An algorithm for autonomously plotting solution sets in the presence of turning points

TL;DR

This paper introduces a general algorithm for plotting solution sets of equations that effectively handles turning points, with applications demonstrated through verification and complex examples, including potential extensions to three-dimensional curves.

Contribution

The paper presents a novel, general algorithm for plotting solution sets with turning points, applicable to bivariate and potentially three-dimensional equations.

Findings

Algorithm successfully overcomes turning points in solution plotting

Demonstrated with verification and complex application examples

Includes thorough run-time analysis and discusses generalization to 3D

Abstract

Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications of the algorithm are highlighted through two examples: the first provides verification, while the second demonstrates a non-trivial application. The latter is followed by a thorough run-time analysis. While both examples deal with bivariate equations, it is discussed how the algorithm may be generalized for space curves in $\R^{3}$.