Unified Representation of Curves and Surfaces

Aizeng Wang, Gang Zhao, Chuan He
2021 Mathematics  
In conventional modeling, shared control points can be employed to realize a unified representation for an object consisting of only curves or only surfaces touching one another. However, this method fails in treating the following two cases: (a) a system consisting of detached curves or surfaces; (b) a system having both curves and surfaces. The purpose of the present paper is to develop a new theoretical tool to solve such problems. By introducing the definitions of naked knot and I-mesh, the
more » ... concept of I-spline is put forth, which is, in essence, an expanded B-spline or T-spline. It is verified by examples that the naked knots make I-splines flexible and effective in transforming different surfaces and/or curves into a unified one, especially in the above two cases.
doi:10.3390/math9091019 doaj:05d67c346acc47638867d630ffb0176a fatcat:6mfhjsmnm5aynjjx5be4crx3ny