Original Research

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

W.F. Harris
African Vision and Eye Health | South African Optometrist: Vol 64, No 4 | a235 | DOI: https://doi.org/10.4102/aveh.v64i4.235 | © 2005 W.F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 19 December 2005 | Published: 19 December 2005

About the author(s)

W.F. Harris, Optometric Science Research Group, Department of Optometry, and Department of Mathematics and Statistics, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa, South Africa

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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.

Keywords

Curves, curvature, torsion, varifocal lenses, theory of contact, differential geometry

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