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DTSTART:19820101T123000
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BEGIN:VEVENT
DTSTAMP:20201212T050125Z
LOCATION:Zoom Room 1
DTSTART;TZID=Asia/Singapore:20201213T120600
DTEND;TZID=Asia/Singapore:20201213T121200
UID:siggraphasia_SIGGRAPH Asia 2020_sess104_papers_159@linklings.com
SUMMARY:Conforming Weighted Delaunay Triangulations
DESCRIPTION:Technical Papers, Technical Papers Q&A\n\nConforming Weighted
Delaunay Triangulations\n\nAlexa\n\nGiven a set of points together with a
set of simplices\nwe show how to compute weights associated with the point
s such that the weighted Delaunay triangulation of the point set contains
the simplices, if possible. For a given triangulated surface, this process
provides a tetrahedral mesh conforming to the triangulation, i.e. solves
the problem of meshing the triangulated surface without inserting addition
al vertices. The restriction to weighted Delaunay triangulations ensures t
hat the orthogonal dual mesh is embedded, facilitating common geometry pro
cessing tasks.\n\nWe show that the existence of a single simplex in a weig
hted Delaunay triangulation for given vertices amounts to a set of linear
inequalities, one for each vertex. This means that the number of inequalit
ies for a given triangle mesh is quadratic in the number of mesh elements,
making the naive approach impractical. We devise an algorithm that increm
entally selects a small subset of inequalities, repeatedly updating the we
ights, until the weighted Delaunay triangulation contains all constrained
simplices or the problem becomes infeasible. Applying this algorithm to a
range of triangle meshes commonly used graphics demonstrates that many of
them admit a conforming weighted Delaunay triangulation, in contrast to co
nforming or constrained Delaunay that require additional vertices to split
the input primitives.\n\nRegistration Category: Ultimate Supporter, Ultim
ate Attendee
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