Homogeneous ¯q-blossoming and Bézier curves


Montes Taurus Journal of Pure and Applied Mathematics, vol.4, no.2, pp.86-102, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 2
  • Publication Date: 2022
  • Journal Name: Montes Taurus Journal of Pure and Applied Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.86-102
  • Keywords: (q1 q2)-Bernstein basis functions, (q1 q2)-Bézier curves, de Casteljau algorithm, homogeneous ¯q-blossom, q-blossom, subdivision
  • Dokuz Eylül University Affiliated: Yes


Homogeneous ¯q-blossom is introduced by altering the diagonal property of classical homogeneous blossom. We apply this new blossom to define two parameter family of Bernstein basis functions and Bézier curves. A special case of homogeneous ¯q-blossom gives infinitely many de Casteljau type algorithms for classical Bézier curves. An analogue of Marsden’s identity is also derived by applying homogeneous ¯q-blossom. Properties and identities of new Bernstein basis functions and Bézier curves including affine invariance, linear precision and end point interpolation derived. De Casteljau type evaluation algorithm is used to develop a subdivision procedure for (q1, q2)-Bézier curves. Finally, it is shown that the control polygons generated by recursive midpoint subdivision converge uniformly to the original (q1, q2)-Bézier curve.