The design, implementation, and testing of a C++ software library for univariate polynomials in Bernstein form is described. By invoking the class environment and operator overloading, each polynomial in an expression is interpreted as an object compatible with the arithmetic operations and other common functions (subdivision, degree, elevation, differentiation and integration, composition, greatest common divisor, real-root solving, etc.) for polynomials in Bernstein form. The library allows compact and intuitive implementation of lengthy manipulation of Bernstein-form polynomials, which often arise in computer graphics and computer-aided design and manufacturing applications. A series of empirical tests indicates that the library functions are typically very accurate and reliable, even for polynomials of surprisingly high degree. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 10 articles , 1 standard article )

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  1. Bourne, Martin; Winkler, Joab R.; Yi, Su: The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials (2017)
  2. Dong, Bohan; Farouki, Rida T.: Algorithm 952: PHquintic: a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph curves (2015)
  3. Sánchez-Reyes, J.: Detecting symmetries in polynomial Bézier curves (2015)
  4. Corless, Robert M.; Fillion, Nicolas: A graduate introduction to numerical methods. From the viewpoint of backward error analysis (2013)
  5. Farouki, Rida T.: The Bernstein polynomial basis: a centennial retrospective (2012)
  6. Farouki, Rida T.; Han, Chang Yong: Robust plotting of generalized lemniscates (2004)
  7. Farouki, Rida T.; Han, Chang Yong; Hass, Joel; Sederberg, Thomas W.: Topologically consistent trimmed surface approximations based on triangular patches (2004)
  8. Heitzinger, Clemens; Hössinger, Andreas; Selberherr, Siegfried: An algorithm for smoothing three-dimensional Monte Carlo ion implantation simulation results (2004)
  9. Song, Xiaowen; Sederberg, Thomas W.; Zheng, Jianmin; Farouki, Rida T.; Hass, Joel: Linear perturbation methods for topologically consistent representations of free-form surface intersections (2004)
  10. Tsai, Yi-Feng; Farouoki, Rida T.: Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form (2001)