Abstract
In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.
Highlights
Computer Aided Geometric Design (CAGD) considers the mathematical description of curves and surfaces utilized in computer graphics, data structure and computational algebra
This paper aims to construct a tensor product of nine-tic B-spline subdivision scheme to reduce the execution time needed to compute the subdivision process of quad meshes
By applying the above procedure repeatedly, we found that the proposed subdivision scheme (SS) has C9 continuity
Summary
Computer Aided Geometric Design (CAGD) considers the mathematical description of curves and surfaces utilized in computer graphics, data structure and computational algebra. Subdivision schemes (SSs) are iterative algorithms of surface modeling in CAGD. In 2013, Mustafa et al [15] worked on odd point ternary families of approximating SSs, in which they showed that their SSs have high smoothness. Ghaffar et al [25] introduced odd and even point non-stationary binary SSs for curve designing. The numerical results illustrate that the proposed SS reconstruct refined version of the models by using smoothing operation on regular meshes, but it doesn’t reproduced parametric curves/surfaces that have logarithmic functions and division terms i.e non-exponential polynomials, which needs non-uniform masks of SS for the exact reproduction of such models.
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