Asymptotes of Space Curves

TL;DR

This paper extends previous work on asymptotes to real algebraic space curves, providing a method to compute generalized asymptotes using the concept of perfect curves.

Contribution

It introduces a new approach to compute asymptotes of space curves based on the notion of perfect curves, generalizing earlier results.

Findings

Method to compute generalized asymptotes of space curves

Extension of asymptote concepts to space curves

Utilization of perfect curves for asymptote computation

Abstract

In this paper, we generalize the results presented in [5] for the case of real algebraic space curves. More precisely, given an algebraic space curve C (parametrically or implicitly defined), we show how to compute the generalized asymptotes. The approach is based on the notion of perfect curve introduced from the concepts and results presented in [4].