Rotations 2D & 3D, & about arbitrary axis. Rotation is linear (as in figure)

Transcription

1 Rottion D & 3D, & bout bit i Rottion i line in figue ot b ot ot b ot α α ot b b ot b otb ot

2 Deiing Rottion Mti in D

3 Rottion Mti in D, continued

4 D Rottion Mti, concluion

5 Rottion 3D, ound,, e co in in co co in in co co in in co R R R

6 Rottion bout n bit i Rotte b ound unit i How to eeent?

7 Rottion bout n bit i Pojection oeto: Vecto without ecto b men emoe ome mount of ecto b o tht the eult i eendicul to ecto b. b b b α b \ b b b α \

8 Rottion bout n bit i Cete n othonoml bi: e 3 \ e \ e e 3 e

9 Rottion bout n bit i Decomoe befoe otting: α \ e e e ot e ot ot ot ot ot in \ co in co \ \ \ \ \ α α α α α

10 Rottion uing Qutenion Qutenion k j i k j i k j i

11 Rottion uing Qutenion Qutenion multiliction Aocitie Not Commuttie

12 Rottion uing Qutenion Qutenion mgnitude 3 4 Qutenion inee

13 Rottion uing Qutenion Qutenion ottion: co in / / ot

14 Rottion uing Qutenion Poof of utenion ottion fom: c c c

15 Rottion uing Qutenion Poof of utenion ottion fom: c c ot

16 Rottion uing Qutenion Poof of utenion ottion fom: in co c c c c c c c c c c c ot

17 Rottion uing Qutenion Combining ottion: ot ot ot ot ot

18 Rottion uing Qutenion Mti Fom: w w w w w w w w w w k j i w

19 Defomtion Tnfomtion tht do not eee he Non-unifom cling Sheing Teing Twiting Bending

20 Sheing ' ' '

21 Teing ' ' ' f f Imge coute of Wtt, 3D Comute Ghic

22 Twiting co in in co ' ' ' Imge coute of Wtt, 3D Comute Ghic

23 Bending ' ' ' k h g f Imge coute of Wtt, 3D Comute Ghic

24 Hiechicl Tnfomtion m hnd φ be M be T be Tbe M M m hnd M M be m R T R φ T be be R R R φ

25 Coodinte Stem b T M b M T b T M O u b u u b T nd u u M

26 Othonoml Coodinte Iff u nd e othonoml: T M u u M u u u u u T M

27 Coodinte Stem Object coodinte Wold coodinte Cme coodinte on film lne Nomlied deice coodinte mke it e fo cliing Window coodinte

28 Object Coodinte Conenient lce to model the object O

29 Wold Coodinte Common coodinte fo the cene O O W

30 Cme Coodinte Coodinte tem with the cme in conenient oe u n n u n n n u u u M

31 Nomlied Deice Coodinte Deice indeendent coodinte Viible coodinte uull nge fom:

32 Window Coodinte Adjuting the NDC to fit the window, i the lowe left of the window w nd width w nd height

33 Peectie Pojection Tking the cme coodinte to NDC ne

34 Peectie Pojection ' ne ' ne ' ne

35 Peectie Pojection M left,ight to -, when -ne ' ne f ne left ne ight left left ne left ight left ne ight left ight left ight left left ight ne

36 Peudodeth M -ne,-f to -, f ne ' f ne f ne f ne Line e eeed though the tnfomtion See Newmn nd Soull 8 fo the full deition

37 Peectie Pojection ne f ne f ne f ne f bottom to bottom to bottom to ne left ight left ight left ight ne P

38 Peectie Pojection Peee Stight Line b t t b t b b t F b t E b t D t b C b t B t b A m to Comute t -t, t -t, t -t. All he numeto tht deend on t -t. All he the me denominto. Theefoe, the tio e contnt. t t t t

39 Othoghic Pojection ne

40 Othoghic Pojection ' ne '

41 Othoghic Pojection M left,ight to -, ' left ight left ight left ight left left left ight ight left left

42 Othoghic Pojection M ne,f to -, ne f f f ne ne ne ne ne f f ne ne

43 Othoghic Pojection ne f ne f ne f bottom to bottom to bottom to left ight left ight left ight P

44 Othoghic Pojection Peee Stight Line b t t b t b F b t E D t b C B t b A m to