notes/docs/lectures/graphics/05_2d_to_3d.md

2D to 3D

Spaces and Transformations

• 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 top 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 now 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

Everything outside the frustum isn’t rendered