Last Time? Inverse Kinematics. Today. Keyframing. Physically-Based Animation. Procedural Animation

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1 Lat Time? Invere Kinematic Navier-Stoke Equation Conervation o Momentum & Ma Incompreible Flow Today How do we animate? Keyraming Procedural Animation Pyically-Baed Animation Forward and Invere Kinematic Motion Capture Keyraming Ue pline curve to automate te in betweening Good control Le tediou tan drawing every rame Creating a good animation till require coniderable kill and talent Rigid Body Dynamic Finite Element Metod ACM 1987 Principle o traditional animation applied to 3D computer animation Procedural Animation Decribe te motion algoritmically, a a unction o mall number o parameter Example: a clock wit econd, minute and our and expre te clock motion in term o a econd variable te clock i animated by varying te econd parameter Example: A bouncing ball Ab(in(ωt+θ 0 ))*e -kt Pyically-Baed Animation Aign pyical propertie to object (mae, orce, inertial propertie) Simulate pyic by olving equation Realitic but diicult to control m v 0 g 1

2 Articulated Model Articulated model: rigid part connected by joint Tey can be animated by peciying te joint angle a unction o time. q i q t i( ) Skeleton Hierarcy Eac bone tranormation decribed relative to te parent in te ierarcy: x, y, z, q,, q,, q, z y ip let-leg... r-tig x r-cal r-oot t 1 t 2 t 1 t 2 1 DOF: knee 2 DOF: writ 3 DOF: arm Forward Kinematic Invere Kinematic (IK) Given keleton parameter p, and te poition o te eecter in local coordinate V, wat i te poition o te eector in te world coordinate V w? x, y, z, q,, q,, q, z y x Given te poition o te eecter in local coordinate V and te deired poition V w in world coordinate, wat are te keleton parameter p? Muc arder require olving te invere o te non-linear unction: x, y, z, q,, q,, q, V V w V w = T(x,y,z )R(q,, )T R(q t, t, t )T t R( )T c R(q, )V V w = S(p)V ind p uc tat S(p)V = V w Under-/Over- Contrained IK Searcing Coniguration Space No olution Application: Robot Motion Planning poe pace aded by ditance to target One olution Two olution Many olution Ue gradient decent to walk rom tarting coniguration to target Angle retriction & colliion can introduce local minima Te good-looking textured ligt-ourced bouncy un mart and tretcy page Hugo Elia, ttp://reepace.virgin.net/ugo.elia/model/m_ik.tm Te good-looking textured ligt-ourced bouncy un mart and tretcy page Hugo Elia, ttp://reepace.virgin.net/ugo.elia/model/m_ik2.tm 2

3 IK Callenge Find a natural keleton coniguration or a given collection o poe contraint A vector contraint unction C(p) = 0 collect all poe contraint A calar objective unction g(p) meaure te quality o a poe, g(p) i minimum or mot natural poe. Example g(p): deviation rom natural poe joint tine power conumption Motion Capture Optical marker, ig-peed camera, triangulation 3D poition Capture tyle, ubtle nuance and realim You mut oberve omeone do ometing How do tey Animate Movie/Game? Quetion? Keyraming motly Articulated igure, invere kinematic, motion capture Skinning Complex deormable kin, mucle, kin motion Hierarcical control Smile control, eye blinking, etc. Keyrame or tee iger-level control A uge time i pent building te 3D model, it keleton and it control Pyical imulation or econdary motion Hair, clot, water Image rom te Maya tutorial, Syntei o Complex Dynamic Caracter Motion rom Simple Animation, Rapid prototyping o realitic caracter motion rom roug low-quality animation Obey te law o pyic & tay witin pace o naturally-occurring movement Wat a Natural Poe? Training databae o ~50 natural poe For eac, compute center o ma o: Upper body Arm Lower body Te relative COM o eac generated poe i matced to mot te mot imilar databae example 3

4 Linear and Angular Momentum In uncontrained animation (no contact), bot linear & angular momentum ould be conerved Te center o ma ould ollow a parabolic trajectory according to gravity Te joint ould move uc tat te angular momentum o te wole body remain contant During Contrained Motion During contrained motion (wen in contact wit te ground), te angular momentum ollow a pline curve modeled ater biomecanic data uncontrained contrained uncontrained Sytem Feature Quetion? Automatically detect point/line/plane contraint Divide animation into contrained portion (e.g., eet in contact wit ground) and uncontrained portion (e.g., ree ligt) Linear and angular momentum contraint witout aving to compute mucle orce Minimize: Ma diplacement Velocity o te degree o reedom (DOF) Unbalance (ditance te COM projected to ground i outide o contraint) Today How do we animate? Keyraming Procedural Animation Pyically-Baed Animation Forward and Invere Kinematic Motion Capture Rigid Body Dynamic Finite Element Metod Rigid Body Dynamic Could ue particle or all point on te object But rigid body doe not deorm Few degree o reedom 1 (t) Ue only one particle at te 2 (t) v(t) center o ma x(t) Compute Net Force & 3 (t) Net Torque Net Torque Net Force Nice Reerence Material: ttp:// 4

5 Rigid Body Dynamic Pyic Velocity Acceleration Angular Momentum Colliion Friction Simulation o Non-Rigid Object We modeled tring & clot uing ma-pring ytem. Can we do te ame? Ye But a more pyically accurate model ue volumetric element: rom: Darren Lewi ttp://www-c-tudent.tanord.edu/~dalewi/c448a/rigidbody.tml Image rom O Brien et al Strain & Stre Stre te internal ditribution o orce witin a body tat balance and react to te load applied to it normal tre & ear tre ttp://en.wikipedia.org/wiki/image:stre_tenor.png Strain material deormation caued by tre. meaured by te cange in lengt o a line or by te cange in angle between two line Finite Element Metod To olve te continuou problem (deormation o all point o te object) Dicretize te problem Expre te interrelationip Solve a big linear ytem More principled tan Ma-Spring object inite element large matricial ytem Diagram rom Debunne et al Reading or Friday 2/23: Gille Debunne, Matieu Debrun, Marie-Paule Cani, & Alan H. Barr Dynamic Real-Time Deormation uing Space & Time Adaptive Sampling SIGGRAPH 2001 Jame O Brien & Jeica Hodgin Grapical Modeling and Animation o Brittle Fracture SIGGRAPH