Exact Volume Preserving Skinning with Shape Control Damien ROHMER, - PowerPoint PPT Presentation

Exact Volume Preserving Skinning with Shape Control Damien ROHMER, Stefanie HAHMANN, Marie-Paule CANI Grenoble University, France Symposium on Computer Animation 2009, New Orleans, USA Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 1 / 22

Classical character animation pipeline Interactive character deformation Skinning deformation (Skeleton Subspace Deformation) Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 2 / 22

Motivations: character animation Fits into the standard pipeline . Interactive deformation. Natural -looking behavior ⇒ Constant volume. Intuitive control . Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 3 / 22

Volume correction: Overview Post-process volume correction on skeleton deformed shaped. Exact volume preservation. Controlable using 1D profil curve . Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 4 / 22

Previous work: Skinning deformation Training based approaches ( ⊕ Freedom, ⊖ Need of training poses) [Lewis et al. , SIGGRAPH 2000] [Wang et al. , SCA 2002] [Weber et al. , EG 2007] Mathematical interpolation improvement [Angelidis and Singh SCA 2007] ( ⊕ Constant volume, ⊖ Control) [Kavan et al. TOG 2008] ( ⊕ General, ⊖ No constant volume) Geometrical constraints ( ⊕ Constant volume, ⊖ Control) [Funck et al. VMV 2008] [Rohmer et al. PG 2008] Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 5 / 22

Improvements from our previous work [Rohmer et al. Our Method PG 2008] Constant volume approximated exact Final shape control skinning weights 1D-profil curve R N R 3 N Deformation space Mesh triangles triangles+quads Overlaping defor- no yes mation Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 6 / 22

Overview 1 Exact volume compensation 2 Local control of the deformation 3 Application to complex characters Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 7 / 22

Enclosed volume of the mesh Triangular mesh Quadrangular mesh [Gonzalez-Ochoa 99] � � z M k T V = V q = � � V = V t = z avg A quads quads triangles triangles Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 8 / 22

Volume correction expression Per-Vertex displacement u � � � u � 2 min constraint to V ( p + u ) = V 0 Lagrange multipliers expression � u i � 2 + λ ( V ( p + u ) − V 0 ) � Λ( u , λ ) = i V is trilinear in ( u x , u y , u z ) . Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 9 / 22

Exact closed-form correction in 3 steps Extend the idea from [Elber, Technion report 2000] : 1 Deform along x and correct µ 0 % of the volume. 2 Deform along y and correct µ 1 % of the volume. Deform along z and correct µ 2 % of the volume. 3 u i = ( u x , u y , u z ) � � ∇ x i V ∇ y i V ⋆ ∇ z i V ⋆⋆ = ∆ V µ 0 k �∇ x k V � 2 , µ 1 k �∇ y k V ⋆ � 2 , µ 2 k �∇ z k V ⋆⋆ � 2 P P P µ 0 + µ 1 + µ 2 = 1 ⇒ exact volume preservation. Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 10 / 22

Localizing the deformation Use of local frames for each joint. Use of vertex-displacement weights  � u i � 2 � min   γ i vertices i  constraint to V ( p + u ) = V 0  Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 11 / 22

1D-Profil curve Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 12 / 22

Application to complex characters Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 13 / 22

Animal animation Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 14 / 22

Adaptative refinement Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 15 / 22

Overlaping deformations Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 16 / 22

Giraffe deformation Rubber effect automatically oriented Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 17 / 22

Animal animation Video Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 18 / 22

Computational Time vertices joint number cost giraffe 1673 1 0.011s elephant 6646 1 0.053s subdivided 13439 1 0.110s elephant elephant 6646 17 0.407s Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 19 / 22

Limitations ∆ V is computed globally (computation time). Tradeoff: Speed VS Local limitations . Ordering in x , y , z deformation (20 % r ). Ordering in skeleton hierarchy ( < 2 % r ). Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 20 / 22

Conclusion and future work Advantages Exact volume preservation. Controlability using 1D-curve profil. No limitation on locality, overlaping influences. Future Work Build a GUI / Profil sketch. Local cutting to compute ∆ V locally. Self collision. Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 21 / 22

Thank you Rohmer, Hahmann, Cani (Grenoble) Constant Volume Skinning SCA’09 22 / 22