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A new family of shape-adjustable generalized Bézier curves and surfaces based on the Bernstein basis

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  • Rashidi, Mahdis
  • Eslahchi, M.R.

Abstract

This study presents a new family of generalized Bernstein basis functions (G-basis) and their corresponding generalized Bézier curves (G-curve), in both rational and non-rational forms. By introducing shape parameters and a shape-controlling function, the framework extends traditional Bernstein basis to support a wider range of functional spaces while maintaining essential shape-preserving properties. The G-basis family improves geometric control without changing control points and allows both global and local shape manipulation. A stable and efficient corner-cutting algorithm is proposed for computing G-curve, and the approach is extended to surface modeling (G-surface) in computer aided geometric design (CAGD) and computer graphics (CG). Conditions for continuity are derived to ensure smooth transitions. Experimental results demonstrate the method’s effectiveness and flexibility compared to classical approaches.

Suggested Citation

  • Rashidi, Mahdis & Eslahchi, M.R., 2026. "A new family of shape-adjustable generalized Bézier curves and surfaces based on the Bernstein basis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 250(C), pages 786-812.
    • Handle: RePEc:eee:matcom:v:250:y:2026:i:c:p:786-812
    DOI: 10.1016/j.matcom.2026.07.008
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