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Computer Graphics Part 3 (Transformations)

  1. translation matrix equation (2d / Basic)
    P'=T+P

    x'  =  x  +  dx
    y'      y      dy
  2. scale matrix equation (2d / Basic)
    P'=S.P

    x'  =  sx  0  .   x
    y'      0  sy      y
  3. rotation matrix equation (2d / Basic)
    P'=R.P

    x'  =  cos#  -sin#  .   x
    y'      sin#   cos#      y
  4. Homogeneous Transformations
    Image Upload 1
  5. What is the homogeneous coordinate?
    The last coordinate, called homogeneous coordinate. Used to project the scene onto the screen.
  6. What is concatenation in the context of Transformation?
    sequentially multiplying matrices to combine scaling, rotation and translation in just one step.

    • e.g.
    • Scale then Translate
    • p' = T S p
    • T S = 1 0 3 . 2 0 0   = 2 0 3
    •         0 1 1   0 2 0       0 2 1
    •         0 0 1   0 0 1       0 0 1

    remember: AB != BA
  7. Whats matrix inversion good for?
    • Vg = M    Vi
    • Vi  = M-1 Vg

    where V are coordinate systems
  8. coordinate system transformation
    Image Upload 2
  9. 3D translation
    Image Upload 3
  10. 3D scaling
    Image Upload 4
  11. 3D rotation about x-axis
    Image Upload 5
  12. 3D rotation about y-axis
    Image Upload 6
  13. 3D rotation about z-axis
    Image Upload 7
  14. 3D rotation about arbitrary axis
    Image Upload 8
  15. View transformation detail
    Image Upload 9
Author
simon123
ID
216683
Card Set
Computer Graphics Part 3 (Transformations)
Description
University of Edinburgh School of Informartics Copmuter Graphics (Level 10) Revision Cards created by Simon M.
Updated

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