Body Animation

• Main Approaches to Animation
• Motion Editing Techniques
• Arc Length Parameterization

Keyframe

Animation

Animation=Post(time)

Collections of motion curves

• Single degree of freedom(DOF)
• Single Joint (up to 6 DOF)
  • 3 rotation
  • 3 translation (if root or changing bone lengths)
• Entire body

Motion curve representation

• Usually cubic splines
  • Bezier (Catmul-Rom) splines
  • B-Splines

Main Approaches to Animation

Keyframe

• Key poses specified at selected points in time

• Spline curves used to interpolate body position and orientation between key poses

Mocap

• motion data representing position of root and joint angles as a function of time

  • No splines -> every frame a key

• Usually generated by capturing a live actor’s performance

Procedural

• IK-based (Ubisoft)

• Optimization-based

• Physically-based (Ragdoll)

  • Motions generated based on the law of physics

Pose Space

Channels

Many animation systems typically separate the n-dimensional animation into 1-dimensional curves (one for each DOF) called “Channels”

• a channel typically stores the value of a scalar function over some 1D domain (time, distance, health, etc).
• Can be a joint angle or arbitrary parameter value (such as mass)
• normally refers to “scripted” data for a DOF
  • does not refer to the more general case of a DOF changing over time due to physics, procedural animation, etc.

IK can change length of link

Array of channels

• An animation can be stored as an array of channels

• an animation is stored as a 2D array of floats (NumDOFs x NumFrames)

Array of Poses

• An alternative way to store an animation is as an array of poses
• This also forms a 2D array of floats (NumDOFs x NumFrames)

Poses vs. Channels

Which is better

• Array of poses is great for playing back relatively simple animations that need maximum performance. This is often the case in many video games
• Array of channels is used when flexibility is important or generality is valued over raw performance

The bottom line:

• Poses are faster
• Channels are more flexible and can potentially use less memory

Main Editing Techniques

• Interactive Posing
• Adding constraints
  • Position
  • Orientation
• Optimizing motion over a sequence of poses

Warp

Change Playback speed

Given motion curve $m(t)$

$t=h(\tau)=s\cdot\tau$

$\tau$ is the new independent variable (i.e. normal time)

$s$ controls the speed of motion

• To speed up motion adjust time and/or spline knots
  • $t=h(\tau)=s\cdot\tau$ where s > 1
• To slow down motion adjust time and/or spline knots
  • $t=h(\tau)=s\cdot\tau$ where 0 < s < 1

Blending

blend two or more motion (lerp)

Allows two motion curves m1(t) and m2(t) to be interpolated

$m(t_k)=(1-\alpha)m_1(t_k)+\alpha m_2(t_k),\alpha\in[0,1]$

Layering (compositing)

Cross Dissolve

transition from one animation to another (lerp)

linear blend

$m(t)=(1-\alpha(t))m_1(t)+\alpha(t) m_2(t)$

$\alpha\in[0,1],t\in[t_1,t_2]$

$\alpha(t)=\frac{t-t_1}{t_2-t_1}$

• Walk cycle

• run cycle

• Transition form walk to run

  脚着地

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Arc Length Parameterization

Animation Guide

Problem – After playing an animation with root translation, the root joint will snap back to the initial position and orientation after playing the animation  Solution – Add a virtual joint called a “Guide” as a parent of root joint – As a result, root position and orientation transforms are now with respect to the guide frame of reference – At the end of each animation, update the guide joint position to the current position of the character in the world

Foot IK

Allow characters walk over uneven terrain

IK target

Root position

• determine which foot is lower
• Update vertical position of root joint

Foot Position

• use Limb IK with Lfoot_target and Rfoot_target to position feet

Animation Blending

We can define blending operations that affect poses

A blend operation takes one or more animations/poses as input and generates one animation/pose as output

Parameters such as speed, direction, angle, height etc. are used to control the blend

Cross Dissolve

The most common and useful pose blend operation is the ‘cross dissolve’ of two poses p1 and p2

It is ok for Euler Angles to use Lerp

 … but quaternions need to use … Slerp

Handling Angles

If a DOF represents an angle, we need to have the interpolation check for crossing the 0/360 boundary

• Always want to take the shortest path
• Assumes angles range from 0 to 360

if (theta1-theta2 > 180) theta=lerp(theta1-360,theta2,u);
else if (theta2-theta1 > 180) theta=lerp(theta1,theta2-360,u);
else theta=lerp(theta1,theta2,u);

Quaternions

Same goes for quaternions. Since there are always two solutions, we need to force the interpolation to go the ‘short way’.

if (q1 * q2 > 0) q=slerp(q1,q2,u);
else  q=slerp(-q1,q2,u);

Stand to Walk

Consider a situation where we want a character to blend from a stand animation to a walk animation

$s_{walk}=Lerp(1,\frac{T_{walk}}{T_{run}},u)$

Basic Math Blend Operations

• Add
• Subtract
• Scale

Body Turn

As an example of math blending operations, consider a character that walks and turns  One approach to achieving this is to have an underlying walk animation and ‘layer’ (add) some body turn on top of it  We use a ‘turn_right’ animation and a ‘default’ straight forward walk animation as building blocks  The subtract blender gives us the difference between the turn_right and default walk animations at each point in time  We then scale this turning delta and add it on top of the underlying walk animation. The scale factor value (u) can be based on how sharply the character should turn (-1…1)

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• Bilinear Blend
• Combine Blender
• Mirror Blender