# PBR读书笔记四：Sampling Theory

## 傅立叶分析

$F(\omega)=\int^\infty_{-\infty}f(x)\exp{(-\text{i}2\pi \omega x)}\text{d}x$

$\text{F}\{f(x)g(x)\} = F(\omega)\circledast G(\omega)$

## 反走样

### 预滤波

$f(x)\circledast \text{sinc}(2\omega_s x)$

## 图像重建

radius是所有滤波器共有的属性，所有的滤波器也都继承自基类：

### Gaussian Filter

pbrt中对其评价为：

The Gaussian does tend to cause slight blurring of the final image compared to some of the other filters, but this blurring can actually help mask any remaining aliasing in the image.

$f(x) = \exp{(-\alpha x^2)} - \exp{(-\alpha r^2)}$

Carbene Hu

2022-01-11

2022-05-12