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Composite Transformations and Forward Kinematics

Composite Transformations and Forward Kinematics. Jinxiang Chai. Outline. 2D Coordinate transformation Composite transformation & Forward kinematics 3D transformation. Coordinate Transform: 3D Geometry Pipeline. Rotate and translate the camera. Object space. World space. View space.

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Composite Transformations and Forward Kinematics

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  1. Composite Transformations and Forward Kinematics Jinxiang Chai

  2. Outline 2D Coordinate transformation Composite transformation & Forward kinematics 3D transformation

  3. Coordinate Transform: 3D Geometry Pipeline Rotate and translate the camera Object space World space View space Focal length Aspect ratio & resolution Normalized project space Image space 2

  4. Coordinate Transformation: 3D Modeling/Design Coordinate transformation from one reference frame to another

  5. Coordinate Transformation: Animation/Robotics Click here How to model 2D movement of animated characters or robots?

  6. Coordinate Transformation Coordinate transformation from one reference frame to another

  7. Coordinate Transformation Coordinate transformation from one reference frame to another

  8. Coordinate Transformation Coordinate transformation from one reference frame to another 7

  9. Coordinate Transformation ? Coordinate transformation from one reference frame to another 8

  10. Review – Vector Operations Dot Product

  11. Review – Vector Operations Dot Product: measuring similarity between two vectors

  12. Review – Vector Operations Dot Product: measuring similarity between two vectors

  13. Review – Vector Operations Unit vector: Dot Product: measuring similarity between two vectors

  14. Review – Vector Operations Dot Product: measuring similarity between two vectors

  15. Review – Vector Operations Dot Product: measuring similarity between two vectors

  16. Review – Vector Operations Cross Product: measuring the area determined by two vectors 15

  17. Review – Vector Operations Cross Product: measuring the area determined by two vectors 16

  18. 2D Coordinates P: (x,y) 2D Cartesian coordinate system:

  19. 2D Coordinate Transformation P: (x,y) 2D Cartesian coordinate system:

  20. 2D Coordinate Transformation P: (x,y) 2D Cartesian coordinate system: 19

  21. 2D Coordinate Transformation p Transform object description from to

  22. 2D Coordinate Transformation p • Given the coordinates (x’,y’) in i’j’ • how to compute the coordinates (x,y) in ij? Transform object description from to 21

  23. 2D Coordinate Transformation p • Given the coordinates (x’,y’) in i’j’ • how to compute the coordinates (x,y) in ij? Transform object description from to 22

  24. 2D Coordinate Transformation p • Given the coordinates (x’,y’) in i’j’ • how to compute the coordinates (x,y) in ij? Transform object description from to 23

  25. 2D Coordinate Transformation p Transform object description from to

  26. 2D Coordinate Transformation p Transform object description from to

  27. 2D Coordinate Transformation p Transform object description from to

  28. 2D Coordinate Transformation p Transform object description from to

  29. 2D Coordinate Transformation p Transform object description from to

  30. 2D Coordinate Transformation p Transform object description from to

  31. 2D Coordinate Transformation p Transform object description from to

  32. 2D Coordinate Transformation p Transform object description from to

  33. 2D Coordinate Transformation p Transform object description from to

  34. 2D Coordinate Transformation p Transform object description from to

  35. 2D Coordinate Transformation p Transform object description from to

  36. 2D Coordinate Transformation p Transform object description from to

  37. 2D Coordinate Transformation p What does this column vector mean?

  38. 2D Coordinate Transformation p What does this column vector mean? Vector i’ in the new reference system Transform object description from to

  39. 2D Coordinate Transformation p What does this column vector mean? Transform object description from to

  40. 2D Coordinate Transformation p What does this column vector mean? Vector j’ in the new reference system Transform object description from to

  41. 2D Coordinate Transformation p What does this column vector mean? Transform object description from to

  42. 2D Coordinate Transformation p What does this column vector mean? The old origin in the new reference system Transform object description from to

  43. 2D Coordinate Transformation p 2D translation

  44. 2D Coordinate Transformation ? ? p ? ? 2D translation

  45. 2D Coordinate Transformation 0 1 p 0 1 2D translation

  46. 2D Coordinate Transformation ? p 2D translation&rotation

  47. 2D Coordinate Transformation p ? 2D translation&rotation

  48. 2D Coordinate Transformation p 2D translation&rotation

  49. 2D Coordinate Transformation ? p 2D translation&rotation

  50. 2D Coordinate Transformation p 2D translation&rotation

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