 Solution

At each primary hit $p$, send a shadow ray toward each point light. An especially clear parameterization isIf an opaque scene surface intersects this open segment, the source is hidden. The finite interval is essential: an object beyond the light must not cast a shadow at $p$. Exclude the launch surface with a small geometrically appropriate origin offset or positive minimum parameter, so floating-point arithmetic does not create a false self-intersection.

Introduce a visibility factor $V_j(p)$ equal to zero when blocked and one otherwise. The modified equation isA blocked light loses both its diffuse and specular contributions. The simple ambient approximation remains. Opaque point lights produce hard shadow boundaries. Use a consistent sidedness policy for occluders: an opaque closed solid blocks from either crossing side, so a two-sided blocker test is appropriate even when primary visibility uses back-face culling. An any-hit query can stop as soon as it finds one blocker before the light.