The rendering equation

Full formulation

  • - position in space
  • - outgoing direction of light (towards the eye)
  • - incoming direction of light (towards the light)
  • - surface normal vector at
  • - hemisphere of unit directions oriented around
  • - light leaving in direction
  • - light emitted at in direction
  • - proportion of light reflected from to (BRDF)
  • - light incoming at from direction
  • - Cosine term (N dot L)

Simplified formulation

  • - Outgoing light from the given point
  • - Emitted light from the given point
  • - The hemisphere of directions oriented around the normal
  • - Ratio of incoming and outgoing light (BRDF)
  • - Light incoming to the given point
  • - Cosine term (N dot L) - more on this later

Why do we need monte carlo?

Can we calculate the rendering equation analytically? No, because the incoming light from a given direction depends on the scene we are rendering! There exists no general solution to the rendering equation, so what can we do - we use Monte carlo methods!

#light-transport #global-illumination