Fairing of planar curves to log-aesthetic curves

TL;DR

This paper introduces an algorithm for approximating planar curves with log-aesthetic curves, providing a tool for reverse engineering in geometric design, demonstrated through a 3D scan application.

Contribution

It presents a novel parametric approximation method for fitting log-aesthetic curves to planar data, characterized by seven parameters.

Findings

Unique characterization of LAC segments by seven parameters

Effective approximation method demonstrated on 3D scan data

Tool useful for reverse engineering in CAD applications

Abstract

We present an algorithm to fair a given planar curve by a log-aesthetic curve (LAC). We show how a general LAC segment can be uniquely characterized by seven parameters and present a method of parametric approximation based on this fact. This work aims to provide tools to be used in reverse engineering for computer aided geometric design. Finally, we show an example of usage by applying this algorithm to the point data obtained from 3D scanning a car's roof.