Computer Graphics Part 3 (Transformations)

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Author:
simon123
ID:
216683
Filename:
Computer Graphics Part 3 (Transformations)
Updated:
2013-04-29 20:38:23
Tags:
computer graphics informatics science
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Description:
University of Edinburgh School of Informartics Copmuter Graphics (Level 10) Revision Cards created by Simon M.
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  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
  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
  9. 3D translation
  10. 3D scaling
  11. 3D rotation about x-axis
  12. 3D rotation about y-axis
  13. 3D rotation about z-axis
  14. 3D rotation about arbitrary axis
  15. View transformation detail

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