Affiliations: Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
Correspondence:
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Corresponding author: Milan Ćurković, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boskovica 32, 21000 Split, Croatia. Tel.: +385 21 305 658; E-mail: [email protected].
Abstract: In computer aided design and particularly in reverse engineering, one of the main problems is the selection of an appropriate shape representation model (for ship hull, boat propeller, turbine blades, …). An appropriate model should have a small number of shape variables while keeping the shape generality and allowing easy modifications. Ideally, the surface construction would be automatized, and the user should be able to easily and intuitively modify the shape. This paper proposes a geometric model for surface representation which can reduce the required number of shape variables and is simple to implement. Since the ultimate objective is the application in reverse engineering, we examine whether the proposed method has suitable properties. The proposed surface representation model called the hybrid surface is constructed from the basis set that includes both the B-spline functions and the radial basis functions (RBFs). The RBFs can be distributed evenly or used for localized enrichment. The hybrid surface model is simple to implement, but several problems arise when it is applied to engineering objects. The problems addressed in this paper include: (i) what is the optimal RBF shape constant, (ii) for which surfaces the hybrid surface offers advantage over B-spline, (iii) how to manipulate local shape and (iv) which fitting method can achieve a smooth fitted surface. Finally, the performance of B-spline, RBF, and hybrid surface are compared by fitting to engineering objects of various complexity. The results show that the hybrid surface commonly performs the best regarding the mean fitting error while achieving a smooth final surface. Since the method has suitable properties for reverse engineering and is simple to implement, it can be used as a viable alternative to other models.
