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

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

Symmetry, vol.17, no.2, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.3390/sym17020219
  • Journal Name: Symmetry
  • Journal Indexes: 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
  • Keywords: B & eacute;zier curve, B & eacute;zier surface, surfaces of revolution, convex hull containment
  • Dokuz Eylül University Affiliated: Yes

Abstract

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.