Linear Linear Transformation Transformation with CG & animation with CG & animation Ogose Ogose Shigeki Shigeki Kawai Kawai- Juku Juku Tokyo, Japan Tokyo, Japan http://mixedmoss.com/atcm/2012/ http://mixedmoss.com/atcm/2012/ 1. Advantages of using Computer Graphics (CG). • Grids can be drawn easily. • Effects of changing the ‘original objects’ or ‘matrix’ can be seen immediately. • Exotic objects such as photos can be transformed. • Animations can be used.
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Linear Transformation with CG & animation · 2014. 1. 18. · Animation of Rotation&Enlargement by 12 ex3. F − = animation by rotation current matrix is 10 01 current matrix is
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LinearLinear Transformation Transformation with CG & animationwith CG & animation
Ogose Ogose ShigekiShigekiKawaiKawai--JukuJuku
Tokyo, JapanTokyo, Japanhttp://mixedmoss.com/atcm/2012/http://mixedmoss.com/atcm/2012/
1. Advantages of using Computer Graphics (CG).
• Grids can be drawn easily.
• Effects of changing the ‘original objects’ or ‘matrix’ can be seen immediately.
• Exotic objects such as photos can be transformed.
• Animations can be used.
2
2 1 Transformatioex n by
1 11.
−
original transformed
muffine.jar
(2,1)(-1,1)
Example of linear
OA 3OB OA' 3O2
i
B'2
ty
+ → +
(1,0)
(0,1)
Transformation of a photo bcos sin
ex2 )sin c
y s
. (o
Rθ θ
θθ θ
−=
original transformed
muffine.jar
Use a palette or type it in the field.
cos30 ,sin( )30° °( ,sin 30 c )os30° °−
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2 1 Animation of Rotation&Enlargement by
1 2ex3. F
− =
animation by rotation
current matrix is1 0
0 1
current matrix is2 1
1 2
−
is right-at-the-moment matrix. Which starts from the unit matrix and finishes as the target matrix.Curr matrixent
2. EigenVectors & Animation
Animation is useful for rotation - which has no real eigenvectors- , but it works even better for transformationswhich have real eigenvectors.