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DTSTAMP:20250110T023313Z
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:Technical Papers\n\nXu Wang and Weiyin Ma (City University of 
 Hong Kong)\n\nWe propose a unified tuning framework for primal subdivision
  schemes that are generalizations of odd-degree uniform B-spline surfaces 
 for unstructured quadrilateral meshes of arbitrary topology. The subdivisi
 on of the resulting tuned primal subdivision (TPS) schemes is performed th
 rough efficient repeated local refinement operations. One level of subdivi
 sion of TPS-schemes is decomposed into one step of simple topological spli
 tting plus an additional series of repeated local smoothing operations. Th
 e unified tuning framework optimizes subdivision rules for both topologica
 l splitting and smoothing operations near extraordinary vertices by minimi
 zing the curvature fluctuation of the second-order characteristic maps of 
 the respective TPS-scheme. To validate the limit surface quality of TPS-sc
 hemes in extraordinary regions, a mesh-independent metric is also devised 
 to estimate local curvature variation in addition to highlight lines and d
 irect curvature evaluation. With $(p-1)/2$ steps of smoothing operations i
 n each level of subdivision, the respective TPS-scheme is termed as a degr
 ee-$p$ scheme that produces global $C^{p-1}$ limit surfaces everywhere exc
 ept at a finite number of extraordinary positions where near-$G^2$ continu
 ity is achieved. The limit surface of TPS-schemes in extraordinary regions
  also exhibits appealing highlight lines, and the larger the number of smo
 othing operations applied in each level of subdivision, the better the fin
 al limit surface quality. One of the key advantages of the proposed tuning
  framework for TPS-schemes is that the optimization of relevant subdivisio
 n rules is performed by tuning structured operations of topological splitt
 ing and repeated smoothing that involve direct neighbors of an extraordina
 ry vertex only without the need of tuning large subdivision stencils. All 
 subdivision operations of TPS-schemes are local, involving one-ring of nei
 ghboring vertices only, which is efficient for high-degree surface subdivi
 sion and convenient for practical implementation. Numerical examples also 
 validate the superiority of TPS-schemes over other state-of-the-art subdiv
 ision methods in terms of both highlight lines and various curvature measu
 res.\n\nRegistration Category: Full Access, Full Access Supporter\n\nLangu
 age Format: English Language\n\nSession Chair: Hao (Richard) Zhang (Simon 
 Fraser University, Amazon)
URL:https://asia.siggraph.org/2024/program/?id=papers_1047&sess=sess145
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