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Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bezier curves

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2016

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Elsevier Science BV

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Abstract

This paper reports new modified Jacobi polynomials (MJPs). We derive the basis transformation between MJPs and Bernstein polynomials and vice versa. This transformation is merging the perfect Least-square performance of the new polynomials together with the geometrical insight of Bernstein polynomials. The MJPs with indexes corresponding to the number of endpoints constraints are the natural basis functions for Least-square approximation of Bezier curves. Using MJPs leads us to deal with the constrained Jacobi polynomials and the unconstrained Jacobi polynomials as orthogonal polynomials. The MJPs are automatically satisfying the homogeneous boundary conditions. Thereby, the main advantage of using MJPs, in multi-degree reduction of Bezier curves on computer aided geometric design (CAGD), is that the constraints in CAGD are also satisfied and that decreases the steps of multi-degree reduction algorithm. Several numerical results for the multi-degree reduction of Bezier curves on CAGD are given.

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Basis Transformation, Modified Jacobi Polynomials, Bernstein Polynomials, Galerkin Orthogonal Polynomials, Multiple Degree Reduction Of Bezier Curves

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Bhrawy, A.H...et al. (2016). Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bezier curves. Journal of Computational and Applied Mathematics, 302, 369-384. http://dx.doi.org/10.1016/j.cam.2016.01.009

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Source

Journal of Computational and Applied Mathematics

Volume

302

Issue

Start Page

369

End Page

384