Unified Representation of Curves and Surfaces

Aizeng Wang, Gang Zhao and Chuan He
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Aizeng Wang: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Gang Zhao: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Chuan He: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China

Mathematics, 2021, vol. 9, issue 9, 1-14

Abstract: 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 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.

Keywords: complex topology; unified representation; I-splines (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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