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Precomputed Optimal One-Hop Motion Transition
for Responsive Character Animation
Yuki Koyama & Masataka Goto
The Visual Co...
Target Problem
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Overview of Our Method
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Related Work
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
1. Formulating a Search Problem
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
2. Solving the Search Problem in Precomputation
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Results
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Discussions
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Summary
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
The paper, videos, and slides are available at
https://koyama.xyz/project/one-hop_motion_transition/
Appendix
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Vis...
Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation [CGI 2019]
Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation [CGI 2019]
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Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation [CGI 2019]

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Details: https://koyama.xyz/project/one-hop_motion_transition/

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Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation [CGI 2019]

  1. 1. Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation Yuki Koyama & Masataka Goto The Visual Computer (CGI )
  2. 2. Target Problem
  3. 3. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) State Machine-Based Control for Interactive Apps State machine-based control is widely used. Each state is associated with a single motion clip (in the basic usage). In response to run-time user input, the state is changed.
  4. 4. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Source (src) motion Destination (dst) motion Transition Triggered by user input
 at an arbitrary frame Goal: Achieve High-Quality Motion Transition
  5. 5. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Direct Approach (Current Practice) ■ Direct approach: • Begin transition immediately after receiving the trigger • Directly interpolate the src and dst motions ■ Problem: • Visual artifacts (e.g., foot skate)
  6. 6. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Requirements for a New Method ■ A new method should • Be compatible with the state machine-based workflow • Run in interactive real-time apps • Finish the transition as quickly as possible
  7. 7. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Requirements for a New Method ■ A new method should • Be compatible with the state machine-based workflow • Run in interactive real-time apps • Finish the transition as quickly as possible
  8. 8. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Requirements for a New Method ■ A new method should • Be compatible with the state machine-based workflow • Run in interactive real-time apps • Finish the transition as quickly as possible
  9. 9. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Requirements for a New Method ■ A new method should • Be compatible with the state machine-based workflow • Run in interactive real-time apps • Finish the transition as quickly as possible Quick
  10. 10. Overview of Our Method
  11. 11. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Our Approach: “One-Hop” Motion Transition
  12. 12. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Example of Our Results
  13. 13. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Overview of This Work ■ Technical Challenges: . How should we choose a hop motion and arrange it? . How can we enable this in real-time apps? ■ Our Solutions: . Formulating a search problem . Solving the searches in precomputation
  14. 14. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Overview of This Work ■ Technical Challenges: . How should we choose a hop motion and arrange it? . How can we enable this in real-time apps? ■ Our Solutions: . Formulating a search problem . Solving the searches in precomputation
  15. 15. Related Work
  16. 16. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Related Frameworks [Holden+ , ][Kovar+ , ] Statistical modelsMotion graphs [Zadziuk , ] Motion matching ➡ These are incompatible with the state machine-based workflow
  17. 17. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Related Frameworks [Holden+ , ][Kovar+ , ] Statistical modelsMotion graphs [Zadziuk , ] Motion matching ➡ These are incompatible with the state machine-based workflow
  18. 18. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Related Frameworks [Holden+ , ][Kovar+ , ] Statistical modelsMotion graphs [Zadziuk , ] Motion matching ➡ These are incompatible with the state machine-based workflow
  19. 19. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Related Frameworks [Holden+ , ][Kovar+ , ] Statistical modelsMotion graphs [Zadziuk , ] Motion matching ➡ These are incompatible with the state machine-based workflow
  20. 20. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Related Frameworks [Holden+ , ][Kovar+ , ] Statistical modelsMotion graphs [Zadziuk , ] Motion matching ➡ These are incompatible with the state machine-based workflow
  21. 21. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) State Machine-Compatible Approach [Ikemoto+07] [Ikemoto+ ] ■ Similar to ours: • They insert “hop” (intermediate) motions to achieve natural transitions ■ Key difference: • We consider not only naturalness but also quickness to finish the overall transition (explained later)
  22. 22. 1. Formulating a Search Problem
  23. 23. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst
  24. 24. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst (Direct approach)
  25. 25. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst Unnatural transition (Direct approach)
  26. 26. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst
  27. 27. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src hop dst
  28. 28. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst More natural transitions hop
  29. 29. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst hop
  30. 30. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst hop Introducing
 “stay durations”
  31. 31. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Even more natural transitions Trigger src dst hop
  32. 32. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) One-Hop Transition Setting Trigger src dst hopOverall transition duration
  33. 33. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Variables Trigger src dst hop
  34. 34. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Variables Trigger src dst hop . Which motion clip to use as hop
  35. 35. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Variables Trigger src dst hop . Which motion clip to use as hop . Time offset of hop
