Motion Graphs

1. Motion Graphs By Lucas Kovar, Michael Gleicher, and Frederic Pighin Presented by Phil Harton

2. Overview • What • Why • Creating • Using

3. What are motion graphs? • Directed graph representing a roadmap of motion data for a character • Edges are clips of motion, some from the original motion capture, some generated as transitions • A vertex defines 2 sets of motion clips where motions from one set can flow seamlessly into motions from the other

4. A simple motion graph Run2/Jog Jog Walk2 Run2 Run2/Run2 Walk2/Walk1 Run1 Walk1/Walk1 Walk1 Jog/Walk1 Original motion data Walk1 Walk2 Run1 Jog Run2

5. Why do we want them? • To better utilize motion capture data because it’s: • Difficult to modify • Time consuming and expensive • Hard to use in animations without having captured the exact motion desired

6. Building motion graphs • Identify transition candidates • Select transition points • Eliminate problematic edges

7. Identify transition candidates • For each frame A, calculate its distance to each other frame B by basically measuring volume displacement • Use a weighted point cloud formed over a window of k frames ahead of A and behind B, ideally from the character mesh • Calculate the minimal weighted sum of squared distances between corresponding points, given that a rigid 2D transformation may be applied to the second point cloud

8. Identify transition candidates

9. Select transition points • The previous step gave us all the local minima of the distance function for each pair of points • Now we simply define a threshold and cut transition candidates with errors above it • May be done with or without intervention • Threshold level depends on type of motion – eg. walking vs. ballet

10. Create transitions • For each pair of frames Ai and Bj which fell under the distance error threshold, blend Ai through Ai+k-1 with Bj through Bj-k+1 • Align frames with appropriate rigid 2D transformation • Use linear interpolation to blend root positions • Use spherical linear interpolation to blend joint rotations • Treat constraints as binary flags – frames in first half of transition use A’s constraints, second half use B’s • Transition tagged with union of A and B’s labels

11. Create transitions • Blend weight function • Root position interpolation • Joint rotation interpolation

12. Eliminate problematic edges • We want to get rid of: • Dead ends – not part of a cycle • Sinks – part of one or more cycles but only able to reach a small fraction of the nodes • Logical discontinuities – eg. boxing motion forced to transition into ballet motion • Goal is to be able to generate arbitrarily long streams of motion of the same type

13. Eliminate problematic edges • Each frame is associated with a set of 0 or more labels • For each unique set of labels, form a subgraph of edges whose frames have exactly this set • Find the strongly connected components (SCCs) – maximal set of nodes where there is a connecting graph walk between each ordered pair • Discard all edges that aren’t in the largest SCC • Give warning if: • A set of labels has below a certain threshold of frames • For any ordered pair of SCCs there is no way to get from the first to the second

14. Using motion graphs • We have a database of motion segments and mappings between them, now we want to find motion streams that conform to user specifications • This is approached as a search problem, where the user specifies a non-negative scalar error function g(w,e) as well as a halting condition • Total error of a path w defined as:

15. Searching • Goal is to find a complete graph walk that minimizes f(w) • Use branch and bound – keep track of the best complete graph walk wopt and cut current branch when the error exceeds f(wopt) • Works best when a tight lower bound is found early • Use a greedy ordering heuristic – for a set of unexplored child nodes, select the one that minimizes g(w,c)

16. Searching • Even with branch & bound and ordering heuristic, search is still exponential • Trade some optimality for speed by searching incrementally • Find optimal graph walk of n frames, retain first m nodes and search again from the last retained node • Their implementation used 80-120 for n (2.67 to 4 sec), 25-30 for m (~1 sec)

17. Defining optimization criteria • So how do you define g(w,e) to find your desired motion?? • First, two guidelines: • g should give some sort of guidance throughout the motion, not just evaluate the end result • g should be no more restrictive than necessary – balance guiding search to a particular result with allowing it to consider many options

18. Path synthesis • The example application they present is to make a character travel along a specified path on the ground • Basic strategy for g is to measure difference between actual path traveled and desired path • P(s) is the point on P whose arc-length distance from the start is s • s(ei) is the arc-length from frame 0 to frame i in edge e

19. Path synthesis • Potential problem if character stands still with no incentive to move, thereby accruing zero error • Fix this by replacing s(ei) with t(ei), which forces a small amount of progress with each frame • If we wish to require different types of motion, break the path into segments by type of motion desired during each part • If character is within threshold distance from end of current path, allow search to consider motion edges of both types, otherwise just the type of the current path • Allow only one type switch per path

20. Path synthesis applications • Interactive control • User controls a character, motion clips are selected in real time • High-level keyframing • Animator decides what the character should do and where, rather than tedious keyframing • Motion dumping • Same as the first, but with AI characters • Crowds • Paths are generated for multiple characters to avoid collisions

21. Questions?