Introduction to. Computer Animation

Transcription

1 Inroducon o 1

2 Movaon Anmaon from anma (la.) = soul, spr, breah of lfe Brng mages o lfe! Examples Characer anmaon (humans, anmals) Secondary moon (har, cloh) Physcal world (rgd bodes, waer, fre) 2 2

3 Anmaon Technques For characer anmaon Keyframng Moon capurng / moon synhess For secondary moon, physcal effecs Procedural Smulaon (physcally based anmaon) 3 3

4 Arsdefnes key frames Compuer nerpolaes Keyframng 4 4

5 Moon Capurng Varous echnques (magnec, mechancal, opcal): Oupu: Trajecores of a se of markers 5 5

6 Moon Synhess Combne recorded moons Couresy Okan Arkan Problems Naural ransons Ineracon wh envronmen (foo sldng, collsons) 6 6

7 Anmaon Technques For characer anmaon Keyframng Moon capurng / moon synhess For secondary moon, physcal effecs Procedural Smulaon (physcally based anmaon) 7 7

8 Procedural Anmaon Procedure anmaes scene explcly Ocean surface as superposon of sne waves Hnsnger e. al. Plan growh anmaed wh L-Sysems (Grammar) 8 8

9 Procedural vs. Smulaon Procedural anmaon Explc descrpon of effec Smple o conrol Hard o model complex effecs / neracons Smulaon Inegraon of physcal equaons (e.g. Newon) Harder o conrol Unlmed complexy (bound only by compung me) 9 9

10 Physcal Smulaons Equaons known for a long me Moon (Newon, 1660) Elascy (Hooke, 1670) Fluds (Naver, Sokes, 1822) Smulaon made possble by compuers 1938: Zuse 1, 0.2 flops, 2004: NEC's Earh Smulaor 36 eraflops d / d ( m v ) = σ = Eε ρ + v v = k ρ + ρ g + µ f v 2 v 10 10

11 Am of Physcal Smulaons Compuaonal Scences Perfec replcaon of he real world Smulaons replace expensve expermens Accuracy more mporan han speed Plausble behavor (user / vewer mus be convnced) Conrollably Speed and sably (for real-me use) 11 11

12 Real-Tme Physcally Based Anmaon Trade accuracy for speed Chea as much as you can whou geng caugh Uncondonal sably Applcaons: Flgh/car Smulaors Surgery raners 3D Games 12 12

13 Examples Brle Deformable Lqud 13 13

14 Technques Parcle sysems Fre, smoke, waer Mass-sprng sysems Deformable objecs Rgd body smulaon Cars, arplanes, furnure, Grd based mehods Waer, smoke, arflow Ohers, e.g. Fne Elemens, 14 14

15 Parcle Sysems Snow, dus, sand Fre Smoke Waer 15 15

16 Collecon of many small smple parcles Parcle moon nfluenced by forces Generaed by emers Deleed when lfeme reached or ou of scene v Parcle Sysems m f generaor 16 16

17 17 17 Parcle Sysem Anmaon Newon s second law of moon ) ( 1 ) ( ) ( ) ( m d d d d f v v x = = Smple updae rule (negraon mehod) m v x x f v v + + 1

18 Force Compuaon Mulple nfluences: f gravy 0 = 0 g m dampng f = dv Addon of nfluences: gravy dampng exernal nerac = f + f + f f f + exernal f ( x f = nerac, ) f = f ( x, x j ) j 18 18

19 Parcle sysems Fre, smoke, waer Mass-sprng sysems Deformable objecs Rgd body smulaon Cars, arplanes, furnure, Grd based mehods Waer, smoke, arflow Technques 19 19

20 Mass-Sprng Sysems Parcle sysem plus sprngs Specal neracon force f nerac 0 { 1,2, } ( x x ) = k L 3 0 x x x x 0 0 x 3 L 3,k 3 x 0 L 2,k 2 x 2 x 1 L 1,k 1 sffness res lengh 20 20

21 Facal anmaon Thalmann Applcaons Cloh smulaon Surgery smulaon Srasser Kuehnapfel 21 21

22 Issues Where o pu sprngs Choce of sffnesses Collson deecon Collson response Sably (me sep or sffness oo hgh) v x v x 1 res confguraon + f m + v overcorrecon 22 22

23 Parcle sysems Fre, smoke, waer Mass-sprng sysems Deformable objecs Rgd body smulaon Cars, arplanes, furnure, Grd based mehods Waer, smoke, arflow Technques 23 23

24 Rgd Body Smulaon Deformable objecs have many degrees of freedom Each verex s smulaed separaely A rgd body only has 6 degrees of freedom Faser smulaon possble orenaon poson 24 24

25 Saes of a Rgd Body Sac saes Poson x Orenaon R Dynamc saes Lnear velocy v Angular velocy ω ω v R x 25 25

26 26 26 Smulaon of Rgd Bodes Newon s law of moon = ) ( ) ( ) ( ) ( ~ ) ( ) ( ) ( ) ( ) ( ) ( M d d τ F R ω v ω I v R x Use negraon mehod o updae saes

27 Collson deecon Collson response for complex confguraons Consrans (jons) Issues 27 27

28 Roboc smulaons 3D compuer games Half Lfe Applcaons 28 28

29 Parcle sysems Fre, smoke, waer Mass-sprng sysems Deformable objecs Rgd body smulaon Cars, arplanes, furnure, Grd based mehods Waer, smoke, arflow Technques 29 29

30 Grd Based Mehods Basc dea: Solve paral dfferenal equaon on (regular) grd Replace dfferenals by fne dfferences 30 30

31 Example: Waer Surface Waer surface defned as hegh u(x,y,) a locaon x,y a me Dynamcs gven by 2D wave equaon: u = c ( u x y u ) u(x,y,) (x,y) 31 31

32 Dscrezaon Replace connuous u(x,y,) by dscree array u [,j] (grd spacng h) Replace dervaves by fne dfferences, e.g. u/ x = (u [+1,j]-u [,j])/h Smple updae scheme (wh cool resuls!) v u [ + 1, j ] + [ 1, j ] + [, j + 1] + [, j 1] 4 [, j ] [, j ] = v [, j ] + c 2 [, j ] = u [, j ] + v u [, j ] u u h u u 32 32

33 Boundary Condons Assumng (1,..,n) Perodc: u [0,j] = u [n,j], u [n+1,j] = u [1,j] Mrror: u [0,j] = u [1,j], u [n+1,j] = u [n,j] Analog for j 33 33

34 Adversemen Sommersemeser : Physkalsch-basere Smulaon n der Compuer Graphk 2V 1U Übung = 1 Semeserprojek n Gruppen 34 hp://graphcs.ehz.ch/~mamuel/eachng/projecs2004/ 34

35 Prüfungshemen 0. Inroducon wrd nch geprüf 1. Graphcs APIs 2. Colors 3. Transformaons 4. Projecons 5. Lghng & Shadng 6. Rayracng 7. Texure Mappng 8. An Alasng 9. Clppng Algorhms 10. Scan Converson 11. Graphcs Hardware kene Produkdeals, kene Shaderbefehle 12. Real-me Renderng Ppelne opmzaon wrd nch geprüf 13. Terran Renderng wrd nch geprüf 14. wrd nch geprüf 35 35