Fill-in Regions

摘要

We approach the problem of three-dimensional shape preserving interpolation by defining fill-in regions that are regions in space which contain all interpolating curves with a desired shape. These regions are defined for special types of curves called coils, which are non-strict versions of curves of geometric order three in three dimensions. We establish that the fill-in regions are a set of tetrahedra and show how they must be restricted to form interpolating curves.