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

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...

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Main Author:	W.F. Harris
Format:	Article
Language:	English
Published:	AOSIS 2005-12-01
Series:	African Vision and Eye Health
Subjects:	Curves, curvature, torsion, varifocal lenses, theory of contact, differential geometry
Online Access:	https://avehjournal.org/index.php/aveh/article/view/235

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spelling	doaj-9847be96c7af49ba85a697c70839cfdc2020-11-24T21:32:40ZengAOSISAfrican Vision and Eye Health2413-31832410-15162005-12-0164411812510.4102/aveh.v64i4.235204Curves and surfaces in the context of optometry. Part 1: Curves*W.F. Harris0Optometric Science Research Group, Department of Optometry, and Department of Mathematics and Statistics, University of Johannesburg, PO Box 524, Auckland Park, 2006 South AfricaThis 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.https://avehjournal.org/index.php/aveh/article/view/235Curves, curvature, torsion, varifocal lenses, theory of contact, differential geometry
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	W.F. Harris
spellingShingle	W.F. Harris Curves and surfaces in the context of optometry. Part 1: Curves* African Vision and Eye Health Curves, curvature, torsion, varifocal lenses, theory of contact, differential geometry
author_facet	W.F. Harris
author_sort	W.F. Harris
title	Curves and surfaces in the context of optometry. Part 1: Curves*
title_short	Curves and surfaces in the context of optometry. Part 1: Curves*
title_full	Curves and surfaces in the context of optometry. Part 1: Curves*
title_fullStr	Curves and surfaces in the context of optometry. Part 1: Curves*
title_full_unstemmed	Curves and surfaces in the context of optometry. Part 1: Curves*
title_sort	curves and surfaces in the context of optometry. part 1: curves*
publisher	AOSIS
series	African Vision and Eye Health
issn	2413-3183 2410-1516
publishDate	2005-12-01
description	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.
topic	Curves, curvature, torsion, varifocal lenses, theory of contact, differential geometry
url	https://avehjournal.org/index.php/aveh/article/view/235
work_keys_str_mv	AT wfharris curvesandsurfacesinthecontextofoptometrypart1curves
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Curves and surfaces in the context of optometry. Part 1: Curves*

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