Cubic and bicubic spline interpolation in Python

Quentin Agrapart (1) , Alain Batailly (1)

1 EPM - École Polytechnique de Montréal

Cubic and bicubic spline interpolations are widely used in a variety of domains. Nonetheless, there are limited resources available to help students or professionals who wish to implement these tools within a computer program. Be it for visualization purposes or for use within sophisticated algorithms, building a 2D or a 3D spline may not be a straightforward process. In this context, the present technical note provides a brief theoretical description of both splines and bicubic splines but also focuses on the practical implementation of both concepts with an emphasis on the various types of boundary conditions that may be used. In particular, different configurations featuring free end conditions, not-a-knot end conditions or particular tangent orientations to build both open and closed parametric curves and surfaces are detailed. Several source codes—written in Python 3.8—are provided with the intent to facilitate the reproduction of presented results.

Mots clés: cubic spline; bicubic parametric surface; Python; spline interpolation on fit knots; influence of control points; B-spline functions; Cox-de-Boor algorithm; free end condition; not-a-knot end condition; end-to-end tangent continuity; cylindrical and spherical closed surface

Domaines: Génie mécanique [physics.class-ph]

Quentin Agrapart, Alain Batailly. Cubic and bicubic spline interpolation in Python. [0] École Polytechnique de Montréal. 2020. ⟨hal-03017566v2⟩