Curvatures at the singular points of algebraic curves and surfaces

TL;DR

This paper introduces algorithms to compute curvatures at singular points of algebraic curves and surfaces by transforming the problem into curvature calculations of related regular parametric entities.

Contribution

The paper presents three novel algorithms for calculating curvatures at singular points of algebraic curves and surfaces, enhancing existing computational methods.

Findings

Algorithms successfully compute curvatures at singular points

Method applies to plane curves, space curves, and surfaces

Improves accuracy and efficiency of curvature computation at singularities

Abstract

In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which have intersections with the original curves and surfaces at the singular points. Three algorithms are presented for three cases of plane curves, space curves and surfaces.