# Assignment 4: Investigating Importance Sampling

## Due: Tuesday May 16th, 11:59PM

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## Description

Rendering requires the computation of many different types of integrals. In the last assignment we numerically integrated over the back element of the realistic camera lens to compute the irradiance indicent on each pixel of the camera's film. As you are now well aware after the camera assignment, the variance of a monte carlo estimator for an integral manifests itself as noise in a rendered image. Thus, when integrating a function, it is important to choose samples from the domain of integration such that variance in the integral estimate is minimized. **Importance sampling** is a variance reduction technique that draws samples using a distribution that is proportional to the value of the function over the domain. In this assignment you will explore various approaches for sampling irradiance on scene objects due to an infinite area light source (environment light) and explain when certain approaches are preferrable to others.

We are happy to inform you that this assignment is designed to be significantly shorter than Homework 2 and 3.

## Step 1: Background Reading

Read chapters 13 (especially 13.5), 14 (especially 14.3.4) and 15 (especially 15.6) in the pbrt book. This assignment will require a solid understanding of importance sampling, so please read the these chapters carefully.