Curves and surfaces in the context of optometry. Part 1: Curves*

W.F Harris

doi:10.4102/aveh.v64i4.235

Abstract

This paper introduces the differential geom-etry of curves in Euclidean 3-space, the motiva-tion being the writer’s belief that, despite their fundamental importance, curves are inadequate-ly treated in optometric educational programs. Curvature and torsion are defined along a curve. Two numerical examples are presented. The fundamental theorem of curves is stated. The relationship of the geometry of varifocal lenses and curves known as involutes are discussed. A brief treatment of the theory of contact is given with suggestions of applications in contact between spectacle lenses and frames, contact lenses and corneas (including orthokeratology), intra-ocular lenses and structures in the eye, and spectacle frames and the face.

Highlights

Despite their fundamental importance in optometry curves and surfaces are treated superficially and naïvely in optometric educational programs
Curvature and torsion are defined along a curve
Involutes and the theory of contact are discussed. The former have a bearing on the geometry of varifocal lenses and the latter on several matters of optometric importance including contact between spectacle lens and frame and contact lens and cornea and orthokeratology

Summary

Introduction

Despite their fundamental importance in optometry curves and surfaces are treated superficially and naïvely in optometric educational programs. A curve is defined as a set of parametrizations. Curvature and torsion are defined along a curve. Vector Function of a Scalar Variable Let x be a function of a scalar t defined on an interval I of the real number line.We write it as x = f(t) t I.

Results

Conclusion