【正文】 MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Using motion graph ? Any walk on the graph is a valid motion ? Generate walks to meet goals 187。 How to connect clips? 187。 Need motion capture (examples) ? Flexible, longrunning, controllable 187。 Over a short period of time 187。 m(t) = a m0(t) + (1a) m1(t) ? Note: this is a perframe operation ? Interpolation between poses 187。 m(t) = m0( f(t) ) 187。 But we don?t know what to preserve 187。 Dense samples (at frames) Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Preliminaries ? A motion maps times to configurations 187。 “close” rotations are “close” in value Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Parameterizations of Rotations ? Rotation Matrices ? Euler Angles ? Axis Angle formulation ? Unit Quaternions Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Comparison of body representation Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Motion definition ? Motion is a function of time 187。 (as few variables as possible) ? Complete 187。 Usually TPose ? Rigid pieces undergo rigid transformation ? Hierarchical representation of the configuration Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Computing positions ? Each joint i provides a local rotation Ri and a local translation Ti. Concatenating Ri and Ti gives local Mi, the local transform at each joint. ? The transformation of the point x on joint j is found by concatenating all previous transforms in the hierarchy as follows: Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Parameterizing Rotations ? Goal: encode rotations in a vector 187。 Hands ? How to describe moving target – “Character” ? How to describe movement mathematically Motion Representation MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Human Model ? Humans are plex! Motion Representation Human motion can be understood at a very fine level of detail! MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Abstractions Representation of plex human structure with varying degrees of simplification 206 bones, muscles, fat, ans, clothing, … Motion Representation 206 bones, plex joints 53 bones Kinematic joints MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Standard simplified models of humans ? Small numbers of degrees of freedom for gross motion ? Articulated figures 187。 actor should have similar proportions as the performer ? joint rotations of the actor are applied to the character ? there are still issues with proportions Alias Motionbuilder: actor and markers Mocap Overview MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 retargeting problems Mocap Overview MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 retargeting problems Mocap Overview MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Applications ? Entertainment ? Medicine ? Arts / Education ? Science / Engineering Mocap Overview MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Entertainment: Live Action Films ? Computer generated characters in live action films (. Battle Droids and many others in Star Wars Prequels, Gullum in The Lord of the Rings, King Kong in King Kong , Davy Jones in Pirates of Caribbean) Mocap Overview MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Entertainment: 3D puter animations ? Characters in puter animated files (. Polar Express, Monster House) Mocap Overview MOTION PLANNING IN REAL AND VIRTUAL ENVIRONMENTS FALL 2022 Entertainment: Video Games ? Video games by Electronic Arts, Gremlin, id, RARE, Square, Konami, Namco, and others, (. Enemy Territory, Devil May Cry)