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MCPT solves the Rendering Equation using Monte Carlo Integration. The space over which is integrated is the space of all photon paths. Relevant paths are only those which carry energy: Starting from the eye and ending in an emissive surface:


The radiance at the end of this path is

(for every photon bounce, there is one term )

MCPT():
    for each pixel
       
        for
           
       

:
   
    if
        (emit)
        return
    else
        (reflect)
        generate random direction over
        return

If we choose

the return statement in the reflect case simplifies to just