1. Imaging

2. Modeling and Imaging Reality model Picture modeling Imaging (vizualisation)

3. Projection Mapping Φ: R n → R k n>k In case of 3D computer graphics Φ: R 3 → R 2 Projection ray –The set of all pictures with the same image –Projection ray is usually a line –The image is in the intersection of the projection ray and the projection plane.

4. Parallel projection Intersection of projection rays (projection center) is in the infinity Projection rays are parallel Their direction is defined by two angels (azimuth,zenith)

5. Axonometry Projection plane intersects coordinate axes dy dx dz

6. Dimetry Projection triangle is isiscelles

7. Izometry Projection triangle is equilateral (dx=dy=dz) Often also azimuth=zenith=45 o

8. Perspective Projection center is a point

9. 1-vanishing point perpective

10. 2-vanishing point perspective

11. 3-vanishing point perspective

12. Wireframe „model“

13. Solving of edges visibility

15. Which faces are visible? The normal leads TO the observer → the face can (but must not) be visible The normal leads from the observer → the face is not visible

16. Painter’s algorithm Display the potentionaly visible faces from the back to the front

17. Painter’s algorithm The face is not visible

18. Painter’s algorithm The face can be visible

19. Painter’s algorithm The face is not visible

20. Painter’s algorithm The face can be visible

21. Painter’s algorithm The face is not visible

22. Painter’s algorithm The face can be visible

23. Painter’s algorithm The face is not visible

24. Painter’s algorithm The face is not visible

25. Painter’s algorithm The face can be visible

26. Painter’s algorithm The face can be visible

27. Counter example of painter’s algorithm

28. Simple imaging of all points of the solid

29. Rendering Light source observer Projection plane Angle α

30. Rendering

31. Light source types Point Point with directed lights (commonly cone shape) Area (commonly approximated by a matrix of points) Ambient

32. Ray Tracing Light sources Projection plane Mirror reflection Diffuse reflection The ray goes through the solid

33. Types of reflection on the solid The ray is absorbed by a solid (solid color) The ray is reflected –Mirror reflection (shine) –Diffuse reflection –Combinated reflection The ray is going through the solid tělesem –Directly (transparent solid) –With a shift –With a diffusion (translucent solid)

34. Ray Tracing

35. Radiosity E i = z i + o i * ∑v ij e j