Character Animation
CGDD 4003
The Skeletal Hierarchy
(aka the “rig”)
 Based on the concept of bones
 Each bone has exactly one parent
 Each bone has a transform
 Not necessarily a matrix (later)
 How it differs from its parent
 If its transform is identity matrix
 Same translation
 Same rotation (orientation)
 The root bone has no parent (e.g. pelvis)
 Rotations/translations are relative to local coordinates
 There are also synthetic root bones (ground shadows)
Kinematics
 Forward kinematics
 Moving a parent bone moves the children
 Easy to program, hard to animate
 Inverse kinematics (IKs)
 Moving child bones affects parent bone
 Easier for animators
 Solve iteratively
 Need to draw this on the board…
Euler Angles
(pronounced “Oi-luh”)
 3 angles to describe orientation around 3 axes
 Order of rotations is important!
 Two rotations can result in the same orientation
 Usually stored in a 3x3 matrix.
 Two similar rotations have similar values in matrices
 Linear blending will be ok
 Size is large
Enter the Quaternion
 Another way to represent rotations
 Great for interpolation (thus, common)
 Uses 4 components (x, y, z, w)
 In general, (x, y, z) is the axis of rotation
 Length of (x, y, z) is sine of half the rotation angle
 w is the cosine of half the rotation angle (20° vs. 340°)
Animation vs. Deformation
 Animation
 Changing poses to the skeleton over time
 No sense of the vertices that surrounds it
 Deformation
 Applying the skeleton to the mesh
 No sense of animation (time)
 Animation Controls
 Need to be able to start, stop, determine time, change speed
 Have a control for each animation for each instance of object
Animation Storage
 How big?
 Store 4x3 matrix for each bone, for each frame
 30 fps, 50 bones
 5 major characters, 100 animations each
 15 minor characters, 20 animations each
 Animation lasts 4 seconds
 𝑆𝑝𝑎𝑐𝑒 = 30𝑓𝑝𝑠 ∙ 4𝑠𝑒𝑐 ∙ 50𝑏𝑜𝑛𝑒𝑠 ∙ 4 ∙ 3 ∙ 4 ∙
5 ∙ 100 + 15 ∙ 20
220𝑀𝐵
 Xbox 360 has 512MB and Wii has 88MB
 The animation system takes up nearly ¼ of all memory?
 Can we do better?
=
Animation Storage
 Eliminate unnecessary data
 Most bones don’t need shear, scaling
 Some don’t need translation (hips, knees, elbows)
 Some characters hardly move!
 Space
 Scaling, Shearing,
Translation = 3
 Rotation
(quaternions) = 4
T.K. Baha from Borderlands
Animation Storage
 Assume:
 10% of bones shear
 20% of bones scale
 50% have translation
 90% have orientation
 One bone / frame is now:
4𝑏𝑦𝑡𝑒𝑠 ∙
0.1 ∙ 3 + 0.2 ∙ 3 + 0.5 ∙ 3 + 0.9 ∙ 4
= 24 𝑏𝑦𝑡𝑒𝑠
vs. the 48 bytes previously
 However, we have to reconstruct the 4x3 matrix for each bone now!
Note: We’re now at 110MB, still 5 times bigger than budget for Wii. Can we do better?
Animation Storage
 Obvious candidate: don’t use 30 fps!
 Keyframing: set important poses and then interpolate (old
animation technique)
 On “average”, 10 keyframes per second
 1/3 the space = 37MB!
 OK for Xbox (64MB), bad for Wii (22MB)
 Keyframing problems:
 Loses data
Note: we’re at 37MB. Can we do better?
Animation Storage
 Linear interpolation between frames
 𝑟𝑒𝑠𝑢𝑙𝑡 =
1 − 𝑡 ∙ 𝐹1 + (𝑡 ∙ 𝐹2 ))
 𝑡 is time and 𝐹1 and 𝐹2 are frames
 Higher Order Interpolation
 Use Bezier (pronounced “Beh-zee-ay”)
 Cubic function, with continuity (C0, C1, C2…)
 Define controls at endpoints (𝑇1 and 𝑇2 )
 Can drop the memory usage by ¼
Continuity
Image from Autodesk.com
Playing Animations
 Local time
 is in reference to the animation
 E.g. 0.0 – 5.0 for a 5 second animation
 Can also normalize from 0.0-1.0 and have playback speed
 Global time is the elapsed time
 May not match the local time
 Can pause
Blending Animations
 Playback of multiple animations together
 Linear Interpolation (aka “lerp”)
 For quaternions
 Normalizing lerp (nlerp) – each component is linearly blended
and then renormalized
 Spherical lerp (slerp) – the most common
 Log-quaternion lerp – complex
Blending Animations
 Bone masks:
 Imagine waving and walking at the same time
 0.0 = don’t use this bone when blending
 1.0 = completely include that bone
 0.5 = fractional blend
Motion Extraction
 Things get hard when the character moves
 Animator may/not model at (0,0,0)
 What happens during walking? Sliding feet?
 What about climbing a ledge?
 Must match world/physics engine!
 Motion Extraction: “process of taking an animation and deriving
the overall movement of a character” – from your text!
Motion Extraction
 What if the model doesn’t stay at the origin?
 Linear Motion Extraction
 Take position of root bone at first/last frame
 Divide by duration
 Works great for straight lines
 Not so great for running in circles
 Composite Motion Extraction
 Takes into account the rotation
 Variable Delta Extraction – just ask the root bone how much
it moved since the last frame
Example
Mesh Deformation
1.
Transform each bone into World Space
1.
2.
3.
4.
Start at the root of the skeleton
Multiply it’s transform by
the instance’s transform
(you now know where
the root bone is in the world)
Take the transform of each child
bone and multiply it by the
root bone’s world transform
Use recursion all the way down
Mesh Deformation
2.
Find the delta from the rest pose
1.
2.
3.
Deform the vertices
1.
2.
4.
Must “undo” the rest pose using the inverse transform
Multiply world transform by the inverse
Each vertex is affected by several bones (4 max)
Influential bones stored as a list of bytes
Deform the vertex normals
Other Considerations