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.