Chapter 62: computer graphics
62.1 Cem Yuksel
62.1.1 introduction
https://www.youtube.com/playlist?list=PLplnkTzzqsZTfYh4UbhLGpI5kGd5oW_Hh
62.1.1.1 2D transformation
https://www.youtube.com/watch?v=EKN7dTJ4ep8&list=PLplnkTzzqsZTfYh4UbhLGpI5kGd5oW_Hh&index=6
62.1.1.1.4 rotation
p=pxˆx+pyˆy=px[10]+py[01]=[1001][pxpy]=Ip
p′=px[cosθsinθ]+py[−sinθcosθ]=[cosθ−sinθsinθcosθ][pxpy]=Rθp
p′=px[cosθ−sinθ]+py[sinθcosθ]=[cosθsinθ−sinθcosθ][pxpy]=R−θp
62.1.1.1.5 skew = rotation + non-uniform scale + rotation
backp′=[p′xp′y]=[cosθsinθ−sinθcosθ][sx00sy][cosθ−sinθsinθcosθ][pxpy]=R−θSRθp
62.1.1.1.6 any 2×2 matrix
p′=Mp
SVD = singular value decomposition
M=UΣV⊺e.g.=RSR⊺=R−θSRθ
any 2×2 matrix + translation
p′=Mp+t
p′=M2(M1p+t1)+t2
62.1.1.2 3D transformation
https://www.youtube.com/watch?v=1z1S2kQKXDs&list=PLplnkTzzqsZTfYh4UbhLGpI5kGd5oW_Hh&index=7
62.1.2 interactive
https://www.youtube.com/playlist?list=PLplnkTzzqsZS3R5DjmCQsqupu43oS9CFN