~/rendering/04$ lesson --open "why-random-rays"

lesson.md

estimator.glsl ●

notes

tutor

rendering / 04 · 74% · 12-day streak

CH 2 · THE ESTIMATOR

HDchapter 2 of 6 · the estimator

vec3 estimate(Ray r, int N) {
vec3 sum = vec3(0.0);
for (int i = 0; i < N; i++) {
vec3 dir = sampleHemisphere(rng());
sum += trace(r, dir) * cosθ / pdf;
}
return sum / float(N); // unbiased
}
// noise ∝ 1/√N ← the price

Why random rays?

lesson 04 · 12 min · renderingThe rendering equation is an integral nobody can solve in closed form, so the estimator guesses: fire a ray in a random direction, weight what comes back, and average. Every guess is wrong; the average is not. What you buy with more samples is not a better answer but a quieter one.

$ ask tutor "why does variance drop?"
tutor Each sample is an unbiased guess. Averaging
N of them shrinks the spread by √N — so the
noise, not the answer, is what you buy down.
reading variance.md · 2 refs
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