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DTSTAMP:20260817T171531Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241203T135800
DTEND;TZID=Asia/Tokyo:20241203T140900
UID:siggraphasia_SIGGRAPH Asia 2024_sess103_papers_1184@linklings.com
SUMMARY:A Progressive Embedding Approach to Bijective Tetrahedral Maps dri
 ven by Cluster Mesh Topology
DESCRIPTION:Valentin Zenon Nigolian (University of Bern), Marcel Campen (O
 snabrück University), and David Bommes (University of Bern)\n\nWe present 
 a novel algorithm to map ball-topology tetrahedral meshes onto star-shaped
  domains with guarantees regarding bijectivity. Our algorithm is based on 
 the recently introduced idea of Shrink-and-Expand, where images of interio
 r vertices are initially clustered at one point (Shrink-), before being se
 quentially moved to non-degenerate positions yielding a bijective map (-an
 d-Expand). In this context, we introduce the concept of the cluster mesh, 
 i.e. the unexpanded interior mesh consisting of geometrically degenerate s
 implices.\nUsing local, per-vertex connectivity information solely from th
 e cluster mesh, we show that a viable expansion sequence guaranteed to pro
 duce a bijective map can always be found as long as the mesh is shellable.
 \nIn addition to robustness guarantees for this ubiquitous class of inputs
 , other practically relevant benefits include improved parsimony and reduc
 ed algorithmic complexity.\nWhile inheriting some of the worst-case high r
 un time requirements of the state of the art, significant acceleration for
  the average case is experimentally demonstrated.\n\nRegistration Category
 : Full Access, Full Access Supporter\n\nLanguage Format: English Language\
 n\nSession Chair: Baoquan Chen (Peking University)\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_1184&sess=sess103
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