appearance problems, e.g. metameric failures that RGB rendering cannot possibly solve. Our spectral renderer, i.e. Manuka [1], was specifically designed to address those issues whilst imaging with a virtual motion picture camera. One recent example I have in mind is The Batman (2022): There are sequences/shots lit with high-pressure sodium lights (HPS), those have a flat spectrum with spikes between 500 and 600nm, the appearance of objects lit under them is very specific and can only be accurately reproduced with a spectral renderer such as Manuka, Mitsuba [2] or Art [3]. - [1] https://www.wetafx.co.nz/research-and-tech/technology/manuka/ https://www.wetafx.co.nz/research-and-tech/technology/manuka... - [2] https://www.mitsuba-renderer.org/ https://www.mitsuba-renderer.org/ - [3] https://cgg.mff.cuni.cz/ART/about/ https://cgg.mff.cuni.cz/ART/about/