= Solution
<Path tracing> estimates the <rendering equation> by a <Monte Carlo method>. Launch camera <rays>; at each surface hit sample an outgoing continuation direction according to a chosen <probability density function>, trace to the next hit, and continue through successive reflections. Accumulate emitted light or environment light with the product of scattering, cosine and inverse-density factors along the path. A bounce sampled with density $p(\omega)$ updates the path weight by
$$
\boxed{\beta\leftarrow\beta\,\frac{f_r(\omega,\omega_o)|\hat N\cdot\omega|}{p(\omega)}.}
$$
Average many independently sampled paths per <pixel>. Multiple bounces account for indirect illumination, including colour bleeding between surfaces, instead of approximating all of it by one ambient constant. Termination can use <Russian roulette (Monte Carlo)>: continue with probability $q>0$ and divide surviving weights by $q$, preserving the expected contribution. A fixed bounce cutoff is simpler but truncates transport.
The elementary strategy that obtains illumination only when a randomly continued path \i[hits an emitter] fails for ideal point lights. From a surface <point>, an ideal point source occupies zero <solid angle>; sampling a direction from an ordinary continuous <probability density function> hits that one direction with probability zero. Thus this strategy almost surely never discovers the light, regardless of the number of samples. An area emitter occupies nonzero <solid angle> and can be hit.
The qualification matters: practical <path tracing> can use point lights by explicitly sampling a source and connecting the current surface to it with a <shadow ray>, a technique called <next-event estimation>. For a point source the connection direction is known exactly, rather than discovered by a random hemisphere hit. Thus the restriction applies to naive emitter-hit <path tracing>, not to all <path tracing> algorithms.<Physically Based Rendering: From Theory to Implementation (4th edition) by Matt Pharr and others>[§12.2: point lights have delta-position emission and deterministic incident directions; §13.4: direct-light sampling is combined with scattering-direction sampling]{ref}
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