For secondary motion, physical effects Simulation (physically based animation) For character animation. Motion capturing / motion synthesis

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1 3 4 Introducton to Anmaton Technques For character anmaton Keyramng Moton capturng / moton synthess For secondary moton physcal eects Procedural Smulaton (physcally based anmaton) Motvaton Anmaton rom anma (lat.) = soul sprt breath o le Brng mages to le! Examples Character anmaton (humans anmals) Secondary moton (har cloth) Physcal world (rgd bodes water re) Keyramng Artstdenes key rames Computer nterpolates 1

2 5 7 8 Moton Capturng Varous technques (magnetc mechancal optcal): Output: Trajectores o a set o markers Anmaton Technques For character anmaton Keyramng Moton capturng / moton synthess For secondary moton physcal eects Procedural Smulaton (physcally based anmaton) Moton Synthess Combne recorded motons Courtesy Okan Arkan 6 Problems Natural transtons Interacton wth envronment (oot sldng collsons) Procedural Anmaton Procedure anmates scene explctly Ocean surace as superposton o sne waves Hnsnger et. al. Plant growth anmated wth L-Systems (Grammar)

3 t Procedural vs. Smulaton 9 Procedural anmaton Explct descrpton o eect Smple to control Hard to model complex eects / nteractons Smulaton Integraton o physcal equatons (e.g. Newton) Harder to control Unlmted complexty (bound only by computng tme) Am o Physcal Smulatons 11 Computatonal Scences Perect replcaton o the real world Smulatons replace expensve experments Accuracy more mportant than speed Plausble behavor (user / vewer must be convnced) Controllablty Speed and stablty (or real-tme use) Physcal Smulatons Equatons known or a long tme Moton (Newton 1660) Elastcty (Hooke 1670) Fluds (Naver Stokes 18) Smulaton made possble by computers 1938: Zuse 1 0. lops 004: NEC's Earth Smulator 36 teralops d / dt ( m v ) = σ = Eε v ρ + v v = k ρ + ρ g + µ v 10 Real-Tme Physcally Based Anmaton Trade accuracy or speed Cheat as much as you can wthout gettng caught Uncondtonal stablty Applcatons: Flght/car Smulators Surgery traners 3D Games 1 3

4 Examples Brttle Deormable Lqud 13 Partcle Systems Snow dust sand Fre Smoke Water 15 Technques Partcle systems Fre smoke water Mass-sprng systems Deormable objects Rgd body smulaton Cars arplanes urnture Grd based methods Water smoke arlow Others e.g. Fnte Elements 14 Partcle Systems Collecton o many small smple partcles Partcle moton nluenced by orces Generated by emtters Deleted when letme reached or out o scene v m generator 16 4

5 j j Partcle System Anmaton Newton s second law o moton d dt d dt x ( t ) = v ( t ) v ( t ) = 1 ( t ) m Smple update rule (ntegraton method) v v + t 1 m x x + t v 17 Technques Partcle systems Fre smoke water Mass-sprng systems Deormable objects Rgd body smulaton Cars arplanes urnture Grd based methods Water smoke arlow 19 Force Computaton Multple nluences: gravty 0 = 0 g m dampng = dv Addton o nluences: gravty dampng external nteract = external x = ( nteract t ) = ( x x ) 18 Mass-Sprng Systems Partcle system plus sprngs Specal nteracton orce x 3 L 3 k 3 x 0 L k x 1 L 1 k 1 nteract 0 ( x x ) = k L 3 0 { 1 } x x x x 0 0 x stness rest length 0 5

6 Applcatons Facal anmaton Cloth smulaton Surgery smulaton Thalmann Strasser Kuehnapel 1 Technques Partcle systems Fre smoke water Mass-sprng systems Deormable objects Rgd body smulaton Cars arplanes urnture Grd based methods Water smoke arlow 3 Issues Where to put sprngs Choce o stnesses Collson detecton Collson response Stablty (tme step or stness too hgh) v v + x x + t v rest conguraton t 1 m overcorrecton Rgd Body Smulaton Deormable objects have many degrees o reedom Each vertex s smulated separately A rgd body only has 6 degrees o reedom Faster smulaton possble orentaton poston 4 6

7 States o a Rgd Body Statc states Poston x Orentaton R Dynamc states Lnear velocty v Angular velocty ω x R ω v 5 Issues Collson detecton Collson response or complex conguratons Constrants (jonts) 7 Smulaton o Rgd Bodes Newton s law o moton x ( t ) v ( t ) d R ( t ) ω ~ ( t ) R ( t ) = dt M v ( t ) F ( t ) I ( t ) ω ( t ) τ ( t ) Use ntegraton method to update states 6 Applcatons Robotc smulatons 3D computer games Hal Le 8 7

8 t t t Technques Partcle systems Fre smoke water Mass-sprng systems Deormable objects Rgd body smulaton Cars arplanes urnture Grd based methods Water smoke arlow 9 Example: Water Surace Water surace dened as heght u(xyt) at locaton xy at tme t Dynamcs gven by D wave equaton: u = c ( u + t x y u ) u(xyt) (xy) 31 Grd Based Methods Basc dea: Solve partal derental equaton on (regular) grd Replace derentals by nte derences 30 Dscretzaton Replace contnuous u(xyt) by dscrete array [j] (grd spacng h) Replace dervatves by nte derences e.g. u/ x = ( [+1j]- [j])/h Smple update scheme (wth cool results!) v t + 1 [ + 1 j ] + [ 1 j ] + [ j + 1] + [ j 1] 4 [ j ] [ j ] = v [ j ] + t c u [ j ] = u [ j ] + t v t [ j ] h 3 8

9 Boundary Condtons Assumng (1..n) Perodc: [0j] = [nj] [n+1j] = [1j] Mrror: [0j] = [1j] [n+1j] = [nj] Analog or j 33 Prüungsthemen 0. Introducton wrd ncht geprüt 1. Graphcs APIs. Colors 3. Transormatons 4. Projectons 5. Lghtng & Shadng 6. Raytracng 7. Texture Mappng 8. Ant Alasng 9. Clppng Algorthms 10. Scan Converson 11. Graphcs Hardware kene Produktdetals kene Shaderbeehle 1. Real-tme Renderng Ppelne optmzaton wrd ncht geprüt 13. Terran Renderng wrd ncht geprüt 14. wrd ncht geprüt 35 Advertsement Sommersemester : Physkalsch-baserte Smulaton n der Computer Graphk V 1U Übung = 1 Semesterprojekt n Gruppen