1. Transformations in Ray Tracing MIT EECS 6.837, Durand and Cutler

2. Linear Algebra Review Session Tonight! 7:30 –9 PM MIT EECS 6.837, Durand and Cutler

3. Last Time:

4. Today Motivations Transformations in Modeling Adding Transformations to our Ray Tracer Constructive Solid Geometry (CSG) Assignment 2 MIT EECS 6.837, Durand and Cutler

5. Modeling Create / acquire objects Placing objects Placing lights Describe materials Choose camera position and camera parameters Specify animation.... MIT EECS 6.837, Durand and Cutler

6. Transformations in Modeling

7. Today Motivations Transformations in Modeling –Scene description –Class Hierarchy –Transformations in the Hierarchy Adding Transformations to our Ray Tracer Constructive Solid Geometry (CSG) Assignment 2 MIT EECS 6.837, Durand and Cutler

8. Scene Description

9. Simple Scene Description File

10. Class Hierarchy

11. Why is a Group an Object3D?

12. Simple Example with Groups

13. Adding Materials

15. Adding Transformations

16. Class Hierarchy with Transformations

17. Why is a Transform an Object3D?

18. Simple Example with Transforms

19. Nested Transforms

20. Questions? MIT EECS 6.837, Durand and Cutler

21. Today Motivations Transformations in Modeling Adding Transformations to our Ray Tracer – Transforming the Ray –Handling the depth, t –Transforming the Normal Constructive Solid Geometry (CSG) Assignment 2 MIT EECS 6.837, Durand and Cutler

22. Incorporating Transforms 1.Make each primitive handle any applied transformations Sphere { center1 0.5 0 radius 2 } 2.Transform the Rays Transform { Translate { 1 0.5 0 } Scale { 2 2 2 } Sphere { center 0 0 0 radius 1 } }

23. Primitives handle Transforms

24. Transform the Ray

25. Transform Ray

26. Transforming Points & Directions

27. What to do aboutthe depth, t If Mincludes scaling, direction OS will NOT be normalized 1.Normalize the direction 2.Don't normalize the direction MIT EECS 6.837, Durand and Cutler

28. 1. Normalize direction

29. 2. Don't normalize direction

30. Questions? MIT EECS 6.837, Durand and Cutler

31. New component of the Hit class

32. Why is the Normal important?

33. Visualization of Surface Normal

34. How do we transform normals?

35. Transform the Normal like the Ray?

37. What class of transforms?

38. Transformation for shear and scale

39. More Normal Visualizations

40. So how do we do it right?

41. Transform tangent vector v

42. Comment

43. Questions? MIT EECS 6.837, Durand and Cutler

44. Today Motivations Transformations in Modeling Adding Transformations to our Ray Tracer Constructive Solid Geometry (CSG) Assignment 2 MIT EECS 6.837, Durand and Cutler

45. Constructive Solid Geometry (CSG)

46. How can we implement CSG?

47. Collect all the intersections

48. Implementing CSG

49. "Fredo'sFirst CSG RaytracedImage"

50. Questions? MIT EECS 6.837, Durand and Cutler

51. Today Motivations Transformations in Modeling Adding Transformations to our Ray Tracer Constructive Solid Geometry (CSG) Assignment 2 –Due Wednesday Sept 24th, 11:59pm MIT EECS 6.837, Durand and Cutler

53. Adding Perspective Camera

54. Triangle Meshes (.obj)

55. Acquiring Geometry 3D Scanning (Images removed due to copyright considerations.) MIT EECS 6.837, Durand and Cutler

56. Next Week: Ray Tracing Surface reflectance MIT EECS 6.837, Durand and Cutler