On the variety of planar spirals and their applications in computer aided design

TL;DR

This paper explores various planar spiral segments with monotonic curvature functions, highlighting their importance in geometric modeling, aesthetic shape design, and applications in computer-aided design.

Contribution

It provides an overview of the variety of planar spirals and discusses their applications in CAD and aesthetic shape modeling.

Findings

Planar spiral segments with monotonic curvature are significant in geometric modeling.

They are used for G1 and G2 Hermite interpolation.

These curves are crucial for generating aesthetically pleasing splines.

Abstract

In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and computer aided geometric design as fair curves, and they are very significant in aesthetic shape modelling. Fair curve segments are used for two-point G1 and G2 Hermite interpolation, as well as for generating aesthetic splines.