Computer Graphics Part 3 (Transformations)

The flashcards below were created by user simon123 on FreezingBlue Flashcards.

  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
  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
  9. 3D translation
    Image Upload
  10. 3D scaling
    Image Upload
  11. 3D rotation about x-axis
    Image Upload
  12. 3D rotation about y-axis
    Image Upload
  13. 3D rotation about z-axis
    Image Upload
  14. 3D rotation about arbitrary axis
    Image Upload
  15. View transformation detail
    Image Upload
Author:
simon123
ID:
216683
Card Set:
Computer Graphics Part 3 (Transformations)
Updated:
2013-04-30 00:38:23
Tags:
computer graphics informatics science
Folders:

Description:
University of Edinburgh School of Informartics Copmuter Graphics (Level 10) Revision Cards created by Simon M.
Show Answers: