On isophote curve and its characterizations

TL;DR

This paper investigates the properties of isophote curves on surfaces, focusing on their axes via Darboux frames and providing characterizations, especially for isophotes on canal surfaces.

Contribution

It introduces a method to find the axis of isophote curves using Darboux frames and offers new characterizations, including for isophotes on canal surfaces.

Findings

Axis of isophote curves can be determined via Darboux frames.

Characterizations of isophote curves and their axes are established.

Special properties of isophotes on canal surfaces are identified.

Abstract

Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. Main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about isophote and its axis. Particularly, for isophotes lying on a canal surface will be obtained other characterizations again.