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DTSTART:18871231T000000
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DTSTAMP:20230103T035307Z
LOCATION:Auditorium\, Level 5\, West Wing
DTSTART;TZID=Asia/Seoul:20221206T100000
DTEND;TZID=Asia/Seoul:20221206T120000
UID:siggraphasia_SIGGRAPH Asia 2022_sess153_papers_460@linklings.com
SUMMARY:Isotropic ARAP energy using Cauchy-Green invariants
DESCRIPTION:Technical Papers\n\nIsotropic ARAP energy using Cauchy-Green i
 nvariants\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 Cauch
 y-Green (CG) invariants has always been unclear, due to a rotation-pollute
 d trace term that cannot be directly expressed using these invariants.  We
  show how this incongruent trace term can be understood via an implicit re
 lationship to the CG  invariants.  Our analysis reveals this relationship 
 to be a polynomial where the roots equate to the trace term, and where the
  derivatives also give rise to closed-form expressions of the Hessian to g
 uarantee positive semi-definiteness for a fast and concise Newton-type imp
 licit {time} integration. A consequence of this analysis is a novel analyt
 ical formulation to compute rotations and singular values of deformation-g
 radient tensors without explicit/numerical factorization which is signific
 ant, resulting in up-to 3.5x speedup and benefits energy function evaluati
 on for reducing solver time. We validate our energy formulation by experim
 ents and comparison, demonstrating that our resulting eigendecomposition u
 sing the CG invariants is equivalent to existing ARAP formulations. We thu
 s reveal isotropic ARAP energy to be a member of the ``Cauchy-Green club''
 , meaning that it can indeed be defined using CG invariants and therefore 
 that the closed-form expressions of the resulting Hessian are shared with 
 other energies written in their terms.\n\nRegistration Category: FULL ACCE
 SS, EXPERIENCE PLUS ACCESS, EXPERIENCE ACCESS, TRADE EXHIBITOR\n\nLanguage
 : ENGLISH\n\nFormat: IN-PERSON
URL:https://sa2022.siggraph.org/en/full-program/?id=papers_460&sess=sess15
 3
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