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DTSTAMP:20230103T035306Z
LOCATION:Auditorium\, Level 5\, West Wing
DTSTART;TZID=Asia/Seoul:20221206T100000
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UID:siggraphasia_SIGGRAPH Asia 2022_sess153_papers_470@linklings.com
SUMMARY:Compressing Geodesic Information for Fast Point-to-Point Geodesic 
 Distance Queries
DESCRIPTION:Technical Papers\n\nCompressing Geodesic Information for Fast 
 Point-to-Point Geodesic Distance Queries\n\nGotsman, Hormann\n\nGeodesic d
 istances between pairs of points on a 3D mesh surface are a crucial ingred
 ient of many geometry processing tasks, but are notoriously difficult to c
 ompute efficiently on demand. We propose a novel method for the compact st
 orage of geodesic distance information, which enables answering point-to-p
 oint geodesic distance queries very efficiently. For a triangle mesh with 
 n vertices, if computing the geodesic distance to all vertices from a sing
 le source vertex costs O(f(n)) time, then we generate a database of size O
 (mn log n) in O((f(n)+m³n) √n) time in a preprocessing stage, where m is a
  constant that depends on the geometric complexity of the surface. We achi
 eve this by computing a nested bisection of the mesh surface using separat
 or curves and storing compactly-described functions approximating the dist
 ances between each mesh vertex and a small relevant subset of these curves
 . Using this database, the geodesic distance between two mesh vertices can
  then be approximated well by solving a small number of simple univariate 
 minimization problems in O(m log n) worst case time and O(m) average case 
 time. Our method provides an excellent tradeoff between the size of the da
 tabase, query runtime, and accuracy of the result. It can be used to compr
 ess exact or approximate geodesic distances, e.g., those obtained by VTP (
 exact), fast DGG, fast marching, or the heat method (approximate) and is v
 ery efficient if f(n)=n, as for the fast DGG method.\n\nRegistration Categ
 ory: FULL ACCESS, EXPERIENCE PLUS ACCESS, EXPERIENCE ACCESS, TRADE EXHIBIT
 OR\n\nLanguage: ENGLISH\n\nFormat: IN-PERSON
URL:https://sa2022.siggraph.org/en/full-program/?id=papers_470&sess=sess15
 3
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