Construction of Surfaces Defined from Planar Curves in Python

Abstract

This article presents five techniques for constructing surfaces from planar curves. First, the bilinear surface is studied, which requires four points for its definition. By generalizing this surface, the so-called ruled surfaces are obtained, which are widely used in the aeronautical industry. Within the ruled surfaces, a particular case is the cylindrical surfaces, which are generated by moving a planar curve along a straight path. Another technique for generating surfaces consists of rotating a planar curve around an axis in space, giving rise to surfaces of revolution. Finally, the concept of Swung surfaces is introduced, a generalization of surfaces of revolution in which the curve does not rotate around a circumference, but follows an arbitrary trajectory. These concepts have been implemented in Python as a pedagogical tool for undergraduate courses, taking advantage of its accessibility and ease for the visualization of mathematical concepts. Although the article presents the theoretical foundations of each type of surface, it would be relevant to delve into the restrictions and limitations that may arise when generating them. Analyzing these challenges would allow us to develop new strategies for the construction and manipulation of surfaces, thus opening opportunities for future research and applications.