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

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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