INERTIALIZATION: HIGH-PERFORMANCE ANIMATION TRANSITIONS IN GEARS OF WAR DAVID BOLLO PRINCIPAL SOFTWARE ENGINEER THE COALITION (MICROSOFT STUDIOS)

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1 INERTIALIZATION: HIGH-PERFORMANCE ANIMATION TRANSITIONS IN GEARS OF WAR DAVID BOLLO PRINCIPAL SOFTWARE ENGINEER THE COALITION (MICROSOFT STUDIOS)

2 ANIMATION TRANSITIONS

3 ANIMATION TRANSITIONS Transition from one animation state to another Typically a cross-fade blend between poses Source Blend Target

4 ANIMATION TRANSITIONS Optimizations are often focused on the blend step Fast SLERP, optimizing cache and memory usage, etc Source Blend Target

5 ANIMATION TRANSITIONS Biggest cost is evaluating both Source and Target Source/Target cost is much greater than blend cost Source Blend Target

6 MULTIPLE CHARACTERS If we re lucky Only a few active transitions at once

7 MULTIPLE CHARACTERS But in the worst case Everybody transitions at the same time Double the animation cost

8 CAN WE DO BETTER? Intuition: Real humans don t blend (but they do have inertia) Source Blend Target

9 CAN WE DO BETTER? IDEA: Eliminate blended transitions! Fix the discontinuities as a post-process Source Blend Target

10 CAN WE DO BETTER? IDEA: Eliminate blended transitions! Fix the discontinuities as a post-process Source Target

11 TRANSITIONS AS A POST-PROCESS

12 TRANSITIONS AS A POST-PROCESS

13 TRANSITIONS AS A POST-PROCESS

14 GOALS Respect the original animation No changes when not transitioning Believable and aesthetically pleasing Smooth and momentum-preserving Stay on-model No bad / unnatural poses No overshoot

15 IDEA #0: FILTER DISCONTINUOUS POSE Apply a filter to the output pose stream Difficult to tune Introduces lag Deviates from input even when not transitioning

16 IDEA #1: BLEND FROM POSE Capture pose difference between Source and Target Ease out the difference over time

17 IDEA#1: BLEND FROM POSE

18 IDEA #2: MATCH VELOCITY Capture pose difference between Source and Target Ease out the difference over time Remember Source velocity (via finite differences) Match initial velocity Quintic polynomial [Flash and Hogan 1985] T. Flash and N. Hogan The Coordination of Arm Movements: An Experimentally Confirmed Mathematical Model. Journal of Neuroscience 5, 7 (July 1985),

19 IDEA #2: MATCH VELOCITY

20 IDEA #3: LIMIT OVERSHOOT Capture pose difference between Source and Target Ease out the difference over time Remember Source velocity (via finite differences) Match initial velocity Limit overshoot by controlling initial acceleration Choose a 0 to give us zero jerk at t 1

21 IDEA #3: LIMIT OVERSHOOT

22 INERTIALIZATION

23 INERTIALIZATION

24 INERTIALIZATION INITIAL VALUES xx 0 = xx 1 = 0 vv 1 = 0 aa 1 = 0

25 INERTIALIZATION INITIAL VELOCITY xx 0 = vv 0 = dtt xx 1 = 0 vv 1 = 0 aa 1 = 0

26 INERTIALIZATION INITIAL VELOCITY xx 0 = vv 0 = dtt or 0 xx 1 = 0 vv 1 = 0 aa 1 = 0

27 INERTIALIZATION ACCELERATION xx 0 = vv 0 = dtt or 0 aa 0 = 8vv 0tt 1 20xx 0 tt 1 2 xx 1 = 0 vv 1 = 0 aa 1 = 0

28 INERTIALIZATION ACCELERATION xx 0 = vv 0 = dtt or 0 aa 0 = 8vv 0tt 1 20xx 0 tt 1 2 or 0 xx 1 = 0 vv 1 = 0 aa 1 = 0

29 INERTIALIZATION X(T) xx 0 = AA = aa 0tt vv 0 tt xx 0 2tt 1 5 vv 0 = dtt or 0 aa 0 = 8vv 0tt 1 20xx 0 tt 1 2 or 0 xx 1 = 0 vv 1 = 0 aa 1 = 0 BB = 3aa 0tt vv 0 tt xx 0 2tt 1 4 CC = 3aa 0tt vv 0 tt xx 0 2tt 1 3 xx tt = AAtt 5 + BBtt 4 + CCtt 3 + aa 0 2 tt2 + vv 0 tt + xx 0

30 OVERSHOOT REVISITED

31 OVERSHOOT REVISITED xx 0 = 1.2 vv 0 = 12.6 tt 1 = 0.5

32 OVERSHOOT REVISITED xx 0 = 1.2 vv 0 = 20.0 tt 1 = 0.5

33 IDEA #4: CLAMP TRANSITION TIME xx 0 = 1.2 vv 0 = 20.0 tt 1 = 0.5

34 IDEA #4: CLAMP TRANSITION TIME xx 0 = 1.2 vv 0 = 20.0 tt 1 = 0.3

35 IDEA #4: CLAMP TRANSITION TIME xx 0 = 1.2 vv 0 = 20.0 tt 1 = min(tt 1, 5 xx 0 vv 0 ) tt 1 = 0.3

36 INERTIALIZATION ON ONE SLIDE xx 0 = AA = aa 0tt vv 0 tt xx 0 2tt 1 5 vv 0 = dtt or 0 aa 0 = 8vv 0tt 1 20xx 0 tt 1 2 or tt 1 = min(tt 1, 5 xx 0 vv 0 ) 0 BB = 3aa 0tt vv 0 tt xx 0 2tt 1 4 CC = 3aa 0tt vv 0 tt xx 0 2tt 1 3 xx tt = AAtt 5 + BBtt 4 + CCtt 3 + aa 0 2 tt2 + vv 0 tt + xx 0

