1. Joshua Barczak CMSC 435 UMBC
Animation
Joshua Barczak CMSC 435 UMBC

2. Animation

3. Animation What’s really going on… Discrete frames
Incremental change between frames
Illusion of motion

4. Flip Books Hand drawn frames, packed into large texture N M 0,0 1,0
u = (u + (frame % N)) / N;
v = (v + (frame / N)) / M; M
0,0
1,0
0,1 u v
libgdx

5. Animation Traditional Animation Pipeline
Lead animator draws “key” frames
“In-betweener” draws frames between keys
Key
Key

6. Animation Computer Animation Pipeline Animator specifies “key frames”
Computer interpolates
Key
Key

7. Animation

8. Keyframing We can key anything we want: Position Rotation Scale Color
Texture coordinate
Light intensity

9. Animation

10. Splines
BoatDesign.net

11. Hermite Spline T0 P1 P0 T1

12. Piecewise Hermite Splines

13. Piecewise Hermite Splines
Catmull-Rom spline
Shared tangents are vectors between neighbor points
C1 continuous
Endpoint interpolating

14. Kochanek-Bartels Curves
Use different tangents in each segment
Artistic control
TCB
Tension
Continuity
Bias
All zero:
Catmull-Rom curve
See book, pg 420

15. Tension
T=-1
T=0
T=1
How close it is to a straight line

16. Create local discontinuities
Continuity
C=-2
C=0
C=1
Create local discontinuities

17. Overshoot/Undershoot
Bias
B=-1
B=0
B=1
Overshoot/Undershoot

18. Animated Rotation Euler angles Easy to set Doesn’t animate well
Rotations about independent axes
Yaw/Pitch/Roll
Easy to set
Doesn’t animate well
Gimbal lock
Quaternion interpolation used instead
Wikipedia

19. Quaternions Alternate representation for rotations
Rotation 2a radians around axis N:
Q=[sin(a)N, cos(a)]
Convertible to/from rotation matrix
Much more compact
Stable interpolation

20. Ancient DirectX SDK sample
Vertex Blending
Interpolate between meshes
Same topology
Different vertex positions
Models as keyframes
Ancient DirectX SDK sample

21. Ancient DirectX SDK sample
Vertex Blending
Issues
Ease of authoring
Difficult to tweak the animation
Data size
Ancient DirectX SDK sample

22. Skeletal Animation Skeleton:
Hierarchy of joints (bones)
Deform a mesh (skin) based on joint rotation
Okino.com

23. Hierarchical Model Torso Head Left Shoulder Hips Upper Arm
Lower Arm
Hand
Hips
Left Upper Leg
Lower Leg
Foot

24. Forward Kinematics Given a set of joint transforms, where’s the hand?
(or foot or head or …)
End effector
Just apply nested transforms
We know how to do that!

25. FK Example Location of hand: Construct hand to world transform: Head
Hand_to_elbow * Elbow_to_shoulder * Shoulder_to_head * head_to_world
Hand
Shoulder
Elbow

26. Inverse Kinematics Given desired effector position, find joint angles
Common Examples:
Foot placement
Pointing/Grasping
Constrained optimization
Preserve limb length
Arms doesn’t bend that way

27. Skeletal Animation Motion Capture Track markers on actor
Infer joint locations from markers
Often significant manual cleanup
Kevin Durant at Electronic Arts Motion Capture Studio - AP / Richard Lam

28. Skinning Model authored in “rest pose”
Mesh vertices “bound” to skeletal joints
Single joint (rigid)
Multiple joints (weighted blend)
Okino.com

29. Skinning For each bone, store: For each vertex: Bind matrix
Bone to world transform for rest pose (B)
Animation curves
Relative to rest pose
Parent bone
For each vertex:
Bone indices and weights
Okino.com

30. Skinning Skinning a vertex Transform into “bind space”
Apply an animated offset
Transform result up the tree

31. Skinning // Sample animated bone offsets for( bones ) M[i] = Li(time)
// compute new bone->world transforms
for( pre-order traversal of skeleton )
M[i] = M[parent[i]] * M[i];
// apply inverse bind matrix
M[i] = M[i] * Binv[i];
// Each vertex has position p, weights w[] and bone indices idx[]
for( vertices i )
for( bones influences j ) position += w[j]*M[idx[j]]*p

32. Blend Shapes Commonly used for faces Sculpt key poses
Expressions
Phonemes
Animate pose weights
Curve per shape
Maya Documentation

33. Freeform Deformation Define regular grid Move grid points
Moves objects
Lattice defines a “bezier volume”
Sederberg and Parry, 1986

34. Physics Based Animation
Simulate physics to predict motion
Starting point for hand animation
Things too large/difficult to hand animate
In general, must be:
Stable
Not too slow
Art-directible

35. Simulation Rigid Bodies Simulate physics
Detect collisions and apply “penalty forces”
Typically:
Linear/Angular velocity
Discrete time steps
Discrete/Continuous collision detection

36. Simulation Cloth Mass-spring simulations
Cloth/Cloth and cloth/object collision response
Brad Werth
Bridson et al. Robust Treatment of Collisions, Contact and Friction for Cloth Animation

37. Alliez et al. Variational Tetrahedral Meshing
Simulation
Soft-Bodies
Tetrahedral mesh models
Approaches
Mass-spring
Conserve edge lengths
Finite element
Conserve volume
Alliez et al. Variational Tetrahedral Meshing
Irving et al. Volume Conserving Finite Element Simulations of Deformable Models

38. Simulation Hair Simulate a subset of the hairs
Guide hairs
Interpolate dense hair model from neighboring guide hairs
Direct rendering
Millions of anti-aliased lines
Chang et al. 2002
Pixar

39. Coupling Water and Smoke to Thin Deformable and Rigid Shells
Simulation
Fluid Simulation
Grid-based
Simulate velocity field on discrete grid
Particle based
Move particles directly
Fluid Rendering
Level set surface
Guendelman et al.
Coupling Water and Smoke to Thin Deformable and Rigid Shells

40. Simulation Crowds Agent based Continuum based Use AI techniques
Emmergent behavior
Continuum based
Dynamic vector field
Congestion/hazards
Crowd members as particles
Treuille et al.
Continuum Crowds