Properties and Applications to Bezier Curves, B-Splines and Solution of Boundary Value Problems
Keywords:Bernstein polynomials (B-polys), B-Splines, Bezier Curves, BVP solution
Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obtaining B-polys, B-splines or Basis spline functions, Bezier curves and ODE solution curves, is computationally demonstrated. An example is also described showing their application to solving a fourth-order BVP relating to the bending at the free end of a cantilever.
J. S. Racine,”A Primer on Regression Splines”,(Chapter article), 2019. Pdf (downloadable from https://cran.r-project.org/ web/ packages/ crs/vignettes/spline_primer.pdf )
M. I. Bhatti and P. Bracken,” Solutions of differential equations in a Bernstein polynomial basis”, Journal of Computational and Applied Mathematics, Vol. 205(1), pp.272-280, 2007.
J. Magoon, "Application of the b-spline collocation method to a geometrically non-linear beam problem" , MS Thesis, 2010, RIT, 2010. (Access from: http://scholarworks.rit.edu/theses )
R. Jhaveri, "Design of passive suspension system with non-linear springs using b-spline collocation method", MS Thesis, RIT, 2011. (Accessfrom:http://scholarworks.rit.edu/theses)
H.Bachau etal., “Applications of B-splines in atomic and molecular physics”, Rep. Prog. Phys. 64, 1815–1942, 2001.
Johnson, “Lectures in Atomic Physics”, University of Notre Dame, USA, 2006. (access this book from) https:// www3.nd.edu/ ~johnson/Publications/book.pdf
Copyright (c) 2021 Mapana Journal of Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.