Hacker News by YouPan

Loading Stories...

meindnoch

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.

Loading Stories...

The Apparent Simplicity of RGB Rendering