Character Animation

1. Character Animation CGDD 4003

2. 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)

3. 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…

4. Euler Angles(pronounced “Oi-luh”) • 3 angles to describe orientation around 3 axes • Order of rotations is important! • Two rotations can result in the sameorientation • Usually stored in a 3x3 matrix. • Two similar rotations have similar values in matrices • Linear blending will be ok • Size is large

5. 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°)

6. 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

7. 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 • Xbox 360 has 512MB and Wii has 88MB • The animation system takes up nearly ¼ of all memory? • Can we do better?

8. 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

9. Animation Storage • Assume: • 10% of bones shear • 20% of bones scale • 50% have translation • 90% have orientation • One bone / frame is now: 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?

10. 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?

11. Animation Storage • Linear interpolation between frames • is time and and are frames • Higher Order Interpolation • Use Bezier (pronounced “Beh-zee-ay”) • Cubic function, with continuity (C0, C1, C2…) • Define controls at endpoints (and ) • Can drop the memory usage by ¼

12. Continuity Image from Autodesk.com

13. 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

14. 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

15. 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

16. 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!

17. 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

18. Example

19. Mesh Deformation • Transform each bone into World Space • 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

20. Mesh Deformation • Find the delta from the rest pose • Must “undo” the rest pose using the inverse transform • Multiply world transform by the inverse • Deform the vertices • Each vertex is affected by several bones (4 max) • Influential bones stored as a list of bytes • Deform the vertex normals

21. Other Considerations