Real%Time)Example%Based)
Elas0c)Deforma0on)Y.)Koyama1,))K.)Takayama1,2,))N.)Umetani1,))T.)Igarashi1,3)
1The)University)of)Tokyo)

2ETH)Zurich)

3JST)ERATO)Use%

Example-Based Elastic Materials[Martin11]

FEM)
Finite Element Method

Speed%up%

Use%

Our method

Shape Matching[Müller05]

Use%

Example-Based Elastic Materials[Martin11]

FEM)
Finite Element Method

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%

Use%

Example-Based Elastic Materials[Martin11]

FEM)
Finite Element Method

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

Polar%decomposi2on%= Rotation= Stretch and shearExtension)to)mul0%region)• Overlapping%local%regions%– Increasing%the%range)of)deforma0on)

Multiple regions

Use%

Example-Based Elastic Materials[Martin11]FEM)
Finite Element Method

Speed%up%

Use%

Our method

Shape Matching[Müller05]

Deforma0on)Descriptor)

Deforma2on%
Descriptor%(:= S = S S  ST1T2) ∈T Tm6mGoal)pose))(Standard)shape)matching)))
Current%pose%Rest%pose%Goal)pose)

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

Example%Pose%Details)of)projec0on))1.)Linear)projec0on)w

01w

Details)of)projec0on)2.)Clamping)to)avoid)extrapola0on)
Constraints: 0 ≤ wi ≤ 1Details)of)projec0on)3.)Ensuring)the)deforma0on)will)return)

Modifying)the)Shape)Matching)(S = S S  ST1T2

Goal%strain%of%
each%local%region%

Region%i!

Ri
R i S i)

T TmNon%linear)vs)Linear)
Non%linear)interpola0on%

Non%linear)
op0miza0on%[Mar2n11]%
FEM)
Linear%interpola2on%

Our%Method%
Shape)Matching)Linear%projec2on%

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%

Time%[ms]%528%/%3064%

0.33%

Min%/%Max%(twisting cuboid)

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

Future)Work)[Müller11]%

2D structures (e.g. cloth)

1D structures (e.g. hair)%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)%