Title:
Ball-map: Homeomorphism Between Compatible Surfaces
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 |