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Computer Graphics: Coordinate & Composite Transformations Overview

This outline covers 2D/3D coordinate transformations, composite transformations, and their applications in various fields such as modeling, animation, and robotics. It includes concepts like object space, world space, view space, focal length, aspect ratio, resolution, normalized project space, image space, and more. Additionally, vector operations like dot product and cross product are discussed. Learn about 2D Cartesian coordinate systems, object transformation, column vector meanings, translations, rotations, and more in this comprehensive guide.

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Computer Graphics: Coordinate & Composite Transformations Overview

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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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