Title:
Ball-map: Homeomorphism Between Compatible Surfaces
Ball-map: Homeomorphism Between Compatible Surfaces
Files
Authors
Chazal, Frederic
Lieutier, Andre
Rossignac, Jarek
Whited, Brian
Lieutier, Andre
Rossignac, Jarek
Whited, Brian
Authors
Person
Advisors
Advisors
Associated Organizations
Organizational Unit
Series
Series
Collections
Supplementary to
Permanent Link
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.
Sponsor
Date Issued
2006
Extent
2520630 bytes
Resource Type
Text
Resource Subtype
Technical Report