  36. 36. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Variables Trigger src dst hop . Which motion clip to use as hop . Time offset of hop . Stay duration [src] . Stay duration [hop]
  37. 37. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Objective T⇤ t = arg min Tt { S(Tt) + w R(Tt) } <latexit sha1_base64="T4T3GkSkIxMtJugrGSYghaBpGts=">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</latexit>
  38. 38. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Objective Smoothness cost: Encourage each transition to be as natural-looking as possible T⇤ t = arg min Tt { S(Tt) + w R(Tt) } <latexit sha1_base64="T4T3GkSkIxMtJugrGSYghaBpGts=">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</latexit>
  39. 39. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Objective Smoothness cost: Encourage each transition to be as natural-looking as possible Responsiveness cost: Encourage the overall transition to finish as quickly as possible T⇤ t = arg min Tt { S(Tt) + w R(Tt) } <latexit sha1_base64="T4T3GkSkIxMtJugrGSYghaBpGts=">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</latexit>
  40. 40. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Objective Smoothness cost: Encourage each transition to be as natural-looking as possible Responsiveness cost: Encourage the overall transition to finish as quickly as possible Weight: Control the trade-off T⇤ t = arg min Tt { S(Tt) + w R(Tt) } <latexit sha1_base64="T4T3GkSkIxMtJugrGSYghaBpGts=">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</latexit>
  41. 41. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Search Objective Smoothness cost: Encourage each transition to be as natural-looking as possible Responsiveness cost: Encourage the overall transition to finish as quickly as possible T⇤ t = arg min Tt { S(Tt) + w R(Tt) } <latexit sha1_base64="T4T3GkSkIxMtJugrGSYghaBpGts=">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</latexit> Weight: Control the trade-off
  42. 42. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Evaluating Smoothness of Transitions [Kovar+02] Dissimilar ➡ High cost for transition (potentially non natural) Similar ➡ Low cost for transition (expected to be natural)
  43. 43. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Evaluating Smoothness of Transitions [Kovar+02] High cost ➡ Unnatural transition
  44. 44. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Evaluating Smoothness of Transitions [Kovar+02] Low cost ➡ Natural transition
  45. 45. 2. Solving the Search Problem in Precomputation
  46. 46. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Precomputation ■ Solve the search problem for every possible trigger frame and for every possible state transition • May take a few days depending on the dataset size, but required only once ■ Store optimal transitions in a look-up table • In runtime, retrieve an optimal transition by using the triggered frame as the key
  47. 47. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Precomputation ■ Solve the search problem for every possible trigger frame and for every possible state transition • May take a few days depending on the dataset size, but required only once ■ Store optimal transitions in a look-up table • In runtime, retrieve an optimal transition by using the triggered frame as the key
  48. 48. Results
  49. 49. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Supposed Scenario: Interactive Dancing Let a character dance using a game pad in an improvised manner
  50. 50. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Supposed Scenario: Interactive Dancing ■ Run in Unity • It is straightforward to implement our method using Unity’s PlayableAPI ■ Our dance motion dataset • Around motion clips for hop candidates • Each motion clip has around sec ■ Use frames (= . sec) for individual transitions • I.e., src-to-hop ( . sec) and hop-to-dst ( . sec) ■ No postprocessing applied • E.g., footskating removal (e.g., [Ikemoto+ ])
  51. 51. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Result: “Ghost Force” Disappears by a Standing-Up Motion
  52. 52. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Other Results https://koyama.xyz/project/one-hop_motion_transition/
  53. 53. Discussions
  54. 54. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) The Direct Transition is Included in the Search Space When the direct transition is already good, our solver is likely to select the one-hop transition that is equivalent to the direct transition
  55. 55. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Future Work: Positional & Orientational Constraints ■ Current behavior • Depending on the inserted hop motion, the position & orientation may be changed ■ Future work • Add constraints in the search
  56. 56. Summary
  57. 57. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Summary ■ Optimal one-hop motion transition • It inserts a hop motion between the source and destination motions in an optimal way ■ Consider both smoothness and responsiveness • Try to maximize both in balance ■ Can be precomputed • Run in real-time apps
  58. 58. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Summary ■ Optimal one-hop motion transition • It inserts a hop motion between the source and destination motions in an optimal way ■ Consider both smoothness and responsiveness • Try to maximize both in balance ■ Can be precomputed • Run in real-time apps
  59. 59. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Summary ■ Optimal one-hop motion transition • It inserts a hop motion between the source and destination motions in an optimal way ■ Consider both smoothness and responsiveness • Try to maximize both in balance ■ Can be precomputed • Run in real-time apps
  60. 60. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Summary ■ Optimal one-hop motion transition • It inserts a hop motion between the source and destination motions in an optimal way ■ Consider both smoothness and responsiveness • Try to maximize both in balance ■ Can be precomputed • Run in real-time apps
  61. 61. The paper, videos, and slides are available at https://koyama.xyz/project/one-hop_motion_transition/
  62. 62. Appendix
  63. 63. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Changing Weight
  64. 64. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Future Work: Optimizing Blending Durations (c.f., [Wang+08]) Trigger src dst hop Blending durations
 (we assumed fixed durations)
  65. 65. Yuki Koyama and Masataka Goto | Precomputed Optimal One-Hop Motion Transition for Responsive Character Animation | The Visual Computer (CGI ) Future Work: Blend Tree Blend Tree: Each state can also be associated a dynamic mixture of motion clips Challenge: 
 How can we precompute all the possible blends and store the results?

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