Brief

Implementation of Pixel Subsampling, Area Lighting and Importance Sampling.

Pixel Subsampling

$$\textbf{p}_{xy} = \textbf{t}_l + \left( \cfrac{x + \xi}{i_w} \right) \cdot (v_w \textbf{u}) + \left( \cfrac{y + \xi}{i_h} \right) (-v_h \textbf{v})$$

Importance Sampling

• Uniform Hemisphere Sampling

$$\langle L_o (\textbf{x}, \boldsymbol{\omega}_o) \rangle = \cfrac{2 \pi}{N} \sum_{i = 1}^N f(\textbf{x}, \boldsymbol{\omega}_o, \boldsymbol{\omega}_i) L_i(\textbf{x}, \boldsymbol{\omega}_i) \cos \theta$$

• Cosine Sampling

$$\langle L_o (\textbf{x}, \boldsymbol{\omega}_o) \rangle = \cfrac{\pi}{N} \sum_{i = 1}^N f(\textbf{x}, \boldsymbol{\omega}_o, \boldsymbol{\omega}_i) L_i(\textbf{x}, \boldsymbol{\omega}_i)$$

• Area Light Sampling

$$\langle L_o (\textbf{p}, \boldsymbol{\omega}_o) \rangle = \cfrac{\lvert A \rvert}{N} \sum_{i = 1}^N \cfrac{ f(\textbf{p}, \boldsymbol{\omega}_o, \boldsymbol{\omega}_i) L_i(\textbf{p}, \boldsymbol{\omega}_i) \cos \theta \cos \theta_l }{ r^2 }$$

Instructions

Steps to build

git clone --recursive https://github.com/ihsingh2/simple_renderer

mkdir build
cd build
cmake ..
make -j8

Steps to run

git clone https://github.com/ihsingh2/scenes

./build/render <scene_path> <out_path> <num_samples> <sampling_strategy>