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DTSTAMP:20260817T171532Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241206T132800
DTEND;TZID=Asia/Tokyo:20241206T134200
UID:siggraphasia_SIGGRAPH Asia 2024_sess145_papers_1047@linklings.com
SUMMARY:A class of new tuned primal subdivision schemes with high-quality 
 limit surface in extraordinary regions
DESCRIPTION:Xu Wang and Weiyin Ma (City University of Hong Kong)\n\nWe pro
 pose a unified tuning framework for primal subdivision schemes that are ge
 neralizations of odd-degree uniform B-spline surfaces for unstructured qua
 drilateral meshes of arbitrary topology. The subdivision of the resulting 
 tuned primal subdivision (TPS) schemes is performed through efficient repe
 ated local refinement operations. One level of subdivision of TPS-schemes 
 is decomposed into one step of simple topological splitting plus an additi
 onal series of repeated local smoothing operations. The unified tuning fra
 mework optimizes subdivision rules for both topological splitting and smoo
 thing operations near extraordinary vertices by minimizing the curvature f
 luctuation of the second-order characteristic maps of the respective TPS-s
 cheme. To validate the limit surface quality of TPS-schemes in extraordina
 ry regions, a mesh-independent metric is also devised to estimate local cu
 rvature variation in addition to highlight lines and direct curvature eval
 uation. With $(p-1)/2$ steps of smoothing operations in each level of subd
 ivision, the respective TPS-scheme is termed as a degree-$p$ scheme that p
 roduces global $C^{p-1}$ limit surfaces everywhere except at a finite numb
 er of extraordinary positions where near-$G^2$ continuity is achieved. The
  limit surface of TPS-schemes in extraordinary regions also exhibits appea
 ling highlight lines, and the larger the number of smoothing operations ap
 plied in each level of subdivision, the better the final limit surface qua
 lity. One of the key advantages of the proposed tuning framework for TPS-s
 chemes is that the optimization of relevant subdivision rules is performed
  by tuning structured operations of topological splitting and repeated smo
 othing that involve direct neighbors of an extraordinary vertex only witho
 ut the need of tuning large subdivision stencils. All subdivision operatio
 ns of TPS-schemes are local, involving one-ring of neighboring vertices on
 ly, which is efficient for high-degree surface subdivision and convenient 
 for practical implementation. Numerical examples also validate the superio
 rity of TPS-schemes over other state-of-the-art subdivision methods in ter
 ms of both highlight lines and various curvature measures.\n\nRegistration
  Category: Full Access, Full Access Supporter\n\nLanguage Format: English 
 Language\n\nSession Chair: Hao (Richard) Zhang (Simon Fraser University, A
 ugmenta)\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_1047&sess=sess145
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