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BEGIN:VEVENT
DTSTAMP:20250110T023312Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241205T094600
DTEND;TZID=Asia/Tokyo:20241205T095800
UID:siggraphasia_SIGGRAPH Asia 2024_sess124_papers_802@linklings.com
SUMMARY:Polynomial Cauchy Coordinates for Curved Cages
DESCRIPTION:Technical Papers\n\nZhehui Lin and Renjie Chen (University of 
 Science and Technology of China)\n\nBarycentric coordinates are widely use
 d in computer graphics, especially in shape deformation. Traditionally, ba
 rycentric coordinates are defined for polygonal domains. In this work, we 
 relax this requirement by representing the boundary of the domain using a 
 Bézier spline and extend the complex-valued Cauchy barycentric coordinates
  [Weber et al. 2009] to the Bézier case. Compared to the latest polynomial
  2D Green coordinates [Michel and Thiery 2023], we obtain equivalent resul
 ts. We further derive a numerical integration formula for the inverse mapp
 ing based on Cauchy's integral formula, enabling deformation between curve
 d cages through an intermediate step. Notably, our approach allows curved 
 cages as input. We also provide expressions for the nth-order derivatives 
 of the coordinates, which facilitate constrained deformations with positio
 n constraints. Through extensive experiments, we demonstrate the versatili
 ty of our coordinates for interactive deformation.\n\nRegistration Categor
 y: Full Access, Full Access Supporter\n\nLanguage Format: English Language
 \n\nSession Chair: Yotam Gingold (George Mason University)
URL:https://asia.siggraph.org/2024/program/?id=papers_802&sess=sess124
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