Volume 13, Issue 1
Spline R-Function and Applications in FEM

Tianhui Yang ,  Ammar Qarariyah and Jiansong Deng


Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 150-175.

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  • Abstract

R-function is a widely used tool when considering objects obtained through the Boolean operations start from simple base primitives. However, there is square root operation in the representation. Considering that the use of splines will facilitate the calculations within the CAD system, in this paper, we propose a system of R-functions represented in spline form called Spline R-function (SR). After transforming the function ranges of two base primitives to a new coordinate system, a series of sign constraints following a specific Boolean operation are derived and the spline R-function can be formulated as a piecewise function. Representation of SR in both B\'{e}zier form and B-spline form have been given. Among which the B\'{e}zier ordinates are determined with the help of the B-net method through setting up a series of relations according to the sign constraints and properties of R-functions. The construction processes for both Boolean intersection and union operations with different smoothness are discussed in detail. Numerical experiments are conducted to show the potential of the proposed spline R-function.

  • History

Published online: 2019-12

  • AMS Subject Headings

68U07, 65D18, 65D30

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