1. Part I: Basics of Computer Graphics Viewing Transformation and Coordinate Systems Chapter 2 2-1

2. Coordinate Systems Coordinate systems used when rendering geometry objects Object space World space Eye/Camera space Screen space Raster space Linear transformation Linear transformation Non-linear transformation Rasterization 2-2

3. Object Space The most natural coordinate system for the geometry object Local coordinate system. “Local “ to the object Also known as modeling coordinate system e.g. World Space The global (world) coordinate system that is shared by all objects in the modeled scene World coordinate system 2-3

4. Eye/Camera Space The coordinate system with the eye or the center of projection as its origin A space in which the viewing volume is established Facilitates clipping (removing out-of- view objects) Screen Space Transformation to screen space is a process that describes how light rays reach our eyes Screen space is defined to act within a closed volume called the viewing frustum 2-4

5. Screen Space Perspective projection is used to project 3D object to 2D Unlike scaling, translation, and rotation, perspective projection is non-linear. 2-5

6. Raster Space A discretization process Determining onto which pixel (discrete sample) the 3D point is projected Closely related to anti-aliasing as the rasterization is basically a sampling process 2-6