Character Animation
Contents
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Keyframe animation
Mocap
Smooth skin by vertex blending
Rigging & retargeting
Gait analysis
(Ragdoll physics)
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Keyframe & Inbetweening
Keyframe Interpolation1
• Periodic motion, with n keys, period T
– Each key contains the pose-defining parameters
• At time t, subtract integer multiples of T (so that 0  t* < T)
• Use t* to determine the interpolating keys
– the max i with t(i) < t*
• Linearly interpolate key(i) and key(i+1)
Key1
t1
Key2
t2
Key3
t3
T
…
Keyn
tn
Keyframe Interpolation2
Key1
t1
Key(i)
t(i)
…
Key(i+1)
t(i+1)
…
T
t *  t  truncTt  T
t  ti
s
ti 1  ti
*
key  (1  s)  keyi  s  keyi 1
*
Keyn
tn
Quake II（雷神之錘II）
• First-person shooter game by id software in 1997
• Md2: the model format used by Quake II
• Model archive: http://planetquake.gamespy.com/quake2/
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Better than linear interpolation
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MOCAP
• Motion Capture
– File format: ASF/AMC
– Database, mixamo
– Sample program
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ASF/AMC (ref)
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ASF (Acclaim Skeleton File)
AMC (Acclaim Motion Capture data)
:root
:bonedata
:hierarchy
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Root
• "axis" keyword in the root section defines the
rotation order of the root object.
• "order" keyword specifies the channels of motion
that are applied to the root and in what order they
will appear in the AMC file.
• "position" and "orientation" keywords are each
followed by a triplet of numbers indicating the
starting position and orientation of the root. These
are typically, but not always, zero.
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Bonedata (ref)
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"id" unique id for the segment
"name" alphabetic identifier for bone.
"direction" the direction of the segment in (world coordinate system)
"length" The length of the segment.
"axis" an axis of rotation for the segment. The axis line indicates the initial
orientation of a bone’s axes relative to fixed, global axes
• "dof" The dof line tokens determine:
– what degrees-of-freedom exist between a bone and its parent
– the order in which these degrees-of-freedom are written in the AMC file
– the sequence in which rotations are applied to the bone
• "limits" For each channel that appears there will be a pair of numbers
inside parenthesis indicating the minimum and maximum allowed value
for that channel
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Example
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In-Depth Bonedata
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lfemur
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lfoot
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In v’=Mv convention
From Lee and Koh (1995)
Rotx, Rotz,    Rotz,  Rotx, Rotz, Rotz,  
 Rotz,  Rotx, 
Euler angles in ASF
Rotx,  Rot y,  Rotz,    Rotz,  Rot y,  Rotx,  
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Transformation Code
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Skinning
References:
Rotenburg(UCSD), Frost (UCI), code
Skinning Introduction
• 3D character models play an important role in
gaming
• Organic models are more complex to render than
rigid models
– Organic: humans, animals, etc.
– Rigid: building, rock, etc.
– The mesh that defines the shape of the model constantly
changes as the models animate
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Skinning Introduction (cont)
• The animating mesh is referred to as a “skin”
• Skinning is the process of animating the mesh
• Skinning has been traditionally done on the
CPU
• As 3D character models complexity increases,
skinning is done on the video cards using
vertex shaders
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Methods to Animate
Skinned Characters
• Keyframe animation (as in MD2)
– Save characters in “keyframes” and blend
– Suitable for low polygon models
– On high-detail models, it can be memory intensive
• Matrix palette skinning
– Weighting individual points to the bones
– Just the skeletal animation needs to be saved (rather than
the whole models in keyframes)
• Not mutually exclusive
– Face/hand for keyframes; matrix palette for the rest
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Vertex Blending
• Also known as:
– Matrix palette, skeleton-subspace deformation
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How Bones are Created
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Obtain the skin model
Duplicate the skin
Scale down fractionally
Cut the smaller skin into smaller body parts
which are used as bones
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Skinning
Simple Skin
•every vertex of the
continuous skin mesh is
attached to a joint.
•every vertex is transformed
exactly once.
v  v  W
Smooth Skin
•a vertex can be attached to
more than one joint with
adjustable weights that control
how much each joint affects it
•Vertices rarely need to be
attached to more than three
joints
•Each vertex is transformed a
few times and the results are
blended
v  w1 v  M1   w2 v  M 2   ...wN v  M N 
v   wi v  M i  where wi  1
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Smooth Skin – Binding Matrix
• we use a binding matrix B for each joint that
defines where the joint was when the skin was
attached and premultiply its inverse with the
world matrix:
1
M i  B i  Wi
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1.0/0.0
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0.5/0.5
0.7/0.3
0.0/1.0
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• To compute shading, we need to transform
the normals to world space also
• If the matrices have non-rigid transformations,
then technically, we should use:


n 
 w n  M 
 wi n  Mi
1T
1T
i
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Limitation
• Smooth skin is very simple and quite fast, but
its quality is limited
– Joints tend to collapse as they bend more
– Very difficult to get specific control
– Unintuitive and difficult to edit
• Still, it is common in games and commercial
animation!
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Other Topics
Rigging, retargeting, gait analysis,
ragdoll physics
What is rigging (ref)
• A character rig is essentially a digital skeleton
bound to the 3D mesh. Like a real skeleton, a
rig is made up of joints and bones, each of
which act as a "handle" that animators can
use to bend the character into a desired pose.
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Automatic Rigging
(Baran & Popovic, 2007)
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Automatic Rigging (cont)
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Retargeting Animation
from Rig to Rig (ref)
• When you retarget animation between rigs, the
retargeting operator figures out which rig elements
match based on their tags. Then it maps and
generates the animation that is transferred to the
target rig.
• Online motion retargeting 1999
• Youtube (havok)
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Mixamo
• Auto-Rigger (youtube)
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Gait
•
Gait is the pattern of movement of the limbs of animals, including humans, during
locomotion over a solid substrate. Most animals use a variety of gaits, selecting gait based
on speed, terrain, the need to maneuver, and energetic efficiency. Different animal species
may use different gaits due to differences in anatomy that prevent use of certain gaits, or
simply due to evolved innate preferences as a result of habitat differences.
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Ragdoll physics
• Verlet integration
• IK postprocessing
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