1. BPC: Art and Computation – Summer 2007 Computer Graphics Principles Erik Brisson ebrisson@bu.edu

2. BPC: Art and Computation – Summer 20072 Computer Graphics Basic paradigm Modeling Transformations Lighting and shading Scan conversion Texture mapping Alternative rendering methods

3. BPC: Art and Computation – Summer 20073 C.G. paradigm with light

4. BPC: Art and Computation – Summer 20074 Model geometry – two cuboids

5. BPC: Art and Computation – Summer 20075 Model geometry - approximation

6. BPC: Art and Computation – Summer 20076 Math representation Vertices P1 = (4.0, 2.0) P1 = (4.0, 2.0) P2 = (2.0, 2.0) P2 = (2.0, 2.0) P3 = (2.0, 4.0) P3 = (2.0, 4.0) P4 = (4.0, 4.0) P4 = (4.0, 4.0) P5 = (6.0, 3.0) P5 = (6.0, 3.0) P6 = (4.0, 1.0) P6 = (4.0, 1.0) P7 = (7.0, 1.0) P7 = (7.0, 1.0) P8 = (8.0, 2.0) P8 = (8.0, 2.0)Faces: F1 = [P1, P2, P3, P4] F1 = [P1, P2, P3, P4] F2 = [P1, P4, P5] F2 = [P1, P4, P5] F3 = [P7, P6, P1, P5, P8] F3 = [P7, P6, P1, P5, P8]

7. BPC: Art and Computation – Summer 20077 Computer representation Vertices 1: 4.0, 2.0 1: 4.0, 2.0 2: 2.0, 2.0 2: 2.0, 2.0 3: 2.0, 4.0 3: 2.0, 4.0 4: 4.0, 4.0 4: 4.0, 4.0 5: 6.0, 3.0 5: 6.0, 3.0 6: 4.0, 1.0 6: 4.0, 1.0 7: 7.0, 1.0 7: 7.0, 1.0 8: 8.0, 2.0 8: 8.0, 2.0Faces: 1: 1, 2, 3, 4 1: 1, 2, 3, 4 2: 1, 4, 5 2: 1, 4, 5 3: 7, 6, 1, 5, 8 3: 7, 6, 1, 5, 8

8. BPC: Art and Computation – Summer 20078 Rigid body transformations

9. BPC: Art and Computation – Summer 20079 Composition of transformations Rotate first Then translate Translate first Then rotate

10. BPC: Art and Computation – Summer 200710 Other transformations - scaling

11. BPC: Art and Computation – Summer 200711 Objects in 3D Vertices P1 = (0.0, 0.0, 2.7) P1 = (0.0, 0.0, 2.7) P2 = (1.0, 0.0, 0.5) P2 = (1.0, 0.0, 0.5) P3 = (0.998, 0.156, 0.5) P3 = (0.998, 0.156, 0.5) P4 = (0.951, 0.309, 0.5) P4 = (0.951, 0.309, 0.5) P5 = (0.891, 0.454, 0.5) P5 = (0.891, 0.454, 0.5) …Faces: F1 = [P1, P2, P3] F1 = [P1, P2, P3] F2 = [P1, P3, P4] F2 = [P1, P3, P4] F3 = [P1, P4, P5] F3 = [P1, P4, P5] …

12. BPC: Art and Computation – Summer 200712 Transformations in 3D Sphere translated by translated by (-3.0, 2.0, -4.5) (-3.0, 2.0, -4.5) Blue cube translated by translated by (2.0, 0.0, -4.0) (2.0, 0.0, -4.0) rotated 60 deg rotated 60 deg around y-axis around y-axis Purple cube translated by translated by (0.0, 0.0, 0.0) (0.0, 0.0, 0.0)

13. BPC: Art and Computation – Summer 200713 Rotations in 3D

14. BPC: Art and Computation – Summer 200714 C.G. paradigm with light

15. BPC: Art and Computation – Summer 200715 C.G. basic calculation

16. BPC: Art and Computation – Summer 200716 Lighting - vectors V_eye = P_eye - P V_light = P_light - P V_eye = (4, 1, 10) - (5, 2, 3) = (-1, -1, 7) V_light = (3, 7, 2) – (5, 2, 3) = (-2, 5, -1)

17. BPC: Art and Computation – Summer 200717 Unit shading vectors n = surface normal vector u_light = unit vector to light point u_eye = unit vector to view point

18. BPC: Art and Computation – Summer 200718 Shading at vertices, interpolation

19. BPC: Art and Computation – Summer 200719 Flat shading vs Gouraud shading

20. BPC: Art and Computation – Summer 200720 Shading ambient diffuse specular

21. BPC: Art and Computation – Summer 200721 Ray tracing

22. BPC: Art and Computation – Summer 200722 Scan-conversion of polygon

23. BPC: Art and Computation – Summer 200723 C.G. concept - texture map

24. BPC: Art and Computation – Summer 200724 Texture mapping + 

25. BPC: Art and Computation – Summer 200725 Resulting image

26. BPC: Art and Computation – Summer 200726 Result is a digital image

27. BPC: Art and Computation – Summer 200727 The quest for photorealism

28. BPC: Art and Computation – Summer 200728 Alternative rendering techniques

29. BPC: Art and Computation – Summer 200729 Alternative rendering techniques

30. BPC: Art and Computation – Summer 200730 3D object photography http://www.royalalbertamuseum.ca/vexhibit/virtcoll/ index.asp

31. BPC: Art and Computation – Summer 200731 Panoramic photography

32. BPC: Art and Computation – Summer 200732 Other techniques

33. BPC: Art and Computation – Summer 200733 Other techniques, laser scanning

34. BPC: Art and Computation – Summer 200734 Now we can model, transform, illuminate, and render doughnuts