# On Geometry of Isophote Curves in Galilean space

## TL;DR

This paper explores the geometry of isophote curves on surfaces in Galilean 3-space, analyzing their properties, computation methods, and relationships with helices, including specific cases on surfaces of revolution.

## Contribution

It introduces the concept of isophote curves in Galilean space, distinguishes cases based on the nature of the axis vector, and provides methods for their computation on surfaces of revolution.

## Key findings

- Derived formulas for isophote curves on surfaces of revolution
- Established relationship between isophote curves and slant helices
- Provided an example of computing isophote curves on isotropic surfaces

## Abstract

In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an isotropic or a non isotropic vector. We also give the method to compute isophote curves of surfaces of revolution. Subsequently, we show the relationship between isophote curves and slant(general) helices on surfaces of revolution obtained by revolving a curve by Euclidean rotations. Finally, we give an example to compute isophote curves on isotropic surfaces of revolution.