Motion Graphs Davey Krill May 3, 2006

Overview: Project 2 MotionTestBed Framework Motion Graph for 2 motion clips Finding candidate transitions Selecting transition points Creating Transitions (linear blending) Goal / Testing / Results Project 3

Motion Framework Skeleton contains all information about the motion clip Frames indicate the orientation of joints and root position at that time Joints are hierarchically related, defining their position relative to their parent joint and globally with the root joint Poses can be adjusted with rigid transformations [quaternion rotation, (x,y,z) translation]

P2: Find Candidate Transitions Goal: Find the distance between two frames Method: Compute the minimal sum of squared distances between corresponding points within the point clouds of each frame pose Compute this distance for every pair of frames in the motion set

P2: Select Transition Points The 2D distance map can have several local minima Need to select only those below a certain threshold Good transitions vs. high graph connectivity trade-off Finding ways to determine this threshold is one focus of Project 3 Sampled 2D error function (Local minima are red dots)

P2: Creating Transitions Align the second motion with the appropriate 2D transformation (the minimal Θ, x, z). Create the transition frames between the ith frame of motion 1 and jth frame of motion 2. This is done by linearly blending the ith to ith+k-1 frames with the jth-k+1 to jth frames. Use spherical linear interpolation on joint rotations, and linearly interpolate root positions

P2: Testing and Results Goal of P2: Find transition points between two motions and generate linearly blended transitions at those points (i.e. create a 2-motion graph). From this 2-motion graph, generate a new motion clip by manually selecting a single transition point. Distance correctness: 2 identical motions, zero-diagonal on 2D distance function Example: two kicking motions

P2: Two Kicking Motions Empirically, any transition with a distance error <6.00 generated a “good” motion clip Linear blending has been omitted to better illustrate the transition points Clip72-47.bvh Distance error of 5.11 Clip86-70.bvh Distance error of 4.87 Clip62-102.bvh Distance error of 31.66 Example of how linear blending wouldn’t help since the direction of momentum is different Which brings us to…

Project 3 Full motion graph Transition point metrics Handle arbitrary number of motions Pruning the graph Testing Transition point metrics Beyond point cloud matching Evaluate physical state, momentum, footskate

P3: Full Motion Graph Nodes are choice points connecting clips of motion Arcs between nodes are clips of motion Expands on 2-motion graph. Each new motion added to the graph searches for transition points with the rest of the nodes, and creates new arcs appropriately.

P3: Pruning the Graph Goal: Prune the graph such that it is possible to generate arbitrarily long streams of motion. Remove any nodes with few or no outgoing edges. How to handle transition points that are “close neighbors” yet still distinct local minima. Example: (78, 57, 5.48) and (76, 51, 6.83) are very close transitions. How should these be handled? Eliminate one? Let both persist?

P3: Testing Problem of generating arbitrary motion clips from the motion graph not generally addressed. Testing by having advance knowledge of where the good transitions are and manually walking the graph. In progress…

P3: Transition point metrics Problem: Determining what local minima threshold to use when selecting transition points is somewhat of a hack. As was seen from the earlier example, there are cases when using the point cloud distance is not a good enough metric for determining transition points. Need to consider momentum, physical state (imagine a person jumping up and down) Adaptive thresholds for: Slow motions vs. fast motions Familiar (walking) motions vs. strange motions Context of motion determines whether you want a low or high threshold value

Work in Progress Generate examples of an arbitrarily long motion graph walk Develop better graph pruning Evaluating threshold-finding techniques Spacing out transition points Adaptive threshold model

Questions?