The Logarithmic Curvature Graphs of Generalised Cornu Spirals

TL;DR

This paper analyzes the aesthetic qualities of the Generalized Cornu Spiral using Log Curvature Graphs, confirming its status as a generalized aesthetic curve with potential applications in surface design.

Contribution

It introduces an analysis method using LCG to evaluate the GCS's aesthetic value, supporting its classification as a generalized aesthetic curve.

Findings

GCS exhibits monotonic curvature, indicating high surface quality.

LCG analysis confirms GCS as a generalized aesthetic curve.

Supports potential applications in surface design.

Abstract

The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [2]. In this paper, the analysis of GCS segment is carried out by determining its aesthetic value using the log curvature Graph (LCG) as proposed by Kanaya et al.[10]. The analysis of LCG supports the claim that GCS is indeed a generalized aesthetic curve.