Bézier Curves and Surfaces with the Blending (α, λ, s)-Bernstein Basis

KARAKILIÇ İ., KARAKILIÇ S., BUDAKÇI G., Özger F.

Symmetry, cilt.17, sa.2, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17020219
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Bézier curve, Bézier surface, convex hull containment, surfaces of revolution
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

This study presents a generalized approach to Bézier curves and surfaces by utilizing the blending (Formula presented.) -Bernstein basis. The (Formula presented.) -Bernstein basis introduces shape parameters (Formula presented.), (Formula presented.), and s, which allow for more flexibility and control over the curve’s shape compared to the classical Bernstein basis. The paper explores the properties of these generalized curves and surfaces, demonstrating their ability to maintain essential geometric characteristics, such as convex hull containment and endpoint interpolation, while providing enhanced control over the shape. This work aims to contribute to the fields of computer-aided geometric design and related applications by offering a robust tool for curve and surface modeling.