Computer Graphics Part 3 (Transformations)
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translation matrix equation (2d / Basic)
P'=T+P
|x'| = |x| + |dx|
|y'| |y| |dy|
scale matrix equation (2d / Basic)
P'=S.P
|x'| = |sx 0| . |x|
|y'| |0 sy| |y|
rotation matrix equation (2d / Basic)
P'=R.P
|x'| = |cos# -sin#| . |x|
|y'| |sin# cos#| |y|
Homogeneous Transformations
What is the homogeneous coordinate?
The last coordinate, called homogeneous coordinate. Used to project the scene onto the screen.
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
Whats matrix inversion good for?
Vg = M Vi
Vi = M
^{-1}
Vg
where V are coordinate systems
coordinate system transformation
3D translation
3D scaling
3D rotation about x-axis
3D rotation about y-axis
3D rotation about z-axis
3D rotation about arbitrary axis
View transformation detail
Card Set Information
Author:
simon123
ID:
216683
Filename:
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.
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