37 VECTORS AND QUATERNIONS

38 INERTIALIZING VECTORS Obvious choice: Inertialize x,y,z independently Visual artifacts if vx 0,vy 0,vz 0 are too dissimilar (because of transition time clamping) Instead: Decompose vector into direction and magnitude Inertialize the magnitude

39 INERTIALIZING VECTORS xx 0 = xx 1 =

40 INERTIALIZING VECTORS xx 0 = xx 1 = xx 0 = xx 0

41 INERTIALIZING VECTORS xx 0 = xx 0 = xx 0 xx 1 = xx 1 = xx 1 xx 0 xx 0

42 INERTIALIZING VECTORS xx 0 = xx 0 = xx 0 xx 1 = xx 1 = xx 1 xx 0 xx 0 vv 0 = xx 0 xx 1 tt

43 INERTIALIZING VECTORS xx 0 = xx 0 = xx 0 xx 1 = xx 1 = xx 1 xx 0 xx 0 vv 0 = xx 0 xx 1 tt xx t = xx t xx 0 xx 0 + t

44 INERTIALIZING QUATERNIONS Similar construction to vectors: Decompose quaternion into axis and angle Inertialize the angle

45 INERTIALIZING QUATERNIONS qq 0 = qq 1 =

46 INERTIALIZING QUATERNIONS qq 0 = qq 1 = xx 0 = AAAAAAAA(qq 0 ) xx 0 = AAAAAAAAAA(qq 0 )

47 INERTIALIZING QUATERNIONS qq 0 = qq 1 = xx 0 = AAAAAAAA(qq 0 ) xx 0 = AAAAAAAAAA(qq 0 ) xx 1 = xx 1 xx 0 xx 0 2 tan 1 qq xyz xx 0 qq w Twist of qq 1 around xx 0 K. Shoemake Fiber Bundle Twist Reduction Graphics Gems IV,

48 INERTIALIZING QUATERNIONS qq 0 = qq 1 = xx 0 = AAAAAAAA(qq 0 ) vv 0 = xx 0 xx 1 tt xx 0 = AAAAAAAAAA(qq 0 ) xx 1 = xx 1 xx 0 xx 0 2 tan 1 qq xyz xx 0 qq w Twist of qq 1 around xx 0 K. Shoemake Fiber Bundle Twist Reduction Graphics Gems IV,

49 INERTIALIZING QUATERNIONS qq 0 = qq 1 = xx 0 = AAAAAAAA(qq 0 ) vv 0 = xx 0 xx 1 tt xx 0 = AAAAAAAAAA(qq 0 ) xx 1 = xx 1 xx 0 2 tan 1 qq xyz xx 0 xx 0 qq w Twist of qq 1 around xx 0 qq t = AAAAAAAA: xx 0 AAAAAAAAAA: xx t t K. Shoemake Fiber Bundle Twist Reduction Graphics Gems IV,

50 BLENDING VS INERTIALIZATION

51 BLENDING VS INERTIALIZATION Blending Evaluate both Source & Target during transition Variable anim frame cost Inertialization Only evaluate Target during transition Fixed anim frame cost Source Source Target Blend Target

52 BLENDING VS INERTIALIZATION Blending Manage multiple sets of state during transitions Adds complexity Inertialization Only maintain one set of state during transitions Fire and forget Source Source Target Blend Target

53 BLENDING VS INERTIALIZATION Blending Inertialization

54 BLENDING VS INERTIALIZATION Blending Inertialization

55 INERTIALIZATION IN A GAME ENGINE

56 INERTIALIZATION IN A GAME ENGINE Inertialization Node / Filter Animation System Hooks Code Hooks

57 INERTIALIZATION NODE Evaluated after the main animation graph Input is discontinuous pose stream Output is inertialized pose stream

58 INERTIALIZATION NODE When a new inertialization is requested: Compute and store x 0, v 0 for all joints Store t 1 and set t = 0 Every frame: Update t with delta time Evaluate and apply x(t) for all joints Store the OUTPUT pose in the pose history buffer

59 ANIMATION SYSTEM HOOKS Add inertialization as a new blend curve type When a blend is requested with inertialization type: Inertialize with the supplied blend time Zero the blend time to bypass regular blending

60 CODE HOOKS Expose Request Inertialization to code Eliminate other types of discontinuities And other tricks

61 TIPS AND TRICKS

62 SMOOTHING OTHER DISCONTINUITIES Gears of War 3: Snap character rotation when switching to sprint Gears of War 4: Snap character rotation when switching to sprint Inertialize away the discontinuity

63 LOCOMOTION FILTERING Gears controls are very responsive (twitchy) Filter inputs to locomotion blend spaces If filtered values are too far from actual values Snap to actual values Inertialize Fluid pose even with twitchy inputs

64 FIRE & FORGET MOTION WARPING Don t need to maintain warp point data across transitions Only 1 active warp at a time Simplifies bookkeeping Simplifies replication S. Dickinson. Motion Warping in Gears of War 4 : Doing More with Less. GDC 2017

65 THANK YOU DAVID BOLLO

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