The Representation of Line Dirac Delta Function Along a Space Curve

TL;DR

This paper develops a mathematical representation of the line Dirac delta function along space curves, extending it to level set formulations and plane curves, with potential applications in higher dimensions.

Contribution

It introduces a novel representation of the line Dirac delta function along curves and extends the concept to level set and plane curves, applicable in higher dimensions.

Findings

Representation of line Dirac delta in terms of distance functions

Extension to level set and plane curves

Applicability to higher-dimensional spaces

Abstract

In this paper, we describe the line Dirac delta function of a curve in three-dimensional space in terms of the distance function to the curve. Its extension to level set formulation and plane curves are also developed. The main ideas can be applied for general dimension and codimension.