:PROPERTIES: :ID: 49e87a3f-2792-4d1c-adc4-ae354bd8b48d :mtime: 20240309072540 :ctime: 20240309072526 :END: #+title: rasterization #+filetags: :public:graphics:project: * Rasterization ** Rasteriation Algorithm #+BEGIN_SRC python FOR every triangle in the scene: transform its vertices using MVP matrices IF the triangle is within a view frustum: clip the triangle to the screen border FOR each fragment in the triangle: interpolate fragment position and attributes between vertices compute fragment colour IF the fragment is closer to the camera than any pixel drawn so far: update the screen pixel with the fragment colour END IF; END FOR; END IF; END FOR; #+END_SRC ** Interpolating inside Triangles (Barycentric Coordinates) Homogenous barycentric coordinates are used to interpolate colours, normals, texture coordinates and other attributes inside the triangle *** Cartesian to Barycentric Coordinates \[\begin{bmatrix} \lambda_{1} \\ lambda_{2} \end{bmatrix} = T^{-1}(\vec{r} - \vec{r}_{3})\] where \[\mathbf{T} = (\vec{r}_{1} - \vec{r}_{3}|\vec{r}_{2} - \vec{r}_{3})\] You can also convert cartesian to barycentric using the implicit line equation \[\alpha = \frac{f_{cb}(\vec{r})}{f_{cb}(\vec{r}_{a})}\] \[\beta = \frac{f_{ac}(\vec{r})}{f_{ac}(\vec{r}_{b})}\] \[f_{ab}(\vec{r}) = (\vec{r}_{a} - \vec{r}_{b}) \cdot \vec{r} + det(\vec{r}_{a}, \vec{r}_{b}) \]