2. Programming 3D Applications CE00056-1 Displaying Computer Graphics Week 3 Lecture 5 Bob Hobbs Faculty of Computing, Engineering and Technology Staffordshire University

3. Viewing Pipeline 3D Modelling Coordinates Projection transformation Viewport transformation General 3D viewing pipeline Viewing transformation Viewing Coordinates Projection Coordinates 3D World Coordinates Modelling transformation 2D Device Coordinates

4. Viewing Pipeline Modelling transformation Set position, orientation, and size of each object in scene / world use appropriate equations / matrix to: translate each object to its position in scene rotate each object according to relative orientations of scene objects scale each object according to relative proportions of scene objects

5. Viewing Pipeline Viewing transformation Compute position, and orientation of each object with reference to viewer (viewing coordinate system): translate origin of viewing coordinate system to origin of world coordinate system apply up to 3 rotations to align x v, y v, z v axes with x w, y w, z w axes respectively rotate around x w axis to bring z v into ‘x w z w ‘ plane rotate around y w axis to align z v axis with z w axis rotate around z w axis to align y v axis with y w axis

6. Viewing Pipeline Projection transformation Viewing coordinates are mapped onto 2D view window using projection 2D coordinates given by intersection between view window and ‘rays’ from object towards view plane Main types of projections: parallel projection perspective projection

7. yvyv zvzv xvxv Viewing Pipeline Projection transformation View plane View window 3D object in viewing coordinates Centre of projection Perspective projection

8. Viewing Pipeline Projection transformation (perspective projection) Transformation formulas take vertical cross-section through centre of projection, and perpendicular to view plane yvyv zvzv View plane Vertex Centre of projection ypyp d Similar triangles formula:

9. Viewing Pipeline Clipping yvyv zvzv xvxv Centre of projection View window Back plane Front plane View volume for perspective projection Frustum view volume

10. Viewing Pipeline Clipping algorithm z back clipping plane Pass Clipping Fail Scene segment Invisible Fail x clipping plane Pass y clipping plane Pass Visible z front clipping plane

11. Graphics processes generally execute sequentially Typical ‘pipeline’ model There are two ‘graphics’ pipelines The Geometry or 3D pipeline The Imaging or 2D pipeline

12. Viewing Pipeline 3D Modelling Coordinates Projection transformation Viewport transformation General 3D viewing pipeline Viewing transformation Viewing Coordinates Projection Coordinates 3D World Coordinates Modelling transformation 2D Device Coordinates

13. Geometry pipeline Animation/Interaction : time Modeling: shapes Shading: reflection and lighting Transformation: viewing Hidden Surface Elimination Imaging Pipeline

14. Imaging pipeline Rasterization and Sampling Texture Mapping Image Composition Intensity and Colour Quantization Framebuffer/Display Geometry Pipeline Computer Monitor

15. Example

16. Wireframe model – Orthographic views

17. Perspective View

18. Depth Cue

19. Hidden Line Removal – add colour

20. Constant Shading - Ambient

21. Faceted Shading - Flat

22. Gouraud shading, no specular highlights

23. Specular highlights added

24. Phong shading

25. Texture Mapping

27. Reflections, shadows & Bump mapping

28. CRT (the Monitor) Persistence

29. Colour

30. Colour Triads

31. Dot Pitch

32. Interlacing

33. Display Controller

34. True Colour / Pseudo Colour

35. Colour interpretation