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DTSTAMP:20240214T070247Z
LOCATION:Meeting Room C4.8\, Level 4 (Convention Centre)
DTSTART;TZID=Australia/Melbourne:20231214T102000
DTEND;TZID=Australia/Melbourne:20231214T103500
UID:siggraphasia_SIGGRAPH Asia 2023_sess149_papers_793@linklings.com
SUMMARY:Metric Optimization in Penner Coordinates
DESCRIPTION:Technical Papers\n\nRyan Capouellez and Denis Zorin (New York 
 University)\n\nMany parametrization and mapping-related problems in geomet
 ry processing can be viewed as metric optimization problems, i.e., computi
 ng a metric minimizing a functional and satisfying a set of constraints, s
 uch as flatness. \n\nPenner coordinates are global coordinates on the spac
 e of metrics on meshes with a fixed vertex set and topology, but varying c
 onnectivity, making it homeomorphic to the Euclidean space of dimension eq
 ual to the number of edges in the mesh, without any additional constraints
  imposed, and reducing to logarithms of edge lengths when restricted to a 
 fixed connectivity. \nThese coordinates play an important role in the theo
 ry of discrete conformal maps, enabling recent development of highly robus
 t algorithms with convergence and solution existence guarantees for comput
 ing such maps. \n\nWe demonstrate how Penner coordinates can be used to so
 lve a general class of problems involving metrics, including optimization 
 and interpolation, while retaining the key guarantees available for confor
 mal maps.\n\nRegistration Category: Full Access\n\nSession Chair: Marco AT
 TENE (Institute for Applied Mathematics and Information Technologies (IMAT
 I), CNR)
URL:https://asia.siggraph.org/2023/full-program?id=papers_793&sess=sess149
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