An adaptive element subdivision method based on the affine transformations and partitioning techniques for evaluating the weakly singular integrals

Chi, Baotao; Jia, Zhichao; Li, Can; Guo, Qianjian; Yuan, Wei; Ju, Chuanming

doi:10.1016/j.cam.2023.115320

Cited by 4 publications

(1 citation statement)

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“…The subdivision scheme can be considered as the generalization of discrete modeling by spline representation, such as the Catmull-Clark subdivision [17], Doo-Sabin subdivision [18], Loop subdivision [19], and other classes of interpolatory subdivision schemes. The adaptive subdivision algorithm [20][21][22][23] is less cumbersome by defining the refinement rules to add new points as linear combinations of old ones. The process continues until the given terminating criteria for all discrete segments or patches are not met.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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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.

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