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DTSTART:18871231T000000
DTSTART:19881009T020000
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DTSTAMP:20230103T035309Z
LOCATION:Room 324\, Level 3\, West Wing
DTSTART;TZID=Asia/Seoul:20221207T170000
DTEND;TZID=Asia/Seoul:20221207T183000
UID:siggraphasia_SIGGRAPH Asia 2022_sess175_papers_460@linklings.com
SUMMARY:Isotropic ARAP energy using Cauchy-Green invariants
DESCRIPTION:Technical Papers, TOG\n\nIsotropic ARAP energy using Cauchy-Gr
 een invariants\n\nLin, Chitalu, Komura\n\nIsotropic As-Rigid-As-Possible (
 ARAP) energy has been popular for shape editing, mesh parametrisation and 
 soft-body simulation for almost two decades. However, a formulation using 
 Cauchy-Green (CG) invariants has always been unclear, due to a rotation-po
 lluted trace term that cannot be directly expressed using these invariants
 .  We show how this incongruent trace term can be understood via an implic
 it relationship to the CG  invariants.  Our analysis reveals this relation
 ship to be a polynomial where the roots equate to the trace term, and wher
 e the derivatives also give rise to closed-form expressions of the Hessian
  to guarantee positive semi-definiteness for a fast and concise Newton-typ
 e implicit {time} integration. A consequence of this analysis is a novel a
 nalytical formulation to compute rotations and singular values of deformat
 ion-gradient tensors without explicit/numerical factorization which is sig
 nificant, resulting in up-to 3.5x speedup and benefits energy function eva
 luation for reducing solver time. We validate our energy formulation by ex
 periments and comparison, demonstrating that our resulting eigendecomposit
 ion using the CG invariants is equivalent to existing ARAP formulations. W
 e thus reveal isotropic ARAP energy to be a member of the ``Cauchy-Green c
 lub'', meaning that it can indeed be defined using CG invariants and there
 fore that the closed-form expressions of the resulting Hessian are shared 
 with other energies written in their terms.\n\nRegistration Category: FULL
  ACCESS, ON-DEMAND ACCESS\n\nLanguage: ENGLISH\n\nFormat: IN-PERSON, ON-DE
 MAND
URL:https://sa2022.siggraph.org/en/full-program/?id=papers_460&sess=sess17
 5
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