3 Gomril rnsormions Fol & n m, Chr 5 3 Gomril rnsormions 3 oin rrsnion rnslion Sling, rlion Shring oions o, n is Comosiion o roions oion o n rirr is rnsorming lns 3 Coorin Ssms igh-hn oorin ssm: L-hn oorin ssm: minr: Cross ro n 3 oin rsnion A 3 oin is rrsn in homognos oorins 4-imnsionl or: As or oins: 3 Gomril rnsormions In homognos oorins, 3 in rnsormions r rrsn 44 mris: A oin rnsormion is rorm: i h g i h g
3 rnslion in rnsl o : Or: Inrs: 3 Sling S Or S 3 lion A rlion hrogh h ln: lions hrogh h n h lns r in similrl 3 Shring Shring: Chng in h oorin is linr ominion o ll hr rnsorms ino gnrl rllli 3 oion o gnr roion in 3 h o si: is o roion.o.. mon o roion.o.. No, h is sss hrogh h origin 3 oion Conrlokis roion o -is
3 oion Conrlokis roion o -is 3 oion Conrlokis roion o -is Comosi oion,, n, n rorm n roion o n is sg hrogh h origin Inrs roion: Chng o Coorins rolm: Gin h XYZ orhonorml oorin ssm, in rnsormion, h ms rrsnion in XYZ ino rrsnion in h orhonorml ssm W, ih h sm origin h mri rnsorms h W ors o h XYZ ors =,, =,, Chng o Coorins Solion: is roion mri hos ros r,, n W: No: h inrs rnsormion is h rnsos: Chng o Coorins Ls hk h rnsormion o nr : Similrl, gos ino Y, n W gos ino Z X
Chng o Coorins Ls hk h rnsormion o h X is nr - : Similrl, Y gos ino, n Z gos ino W oion Ao n Arirr Ais Ais o roion n lo n oin: 6.o.. ms si oins n h i: mk h is oinin ih on o h oorin s is, ro, n hn rnsorm k oion Ao n Arirr Ais s Iniil osiion rnsl o h Origin s o ono h Ais s 3 o h Oj Aron h Ais s 4 o h Ais o h originl Orinion s 5 rnsl o h Originl osiion oion Ao n Arirr Ais S: S : S 3: S 4: S 5: Comosiion: oion Ao Arirr Ais Consring n orhonorml ssm long h roion is: A or W rlll o h roion is: A or rnilr o W: A or orming righ-hn orhogonl ssm ih W n : s s ; s ; rnsorming lns ln rrsnion: B hr non-ollinr oins B imlii qion: A B C A B C C B A
rnsorming lns On o rnsorm ln is rnsorming n hr non-ollinr oins on h ln Anohr is o rnsorm h ln qion: Gin rnsormion sh h [,,, ] = [,,, ] in [A,B,C,], sh h: A B C rnsorming lns No h: A B C hs, h rnsormion h shol l o h ln qion is: A B C A B C