Coons Surfaces Expressed as B-Spline Surfaces in Python

Abstract

This study analyzes the representation of Coons surfaces using B-Spline, implementing algorithms in Python for their visualization and manipulation. B-Spline basis functions and the Oslo Algorithm are employed to enhance the precision, continuity, and adaptability of surfaces without altering their geometry. The conversion of Coons surfaces to B-Spline optimizes flexibility in Computer-Aided Geometric Design (CAGD). These surfaces are crucial as they allow for smooth surface interpolation from boundary curves, facilitating applications in structural simulation, digital animation, and industrial design. The results demonstrate that the B-Spline-based formulation improves control over surface interpolation without requiring additional structures. Furthermore, these geometric modeling techniques highlight Python as an accessible tool for research and education, as understanding these mathematical aspects enhances the representation of curves and surfaces in computational geometric modeling.