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CSCE441: Computer Graphics Coordinate & Composite Transformations

CSCE441: Computer Graphics Coordinate & Composite Transformations. Jinxiang Chai. Outline. 2D/3D Coordinate transformation 2D/3D Composite transformation Required readings: HB 7-8, 9-6. Coordinate Transform: 3D Geometry Pipeline. Rotate and translate the camera. Object space. World space.

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CSCE441: Computer Graphics Coordinate & Composite Transformations

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  1. CSCE441: Computer GraphicsCoordinate & Composite Transformations Jinxiang Chai

  2. Outline • 2D/3D Coordinate transformation • 2D/3D Composite transformation • Required readings: HB 7-8, 9-6

  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 • How to model 2D movement of animated characters or robots? Click here

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

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

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

  9. Coordinate Transformation Coordinate transformation from one reference frame to another ? Local reference frame Global reference frame 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 • Dot Product: measuring similarity between two vectors Unit vector:

  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 • 2D Cartesian coordinate system:

  19. 2D Coordinate Transformation • 2D Cartesian coordinate system:

  20. 2D Coordinate Transformation 2D Cartesian coordinate system: any 2D vector can be represented as 19

  21. 2D Coordinate Transformation 2D Cartesian coordinate system: any 2D vector starting from the origin can be represented as P: (x,y) 20

  22. 2D Coordinate Transformation 2D Cartesian coordinate system: any 2D point can be described as (x,y) P: (x,y) 21

  23. 2D Coordinate Transformation • Transform object description from to p

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

  25. 2D Coordinate Transformation Transform object description from to p • Given the coordinates (x’,y’) in i’j’ • how to compute the coordinates (x,y) in ij? 24

  26. 2D Coordinate Transformation Transform object description from to p • Given the coordinates (x’,y’) in i’j’ • how to compute the coordinates (x,y) in ij? 25

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

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

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

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

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

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

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

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

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

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

  37. 2D Coordinate Transformation • Transform object description from to p

  38. 2D Coordinate Transformation • Transform object description from to p

  39. 2D Coordinate Transformation Transform object description from to p 38

  40. 2D Coordinate Transformation p What does this column vector mean?

  41. 2D Coordinate Transformation • Transform object description from to p What does this column vector mean? Vector i’ in the new reference system

  42. 2D Coordinate Transformation • Transform object description from to p What does this column vector mean?

  43. 2D Coordinate Transformation • Transform object description from to p What does this column vector mean? Vector j’ in the new reference system

  44. 2D Coordinate Transformation • Transform object description from to p What does this column vector mean?

  45. 2D Coordinate Transformation • Transform object description from to p What does this column vector mean? The old origin in the new reference system

  46. 2D Coordinate Transformation • 2D translation p

  47. 2D Coordinate Transformation • 2D translation ? ? p ? ?

  48. 2D Coordinate Transformation • 2D translation 0 1 p 0 1

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

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

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