Homogeneous ¯q-blossoming and Bézier curves

DİŞİBÜYÜK Ç.

Montes Taurus Journal of Pure and Applied Mathematics, cilt.4, sa.2, ss.86-102, 2022 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Sayı: 2
  • Basım Tarihi: 2022
  • Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.86-102
  • Anahtar Kelimeler: (q1 q2)-Bernstein basis functions, (q1 q2)-Bézier curves, de Casteljau algorithm, homogeneous ¯q-blossom, q-blossom, subdivision
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.