A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

Baotao Chi, Shengmin Bai, Qianjian Guo (), Yaoming Zhang, Wei Yuan and Can Li
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Baotao Chi: School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China
Shengmin Bai: School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China
Qianjian Guo: School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China
Yaoming Zhang: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Wei Yuan: School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China
Can Li: Institute of Advanced Ocean Study, Ocean University of China, Qingdao 266100, China

Mathematics, 2023, vol. 11, issue 16, 1-19

Abstract: The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation curve is mainly applied to solve the difficult geometry defeaturing problems for curve modeling in existing computer-aided technology. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual interpolation curve is flexible and convenient for characterizing a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of characterizing the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

Keywords: dual interpolation curve; adaptive curve refinement; curve modeling; geometry defeaturing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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