Cubic and bicubic spline interpolation in Python

This page contains the source codes associated to the HAL technical note for setting up and plotting cubic splines and bicubic parametric surfaces with various end conditions.

Download pdf and Python 3.8 files

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. Proceed to the bottom of the page for an overview of practical examples.

Python source code: free end condition

cubic spline interpolated on a set of fit knots with free end conditions

Python source code: imposed tangent direction

cubic spline interpolated on a set of fit knots with imposed tangent directions at ends

Python source code: end-to-end tangent continuity

cubic spline interpolated on a set of fit knots with end-to-end tangent continuity

Python source code: not-a-knot end condition

cubic spline interpolated on a set of fit knots with not-a-knot end conditions

Python source code: free end condition

bicubic parametric surface interpolated on a set of fit knots with free end conditions

Python source code: cylindrical closed surface

closed bicubic parametric surface interpolated on a randomized cylindrical set of fit knots

Python source code: spherical closed surface

fully closed bicubic parametric surface interpolated on a randomized spherical set of fit knots

Python source code: not-a-knot end condition

bicubic parametric surface interpolated on a set of fit knots with not-a-knot end conditions