1. Computer Graphics Viewing

2. Tobias IsenbergComputer Graphics – IIa 2007/2008 Overview rendering pipeline: process from model to final image viewing: –model-view transformation: 1 st stage, arranging model w.r.t. camera requires camera reference (coordinate system) –projection: 2 nd transformation stage, coordinate transformation to 2D requires complete camera model many different projections possible

3. ViewingTobias IsenbergComputer Graphics – IIa 2007/2008 Rendering Pipeline modelling of geometry transformation into world coordinates placement of cameras and light sources backface culling projection clipping w.r.t. view volume hidden surface removale (hsr) rasterization illumination and shading usually in one step transformation into camera coordinates

4. ViewingTobias IsenbergComputer Graphics – IIa 2007/2008 Model-View Transformation input / foundations: –object definitions (including lights etc.) –including object positions & orientations –transformations in 3D –camera position & parameters problem: –how to arrange objects in space?

5. ViewingTobias Isenberg 1 st idea: transformation of all objects into a (the) world coordinate system not flexible: complicated animation Model-View Transformation Computer Graphics – IIa 2007/2008 x y (½√2, ½√2) z x y z (5+½√2, 1+½√2) (-2, 1)

6. ViewingTobias Isenberg Model-View Transformation 2 nd idea: transformation directly into camera coordinates: object-dependent each object has its own model-view matrix hierarchies possible, objects reusable Computer Graphics – IIa 2007/2008 x y (½√2, ½√2) z x y z (7+½√2, ½√2) (0, 0)

7. ViewingTobias Isenberg Model-View Transformation model-view transformation steps: 1.translate object origin to camera location 2.rotate to align coordinate axes 3.possibly also scaling this process is used in OpenGL: no explicit world coordinates! object & camera locations and orientations may be specified in a world coordinate system (e.g., in modeling systems) Computer Graphics – IIa 2007/2008

8. ViewingTobias IsenbergComputer Graphics – IIa 2007/2008 Sources: Computer Graphics I lecture by Berhard Preim, Department of Simulation and Graphics, Otto-von-Guericke University of Magdeburg, Germany CPSC 407 and CPSC 453 lectures by Brian Wyvill, Department of Computer Science, University of Calgary, Canada