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DTSTAMP:20240214T070242Z
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:Technical Papers\n\nZhendong 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 dis
 crete bending (DAB) models, i.e. the indefiniteness of their energy Hessia
 n and their vulnerability to geometry degeneracies. To tackle the indefini
 teness issue, we present novel analytic expressions for the eigensystem of
  a DAB energy Hessian. Our expressions reveal that DAB models typically ha
 ve positive, negative, and zero eigenvalues, with four of each, respective
 ly. By using these expressions, we can efficiently project an indefinite D
 AB energy Hessian as positive semi-definite analytically. To enhance the s
 tability of DAB models at degenerate geometries, we propose rectifying the
 ir indefinite geometric stiffness matrix by using orthotropic geometric st
 iffness matrices with adaptive parameters calculated from our analytic eig
 ensystem. Among the twelve motion modes of a dihedral element, our resulti
 ng Hessian for DAB models retains only the desirable bending modes, compar
 ed to the undesirable altitude-changing modes of the exact Hessian with or
 iginal geometric stiffness, all modes of the Gauss-Newton approximation wi
 thout geometric stiffness, and none modes of the projected Hessians with i
 nappropriate geometric stiffness. Additionally, we suggest adjusting the c
 ompression stiffness according to the Kirchhoff-Love thin plate theory to 
 avoid over-compression. Our method not only ensures the positive semi-defi
 niteness but also avoids instability caused by large bending forces at deg
 enerate geometries. To demonstrate the benefit of our approaches, we show 
 comparisons against existing methods on the simulation of cloth and thin p
 lates in challenging examples.\n\nRegistration Category: Full Access\n\nSe
 ssion Chair: Weiwei Xu (State Key Laboratory of CAD&CG, Zhejiang Univerisi
 ty; State Key Lab of CAD and CG, Zhejiang University)
URL:https://asia.siggraph.org/2023/full-program?id=papers_513&sess=sess141
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