AnimationBlending

Animation

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Code Structure for Animation

struct JointPose {
	Quaternion m_rot; //q
	Vector3 m_trans; //t
	F32 m_scale; //s
}

struct AnimationSample{
	JointPose* m_aJointPose;
}

struct AnimationClip{
	Skeleton* m_pSkeleton; //指向骨骼
	F32 m_framePerSecond;
	U32 m_frameCount; 
	AnimationSample* m_aSamples; //每帧的数据
	bool m_isLooping;
}

len(m_aSamples) is m_frameCount+1 when m_isLooping == False, else m_frameCount;

Animation Retargeting

• Animation is usually compatible with only one skeleton
  • But some closely related skeletons can use these animations
  • Only if engine supports ignoring animation channels that cannot be found in skeleton being animated
  • Advanced research on retargeting animations on totally different skeletons

Continuous Channel Functions

• According SQT data format for each sample,
  • 10 scalar-valued functions per joint
  • the time continuous functions per joint is a channel
  • channel functions should be smooth and continuous across the entire animation clip
  • many engines LERP bettwen the samples, making it piecewise linear approximations to the underlying continuous functions

Metachannels

• channels that do not have to do with posing
  • but used to be synchronized with the animation
• event trigger channel
  • sound, particle effects and so on
• animated locator
  • special joint
  • such as camera position, orientation, fov…
• texture coordinates scrolling
• texture animation
• animated parameter
  • material
  • lighting

Skinning and Matrix Palette Generation

Attaching the vertices of a 3D mesh to a posed skeleton is call skinning

Per-Vertex Skinning Information

• a skinned mesh is attached to a skeleton by means of its vertices.
• each vertex can be attached to one or multiple joints
  • if multiple, the position becomes weighted average of the positions that it would have assumed had it bound to each joint independently
  • so each vertex information should including
    • the index of joints to which it is bound
    • the weighting factor for each joint
  • the maximal no of bound joints is usually 4
• data structure:

  struct Skinned Vertex{
  	float m_position[3];
  	float m_normal[3];
  	float m_u, m_v; //u,v for texture cordinates
  	U8 m_jointIndex[4];
  	float m_jointWeight[3];
  }
  

Mathematics of Skinning

• Skinning matrix: transform vertices from original position in bind pose to current position that correspond to the current pose.
  • always in model space
• One joint example
  • (K_j)_W = (B$_{j \to M}$j→M​)^-1C$_{j \to M}$j→M​ M$_{M \to W}$M→W​
  • V$^C_M$MC​ = V$^B_M$MB​K$_{j}$j​
• Multiple Joints:
  • V$^C_M$MC​ = $\Sigma_{i=0}^{N-1}$Σi=0N−1​ w_iV$^B_M$MB​K$_{j_i}$ji​​

Animation Blending

more than 1 animation clip contribute to the final pose of character

LERP Blending

• (P_LERP)_j = LERP((P_A)_j, (P_B)_j, $\beta$β) = (1 - $\beta$β)(P_A)_j + $\beta$β(P_B)_j
• P$_{skel}^{LERP}$skelLERP​ = { (P_LERP)_j } |$^{N-1}_{j=0}~$j=0N−1​ 
• $\beta$β is called the blending percentage or blend factor
• SQT format data is easy to blend, not as 4X4 matrix
• T and S: vector LERP, Q: LERP or SLERP
• independently on each joint, parallel calculated

Applications of LERP Blending

• Temporal Blending
  • finding intermediate poses between sampled poses
• Motion continuity: Cross Fading
  • clip transitions may pop, not smooth
  • C0 continuity: path trace smooth
  • C1 continuity: velocity smooth
  • C2 continuity: second derivatives of the motion path smooth
  • C3 and higher …
  • LERP blending used in transitions to achieve C0 or C1 continuity is called cross fading
  • overlap time, $\beta$β from 0 to 1
  • types of cross fading
    • smooth transition: Clip A and B play simultaneously, $\beta$β changes over time
    • Frozen transition: A stops and B gradually takes over
      • usually used in unrelated clips
    • blend factor $\beta$β functions
      • linear, cubic
      • ease-in, ease-out
    • Core poses
      • every clip starts and ends in these poses
      • C0 continuity: ensure two core poses match
      • C1 continuity: authoring a single smooth animation into A end and B start

Directional Locomotion

pivotal movement: always face to where it turns
targeted movement: moving sideways, backward, forward, keeping its face to a target

• targeted movement
  • forward, strafe left, strafe right
  • LERP blend between two adjacent clips, $\beta$β according to angle
  • backward not included because of legs crossing each other
    • one feasible approach: use to hemispherical blends, one for forward and another for backward; explicit transition animation is played between hemisphere switch
• pivotal movement
  • always play forward clips
  • slightly leaning sideways when turning
  • author three clips: move straight forward, extremely left turn, extremely right turn
  • LERP blending between them to create desired turn pose

Complex LERP Blends (DELETE 583)