Animation of 3D surfaces

Transcription

1 Animation of 3D surfaces

2 Motivations When character animation is controlled by skeleton set of hierarchical joints joints oriented by rotations the character shape still needs to be visible: visible = to be rendered as a continuous shape typically, a surface is rendered 2

3 Motivations visible shape is made of organic tissues 3

4 Motivations visible shape is made of organic tissues 4

5 Motivations What is the goal of 3D animation? 5

6 Motivations 3D animation workflow 6

7 Motivations Animation of 3D surface is actually the most practical thing: direct connection with modeling phase shape and texture light structure, easy to animate possibly real-time works will be focused on workarounds to cope with this approximation of reality 7

8 Overview Skinning Non-linear deformers Shape morphing Mesh edition 8

9 Overview Skinning Non-linear deformers Shape morphing Mesh edition 9

10 Skinning Goal: bind a skeleton and a shape P 1 P P P 2 10

11 Skinning Linear blend skinning P P2 P P1 P = w1*p1 + w2*p2 11

12 Skinning Linear blend skinning B A P Q B A P2 Q P1 P P = w 1 *P1 + w 2 *P2 w i : [0..1], skin weights 12

13 Skinning Linear blend skinning M 2 (θ) P 0 P 2 P 1 P θ M 0,1 M 0,2 M 1 P = w 1 *P 1 + w 2 *P 2 M : R and T with P i = M 0,i M i (θ)m -1 0,i P 0 13

14 Skinning Linear blend skinning A P 0 Q 0 B A Q B M 2 (θ) P θ M 0,1 M 0,2 M 1 P = Σ i w i * M 0,i M i (θ)m -1 0,i P 0 Implemented as Skin>Smooth bind in Maya 14

15 Skinning Linear blend skinning B A P B A P(θ) δ δ λ Q λ θ Q(θ) 15

16 Skinning Limitations P = Σ i w i * M 0,i M i M -1 0,i P 0 = ( Σ i w i * M 0,i M i M -1 0,i ) P 0 Non-rigid transformation 16

17 Skinning Improvements Skinning as a prediction function from joint configuration to 3D shapes V = f a (θ) = Σ i a i f( θ -θ i ) [ θ n, V n ] θ in R m, with m joints dof V in R p, with p mesh vertices a i in R p, n parameters [ θ 1, V 1 ] [Lewis et al., 2000] [ θ i, V i ] a = argmin Σ i V i f a (θ i ) 2 f a (θ) = Σ i a i f( θ -θ i ) Radial Basis Function (RBF) 17

18 Skinning Improvements Incorporate user-defined examples of shapes and automatically add some joints and weights in LBS [Mohr et Gleicher, 2003] 18

19 Skinning Improvements Compute the matrix interpolation while maintaining correct rotations, using dual quaternions P = Σ i w i * M 0,i M i M -1 0,i P 0 = ( Σ i w i * M 0,i M i M -1 0,i ) P 0 [Kavan et al., 2007] 19

20 Overview Skinning Non-linear deformers Shape morphing Mesh edition 20

21 Non-linear deformers Global modification of 3D shapes the transformation matrix is a function of R 3 point 21

22 Non-linear deformers Non-uniform rotation (twisting) 22

23 Non-linear deformers Vortex 23

24 Non-linear deformers Free-Form Deformation (FFD) Object embedded in 3D rubber 24

25 Non-linear deformers FFD : Space interpolation 25

26 Non-linear deformers FFD applications to non-characters objects 26

27 Non-linear deformers Preserving volume V = 4/3 π abc b = ¾ V / ( π ac) Influence object combined with skinning [Scheepers et al., 97] 27

28 Non-linear deformers Preserving volume Motion of Muscles induces a displacement field [Angelidis et Singh, 2007] 28

29 Overview Skinning Non-linear deformers Shape morphing Mesh edition 29

30 Shape blending a 3D shape is a linear combination of reference shapes a linear interpolation for each vertex, S = S 0 +Σ i w i (S i -S 0 ) animation is controlled by blend coefficient w i typical application is facial animation 30

31 Shape blending Blend Shapes 31

32 Shape blending Facial animation : two main domains Emotion any expression is combination of basic expression: fear, disgust, joy, surprise, anger [Ekman, 75] Talking visual perception of speech production 32

33 Lip-synching Difficult task how to post-synchronized video onto audio track one common solution : a phoneme = a 3D shape several visually equivalent phonemes as a viseme [p,b,m], [f,v], etc. 33

34 Lip-synching Problem of the co-articulation effect audio-visual speech signal is continuous audio and visual are not synchronized by nature (anticipation and latency) gesture vs shape [Reveret et Essa, 2001] 34

35 Overview Skinning Non-linear deformers Shape morphing Mesh edition 35

36 Barycentric coordinates Low-resolution «cage» controlling a highresolution mesh each vertex is a linear combination w.r.t cage vertices and normals => local coordinates or weights difficulty: getting the right weights, leading to little artefacts Mean value coordinates, Harmonic coordinates, Green coordinates, etc 36

37 Laplacian mesh edition Character animation without a skeleton Group of vertices are locally deformed while preserving surface details Based on discrete differential geometry [Sorkine et al., 2004] 37

38 Laplacian mesh edition Each vertex coordinate is replaced by the difference to the average of its neighbors D = L V : d i = V i -(1/ N i )Σ kϵni V k Deformation by adding constrains add some rows to L => L* and D => D* Reconstruction of V by approximation V* = argmin V ( L V D ) More details on: Laplacian-mesh-processing.pdf 38

39 Laplacian mesh edition Application to key-frame animation [Xu et al., 2006] 39