Character Animation

Contents

• 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)

Key1t1

Key2t2

Keyntn

Key3t3

…

T

Keyframe Interpolation2

Key1t1

Key(i)t(i)

Keyntn

Key(i+1)t(i+1)

…

T

1*

1

*

*

keykey)1(key

ii

ii

i

Tt

ss

tt

tts

Ttrunctt

1*

1

*

*

keykey)1(key

ii

ii

i

Tt

ss

tt

tts

Ttrunctt

…

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)

• 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)• "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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From Lee and Koh (1995)

Euler angles in ASF

In v’=Mv convention

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,,,,,, xRotyRotzRotzRotyRotxRot

,,

,,,,,,

xRotzRot

zRotzRotxRotzRotzRotxRot

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

• 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.

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

Wvv

1

...2211

iii

NN

wwherew

www

Mvv

MvMvMvv

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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:

iii WBM 1

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1.0/0.0 0.0/1.00.5/0.50.7/0.3

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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:

Tii

Tii

w

w1

1

Mn

Mnn

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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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