Title:
Ball-map: Homeomorphism Between Compatible Surfaces

dc.contributor.author Chazal, Frederic
dc.contributor.author Lieutier, Andre
dc.contributor.author Rossignac, Jarek
dc.contributor.author Whited, Brian
dc.date.accessioned 2006-03-20T19:38:12Z
dc.date.available 2006-03-20T19:38:12Z
dc.date.issued 2006
dc.description.abstract We introduce the ball-map, BM [subscript S],[subscript T], between two manifolds, S and T. It maps each point x of S to a point x = BM[subscript S],[subscript T](x) of T. Its inverse is BM[subscript T],[subscript S]. We define conditions for BM[subscript S],[subscript T] to be a homeomorphism. We show that they hold when the minimum feature size of each surface exceeds their Hausdorff distance. We show that, when S and T are C[superscript k] (n-1)-manifolds in R[superscript n], BM[subscript T],[subscript S] is a C[superscript k-1] diffeomorphism and defines a C[superscript k-1] ambient isotopy that smoothly morphs between S to T. In practice, the ball-map yields an excellent map for transferring parameterizations and textures between ball compatible curves or surfaces. Furthermore, it may be used to define a morph, during which each point x of S travels to the corresponding point y of T along a circular arc that is normal to S at x and to T at y. en
dc.format.extent 2520630 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/8723
dc.language.iso en_US en
dc.publisher Georgia Institute of Technology en
dc.relation.ispartofseries GVU Technical Report;GIT-GVU-06-05 en
dc.subject Mapping en
dc.subject Morphing en
dc.subject Hausdorff Distance en
dc.subject Distortion en
dc.subject Isomorphism en
dc.subject Isotopy en
dc.subject Ball map en
dc.title Ball-map: Homeomorphism Between Compatible Surfaces en
dc.type Text
dc.type.genre Technical Report
dspace.entity.type Publication
local.contributor.author Rossignac, Jarek
local.contributor.corporatename GVU Center
local.relation.ispartofseries GVU Technical Report Series
relation.isAuthorOfPublication d854d72c-9694-4442-bd2f-fb8859bade72
relation.isOrgUnitOfPublication d5666874-cf8d-45f6-8017-3781c955500f
relation.isSeriesOfPublication a13d1649-8f8b-4a59-9dec-d602fa26bc32
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