Abstract
In the current feature-based modelling, some changes are required, because one should better understand the non-parametric doubly curved surface through parametric technique. This paper proposes specific lemmas for detecting concavity, convexity and inflection point of doubly curved surface as well as their physical properties during the surface reconstruction of CAD models. These lemmas are incomparable in the area of reverse engineering and applications of 3-D modelling, based on Serret Frenet equation and complex topology (R³i). The major contribution of this paper is to introduction of a new class of 3-D surface reconstruction of doubly curved surface. These lemmas will be unique for improved surface reconstruction and provide smoothness of outer and inner surface.
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