Real%Time)Example%Based) Elas0c)Deforma0on) Y.)Koyama 1 - PowerPoint PPT Presentation

Real%Time)Example%Based) Elas0c)Deforma0on) Y.)Koyama 1 ,))K.)Takayama 1,2 ,))N.)Umetani 1 ,))T.)Igarashi 1,3) 1 The)University)of)Tokyo) 3 JST)ERATO) 2 ETH)Zurich)

FEM) Use% Example-Based Elastic Materials Finite Element Method [Martin11] Speed% up% Use% Our method Shape Matching [Müller05]

FEM) Use% Example-Based Elastic Materials Finite Element Method [Martin11] Speed% up% Use% Our method Shape Matching [Müller05]

Example%Based)Elas0c)Materials) [Mar0n11])) Rest%shape% Example)pose) Result%of%simula2on%

Advantages ) 1.% Ar0st%friendly)simula0on % – Direct%design%of%deforma2ons% 2.% No % pre%defined)scenarios % – Useful%for%games...? %

Limita0on)of)[Mar0n11] ) • Slow) not%real<2me,%not%interac2ve% – Finite)Element)Method)(FEM) % – Non%linear %op2miza2ons% – Our)mo0va0on:)real%0me,)interac0ve)

Real%Time)Demo ) Rest%shape% Example%pose%

FEM) Use% Example-Based Elastic Materials Finite Element Method [Martin11] Speed% up% Use% Our method Shape Matching [Müller05]

Shape)Matching)[Müller05] ) • Method%for%deformable%objects% – Geometry,)not)physics % – Fast,)robust,) and )stable) [Müller05]%

Key)ideas ) Goal)shape) Rest%shape% Current%shape% = Linear transformation = Rotation Polar%decomposi2on% = Stretch and shear

Extension)to)mul0%region ) • Overlapping%local%regions% – Increasing%the% range)of)deforma0on) Multiple regions

FEM) Use% Example-Based Elastic Materials Finite Element Method [Martin11] Speed% up% Use% Our method Shape Matching [Müller05]

Deforma0on)Descriptor ) T ∈  6 m ( ) T  S m T S 2 Descriptor% : = S = S 1 Deforma2on% T

Goal)pose)) (Standard)shape)matching))) Current%pose% Rest%pose% Goal)pose)

Goal)pose) (Our)method)) Current%pose% Goal)pose) Example%Pose% Rest%pose%

Details)of)projec0on) ) 1.)Linear)projec0on ) w 0 w 1

Details)of)projec0on ) 2.)Clamping)to)avoid)extrapola0on ) 0 ≤ w i ≤ 1 Constraints: �

Details)of)projec0on ) ) 3.)Ensuring)the)deforma0on)will)return

Modifying)the)Shape)Matching ) ( ) T  T   T S =   T S 1 S 2 S m Goal%strain%of% each%local%region% Region% i ! R i R i  S i

Non%linear)vs)Linear) Non%linear) Non%linear) interpola0on % op0miza0on % [Mar2n11]% FEM) Linear%projec2on% Linear% interpola2on% Our%Method% Shape)Matching)

Results)and)Discussions)

Results)

Rough)comparison ) 1.)Quality ) • Very%similar%effect%of%example%pose% [Mar2n11]% Our%Method%

Rough)comparison ) 2.)Performance ) • Two,%or%three%orders%magnitude%faster% [Mar2n11]% Our%Method% Ver2ces% 325% 225% 528%/%3064% Time%[ms]% 0.33% Min%/%Max% (twisting cuboid) �

Limita0on ) • Physical%accuracy% [ Good ]%FEM% [ Poor ]% Shape%Matching%%

Future)Work ) [Müller11]% 1D structures (e.g. hair) % 2D structures (e.g. cloth)

Summary ) • New%method%for% example%based)materials) – Based%on% shape)matching) technique ) – Real%0me,)interac0ve) – Decreased)physical)accuracy)

Case)of)two)examples ) (manifold)should)be)a)plane) )

Local)Examples ) • Separate%groups% • Manipulated%independently%

Comparison )

Shape)Matching) Model%=% A % set)of)par0cles) Rest%configura2on%

Shape)Matching) Current%configura2on% Rest%configura2on%

Shape)Matching) Goal%configura2on%

Shape)Matching) Goal%configura2on% Rigid)transforma0on) (Transla2on%+%Rota2on)%

Shape)Matching) Pull%towards%the%goal%posi2ons% Rigid)transforma0on) (Transla2on%+%Rota2on)%