Reading AssignmentsBasics of Motion GenerationMethods of Motion GenerationApplications  ChoicesKeyframing (I)Keyframing (II)Motion InterpolationBasic TerminologiesForward vs. Inverse KinematicsForward KinematicsInverse KinematicsModeling DeformationMotion Capture (I)Motion Capture (II)Physically-based Simulation (I)Physically-based Simulation (II)High-Level Control (I)High-Level Control (II)UNC Chapel HillM. C. LinReading AssignmentsPrinciples of Traditional Animation Applied to 3D Computer Animation, by J. Lasseter, Proc. of ACM SIGGRAPH 1987 Computer Animation: Algorithms and Techniques, by Richard Parent, 2001. Chapter 1, 4 & 5 and Appendices.Advanced Animation and Rendering Techniques: Theory and Practice, by A. Watt and M. Watt, 1992. Chapter 15 & 16.UNC Chapel HillM. C. LinBasics of Motion Generationlet Xi = configuration of Oi at tk = t0 ,  iEND = falsewhile (not END) do display Oi ,  i tk = tk + t generate Xi at tk ,  i END = function(motion generation)UNC Chapel HillM. C. LinMethods of Motion GenerationTraditional Principles (Keyframing)Performance Capture (Motion Capture)Modeling/Simulation (Physics, Behaviors)Automatic Discovery (High-Level Control)UNC Chapel HillM. C. LinApplications  Choices-Computer Animation -Virtual Environments -Rapid Prototyping -Haptic Rendering -Computer Game Dynamics -Robotics and Automation -Medical Simulation and AnalysisUNC Chapel HillM. C. LinKeyframing (I)1. Specify the key positions for the objects to be animated.2. Interpolate to determines the position of in-between frames.UNC Chapel HillM. C. LinKeyframing (II)Advantages–Relatively easy to use–Providing low-level control Problems–Tedious and slow–Requiring the animator to understand the intimate details about the animated objects and the creativity to express their behavior in key-framesUNC Chapel HillM. C. LinMotion InterpolationInterpolate using mathematical functions:–Linear–Hermite–Bezier… and many others (see Appendices of Richard Parent’s online book)Forward & inverse kinematics for articulation Specifying & representing deformationUNC Chapel HillM. C. LinBasic TerminologiesKinematics: study of motion independent of underlying forcesDegrees of freedom (DoF): the number of independent position variables needed to specify motionsState Vector: vector space of all possible configurations of an articulated figure. In general, the dimensions of state vector is equal to the DoF of the articulated figure.UNC Chapel HillM. C. LinForward vs. Inverse KinematicsForward kinematics: motion of all joints is explicitly specifiedInverse kinematics: given the position of the end effector, find the position and orientation of all joints in a hierarchy of linkages; also called “goal-directed motion”. (See an in-class example.)UNC Chapel HillM. C. LinForward KinematicsAs DoF increases, there are more transformation to control and thus become more complicated to control the motion.Motion capture can simplify the process for well-defined motions and pre-determined tasks.UNC Chapel HillM. C. LinInverse KinematicsAs DoF increases, the solution to the problem may become undefined and the system is said to be redundant. By adding more constraints reduces the dimensions of the solution.It’s simple to use, when it works. But, it gives less control.Some common problems:–Existence of solutions–Multiple solutions–Methods usedUNC Chapel HillM. C. LinModeling DeformationGeometric-based Techniques–Global & local deformation (Barr’84)–FFD (Sederberg & Parry’86) and variants… othersPhysically-based Techniques–particle systems–BEM–FEM & FEAVariational Techniques–Variational surface modeling (Welch & Witkin’92)–dynamic-NURBS (Terzopoulos & Qin’94)UNC Chapel HillM. C. LinMotion Capture (I)1. Use special sensors (trackers) to record the motion of a performer2. Recorded data is then used to generate motion for an animated character (figure)UNC Chapel HillM. C. LinMotion Capture (II)Advantages–Ease of generating realistic motionsProblems–Not easy to accurately measure motions–Difficult to “scale” or “adjust” the recorded motions to fit the size of the animated characters–Limited capturing technology & devices•Sensor noise due to magnetic/metal trackers•Restricted motion due to wires & cables •Limited working volumeUNC Chapel HillM. C. LinPhysically-based Simulation (I)Use the laws of physics (or a good approximation) to generate motionsPrimary vs. secondary actionsActive vs. passive systemsDynamic vs. static simulationUNC Chapel HillM. C. LinPhysically-based Simulation (II)Advantages–Relatively easy to generate a family of similar motions–Can be used for describing realistic, complex animation, e.g. deformation–Can generate reproducible motions Problems–Challenging to build a simulator, as it requires in-depth understanding of physics & mathematics–Less low-level control by the userUNC Chapel HillM. C. LinHigh-Level Control (I)Task level description using AI techniques:–Collision avoidance–Motion planning–Rule-based reasoning–Genetic algorithms… etc.UNC Chapel HillM. C. LinHigh-Level Control (II)Advantages–Very easy to specify/generate motions–Can reproduce realistic motions Problems–Need to specify all possible “rules”–The intelligence of the system is limited by its input or training –May not be reusable across different