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DTSTAMP:20260114T163642Z
LOCATION:Meeting Room C4.9+C4.10\, Level 4 (Convention Centre)
DTSTART;TZID=Australia/Melbourne:20231212T143000
DTEND;TZID=Australia/Melbourne:20231212T144500
UID:siggraphasia_SIGGRAPH Asia 2023_sess141_papers_513@linklings.com
SUMMARY:Stable Discrete Bending by Analytic Eigensystem and Adaptive Ortho
 tropic Geometric Stiffness
DESCRIPTION:Zhendong Wang (Style3D Research); Yin Yang (University of Utah
 , Style3D Research); and Huamin Wang (Style3D Research)\n\nIn this paper, 
 we address two limitations of dihedral angle based discrete bending (DAB) 
 models, i.e. the indefiniteness of their energy Hessian and their vulnerab
 ility to geometry degeneracies. To tackle the indefiniteness issue, we pre
 sent novel analytic expressions for the eigensystem of a DAB energy Hessia
 n. Our expressions reveal that DAB models typically have positive, negativ
 e, and zero eigenvalues, with four of each, respectively. By using these e
 xpressions, we can efficiently project an indefinite DAB energy Hessian as
  positive semi-definite analytically. To enhance the stability of DAB mode
 ls at degenerate geometries, we propose rectifying their indefinite geomet
 ric stiffness matrix by using orthotropic geometric stiffness matrices wit
 h adaptive parameters calculated from our analytic eigensystem. Among the 
 twelve motion modes of a dihedral element, our resulting Hessian for DAB m
 odels retains only the desirable bending modes, compared to the undesirabl
 e altitude-changing modes of the exact Hessian with original geometric sti
 ffness, all modes of the Gauss-Newton approximation without geometric stif
 fness, and none modes of the projected Hessians with inappropriate geometr
 ic stiffness. Additionally, we suggest adjusting the compression stiffness
  according to the Kirchhoff-Love thin plate theory to avoid over-compressi
 on. Our method not only ensures the positive semi-definiteness but also av
 oids instability caused by large bending forces at degenerate geometries. 
 To demonstrate the benefit of our approaches, we show comparisons against 
 existing methods on the simulation of cloth and thin plates in challenging
  examples.\n\nRegistration Category: Full Access\n\nSession Chair: Weiwei 
 Xu (State Key Laboratory of CAD&CG, Zhejiang University)\n\n
URL:https://asia.siggraph.org/2023/full-program?id=papers_513&sess=sess141
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