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

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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.
Funding Information
  • National Natural Science Foundation of China (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • China Postdoctoral Science Foundation, China (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • Shandong Provincial Natural Science Foundation, China (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • Special Funds for the Central Government to Guide Local Science and Technology Development (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • Ministry of Education Industry-school Cooperative Education Project, China (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • China Institute Electronic Labor Industry-school Cooperative Education Project (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • Shandong Provincial Science Foundation for the Enterprises Innovation Ability Development (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)
  • Scientific Research Project of Shandong University of Technology, China (12202251, 12172201, 51805299, 2021M702024, 2022M712393, ZR2022ME122, ZR2022ME120, YDZX2022003, 220606517023742, Ciel2022044, 2023TSGC0965, 4041/420047, 4003/122237, 9101/2222431)

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