Thermal Radiation — View Factors, Radiosity & Monte Carlo

How do view factors work and why are they hard to compute for complex geometry?

View factor F_ij is the fraction of radiation leaving surface i that directly hits surface j. It satisfies reciprocity (Ai*Fij = Aj*Fji) and summation to 1. For complex geometry with occlusions, view factors require ray-tracing or contour integration — computationally intensive when many surfaces are present.

What is the radiosity method and when is it more efficient than Monte Carlo?

Radiosity assumes all surfaces are diffuse (Lambertian) emitters and reflectors, formulating a linear system where each surface's radiosity equals emission plus reflected radiation from all others weighted by view factors. Efficient for gray diffuse surface-to-surface radiation. Monte Carlo handles spectral and specular effects better but is statistically noisy.