Bernstein Polynomials: Properties and Applications to Bezier Curves, B-Splines, and Solution of Boundary Value Problems

Properties and Applications to Bezier Curves, B-Splines and Solution of Boundary Value Problems


  • Anandaram Mandyam Professor of Physics (Retired), Bangalore University, Bangalore, Karnataka, India



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.


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