3D Game Engine Design

1
3D Game Engine Design

• Chapter 9. Animation of Character
• 1. Key Frame Animation
• ???

2
Animation of Characters

• Animation
• Scene graph?? ?? ??? ??? ?? ???? ????? ??
• Character animation? ??? ??????? ??
• Animation of character? ? ?? ??
• Key frame animation
• Inverse kinematics

3
Key frame animation

• character? ??? ??? ??? ?? ??
• Interpolation? ??
• Key frame(? ??)? ??? ??? ?? ?? ??
• ???? animation??? ?? quaternion? interpolation?
  ??
• Interpolating? ?? ??
• Local translation
• Kochanek-Bartels spline(7.3.4)
• easy
• Local Rotation in this chapter
• difficult

4
Linear Interpolation

• lerp(t, q0, q1) (1-t)q0 tq1 t(q1 q0) q0
• ??
• ?? ??
• ?? interpolation??? ?? ??
• ??
• Linear interpolation? magnitude? ???? ??.
• ???? animation ??? ??.
• ?spherical linear interpolation? ??

??1 lerp
5
Spherical Linear Interpolation

• ??quaternion? 4?? hypersphere?? ?? ??
• ???? ?????? q0,q1? ?? ??? ??? ???
  interpolation???? ??(??2)

??2spherical linear interpolation
6
? quaternion? ?? slerp
??1 ??
??3 ??
??3 slerp
7
? quaternion? ?? slerp

• .
• ? q0? q1??? ???4??
• q1? q1 ?? rotation? ??
• But, slerp(tq0,q1) ? slerp(tq0,-q1)
• ??B??
• q0.q1? 1? ????? ?? sin( )? 0? ??????,lerp??

??4 hypersphere? quaternion
8
? quaternion? ?? Slerp ? ?

• ?? A ?? B

9
? quaternion? ?? slerp

• spline interpolation? ??? ? ???
• ??? ??? Slerp? ?? ???
• Slerp(t,q0 ,q1) q0 (q0 1 q1 ) t ??2 ??
• Slerp(t,q0 ,q1) q0 (q0 1 q1 ) t log ( q0 1
  q1 )
• Extra spins interpolation

10
Spherical Linear Interpolation

• ??
• ???? ?????? ????
• ??
• ? ??? ??? quaternion?? slerp? interpolation??
  ?????? ??? ??
• ?, ?????? ??? ??? ??? ??.
• ? spherical cubic interpolation

??5 linear,spline? ??
11
Spherical Cubic Interpolation

• ??? slerp? ???? ??
• P?? q?? ?????? p,q? ?? ??? ??? ??, a,b? ?? ?? ??
  ??? ??

p345?? ??
12
Spline interpolation of Quaternions

• N?? quaternion?? ??
• qn, an , bn (n0, 1, 2, N-1)
• ??n? ??? Sn(0)Sn-1(1)? ?? ??
• an, bn? ???.
• Interpolation? ??? ?? ????? ??.
• Sn(t) squad(t, qn, qn1 , an , bn1) ??3 ??
• ???? interpolation ??? ?? ?? an, bn? ??? ??.
• an bn qn exp-(log(qn-1 qn-1) log(qn-1
  qn1) ) / 4

13
Key frame animation? ?
?? C ?? D
14
Updating a Key Frame Node

• Key frame? ???? node
• local translation Kochanek-Bartels spline or
  linear interpolation
• local rotation slerp or squad
• Pseudocode
• void KeyFrameControllerUpdate (float time)
• InterpolateTranslation(time, localTranslate)
• InterpolateRotation(time,localRotate)
• Controller? update? world transform? ?? ?? ??