1. MIT EECS 6.837, Durand and Cutler Transformations

2. Outline Assignment 0 Recap Intro to Transformations Classes of Transformations Representing Transformations Combining Transformations Change of Orthonormal Basis MIT EECS 6.837, Durand and Cutler

3. Cool Results from Assignment

4. Notes on Assignments Make sure you turn in a linux or windows executable (so we can test your program) Collaboration Policy –Share ideas, not code Tell us how much time you spent on each assignment MIT EECS 6.837, Durand and Cutler

5. Quick Review of Last Week Ray representation Generating rays from eyepoint/ camera –orthographic camera –perspective camera Find intersection point & surface normal Primitives: –spheres, planes, polygons, triangles, boxes MIT EECS 6.837, Durand and Cutler

6. Outline Assignment 0 Recap Intro to Transformations Classes of Transformations Representing Transformations Combining Transformations Change of Orthonormal Basis MIT EECS 6.837, Durand and Cutler

7. What is a Transformation? Maps points (x, y) in one coordinate system to points (x', y') in another coordinate system x' = ax+ by + c y' = dx+ ey + f For example, IFS:

8. Common Coordinate Systems

9. Simple Transformations Can be combined Are these operations invertible? Yes, except scale = 0 MIT EECS 6.837, Durand and Cutler

10. Transformations are used: Position objects in a scene (modeling) Change the shape of objects Create multiple copies of objects Projection for virtual cameras Animations MIT EECS 6.837, Durand and Cutler

11. Outline Assignment 0 Recap Intro to Transformations Classes of Transformations Rigid Body / Euclidean Transforms Similitudes/ Similarity Transforms Linear Affine Projective Representing Transformations Combining Transformations Change of Orthonormal Basis MIT EECS 6.837, Durand and Cutler

12. Rigid-Body / Euclidean Transforms

13. Similitudes/ Similarity Transforms

14. Linear Transformations

16. Affine Transformations

18. Perspective Projection

19. Outline Assignment 0 Recap Intro to Transformations Classes of Transformations Representing Transformations Combining Transformations Change of Orthonormal Basis MIT EECS 6.837, Durand and Cutler

20. How are Transforms Represented?

21. Homogeneous Coordinates

23. Homogeneous Visualization

29. Outline Assignment 0 Recap Intro to Transformations Classes of Transformations Representing Transformations Combining Transformations Change of Orthonormal Basis MIT EECS 6.837, Durand and Cutler

33. Outline Assignment 0 Recap Intro to Transformations Classes of Transformations Representing Transformations Combining Transformations Change of Orthonormal Basis MIT EECS 6.837, Durand and Cutler

35. Change of Orthonormal Basis

42. Next Time: Adding Transformations to the Ray Caster (Assignment 2) MIT EECS 6.837, Durand and Cutler