# 2D to 3D

#### Spaces and Transformations

![1646763917.png](img/1646763917.png)

- **Model Space**
    - Model space is relative to an individual model which is made up of vertices.
    - A cube has one vertex at each corner which are positioned relative to the centre of the cube
    - In model space there is no information about where a model is relative to anything in the world, there is only information about the relative positions of the vertices which make up the model
- **World Space**
    - World space is relative to a larger coordinate system
    - Vertices are positioned in model space and then all moved to the appropriate position in the world
- **View Space**
    - View space has all vertices from the perspective of the viewer
    - Vertices aren’t defined in view space. The world is moved relative to the viewer position
- **Clip space**
    - Clip space is an intermediate space after vertices have been projected to what is going to be drawn to the screen
- **Normalised Device Coordinate space**
    - NDC space is almost identical to the pixels on the screen.
    - Vertices inside the NDC space will be rendered at those positions
- **Screen space**
    - Screen space maps directly to the pixels on the screen
    - From this point, vertices can be used to construct triangles, which are rasterised and the appropriate pixels are coloured

- Model Transform
    - The transformation of vertices from model space to world space
- View transform
    - The transform of vertices from world space to view space
- Projection transform
    - The projection of vertices from view space to clip space
- Perspective Division
    - The division of each component by its homogeneous $w$ component
- Viewport Transformation
    - The mapping of normalised coordinates to vertices at screen pixel coordinates

#### View Space with Frustum

![1646764884.png](img/1646764884.png)

Everything outside the frustum isn’t rendered