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DTSTAMP:20260817T171516Z
LOCATION:Hall C\, C Block\, Level 4
DTSTART;TZID=Asia/Tokyo:20241203T090000
DTEND;TZID=Asia/Tokyo:20241203T120000
UID:siggraphasia_SIGGRAPH Asia 2024_sess223_papers_802@linklings.com
SUMMARY:Polynomial Cauchy Coordinates for Curved Cages
DESCRIPTION:Zhehui Lin and Renjie Chen (University of Science and Technolo
 gy of China)\n\nBarycentric coordinates are widely used in computer graphi
 cs, especially in shape deformation. Traditionally, barycentric coordinate
 s are defined for polygonal domains. In this work, we relax this requireme
 nt by representing the boundary of the domain using a Bézier spline and ex
 tend the complex-valued Cauchy barycentric coordinates [Weber et al. 2009]
  to the Bézier case. Compared to the latest polynomial 2D Green coordinate
 s [Michel and Thiery 2023], we obtain equivalent results. We further deriv
 e a numerical integration formula for the inverse mapping based on Cauchy'
 s integral formula, enabling deformation between curved cages through an i
 ntermediate step. Notably, our approach allows curved cages as input. We a
 lso provide expressions for the nth-order derivatives of the coordinates, 
 which facilitate constrained deformations with position constraints. Throu
 gh extensive experiments, we demonstrate the versatility of our coordinate
 s for interactive deformation.\n\nRegistration Category: Enhanced Access, 
 Full Access, Full Access Supporter\n\nLanguage Format: English Language\n\
 n
URL:https://asia.siggraph.org/2024/program/?id=papers_802&sess=sess124
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