1. UW EXTENSION CERTIFICATE PROGRAM IN GAME DEVELOPMENT 2 ND QUARTER: ADVANCED GRAPHICS The Geometry Pipeline

2. Goals 1. Understand geometry transformations 2. Understand the various spaces involved

3. Basic geometry pipeline spaces  Frames of reference, actually  Model (local) space  Different for each object rendered  World matrix (linear transformation)  World space  View matrix  View (camera) space  X, Y aligned to horizontal-vertical  Z goes into the screen

4. The projection matrix  View (camera) space  Projection matrix  Clip space – reach it by applying projection matrix  X, Y, Z, W – the W defined in terms of Z  -W <= X, Y <= W  0 <= Z <= W (used for the z-buffer)  Clip space makes some math much simpler  The screen is a square  The frustum (limits) is all 90 degree angles

5. Clipping  Clipping of some kind is necessary  Avoids math imprecision around the camera plane  Camera plane is when clip-W is very small  Clip space is linear transformation from view space  Clipping can be done using simple arithmetic  Typically, clipping around some frustum  Either the view frustum or a wider one (the guard band)  When using the guard band, the rasterizer also clips  A common strategy is to generate more triangles

6. Projection space  Clip space  X, Y and Z are divided by W  Not a linear transformation!  Projection space  -1 <= X, Y <= 1  0 <= Z <= 1  1/W also kept around for perspective correction  Anything linear in world/view/clip space, when divided by the W becomes linear in projection/screen space

7. Screen space  Projection space  Adjust X, Y for the screen dimensions  Screen space  0 <= X, Y <= Width, Height

8. Implementation notes  World, view and projection matrices normally combined into one for performance  Other combinations also useful, in various situations  Lighting performed in some uniform space  Model space if possible  View space if necessary If the model is non-uniformly modified  Normals transformed by the inverse-transpose of the 3x3 matrix (and don’t apply the translation!)