Curves and surfaces in the context of optometry. Part 2: Surfaces

Curves and surfaces in the context of optometry. Part 2: Surfaces

This paper introduces the differential geom-etry of surfaces in Euclidean 3-space. The first and second fundamental forms of a surface are defined.   The  first  fundamental  form  provides a metric for calculations of length and area on the surface. The second fundamental form deter-mines surface c...

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Main Author: W.F. Harris
Format: Article
Language:English
Published: AOSIS 2006-12-01
Series:African Vision and Eye Health
Online Access:https://avehjournal.org/index.php/aveh/article/view/246
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spelling doaj-ac6faafab5884559852deab2ce3212112020-11-24T21:38:18ZengAOSISAfrican Vision and Eye Health2413-31832410-15162006-12-0165141110.4102/aveh.v65i1.246215Curves and surfaces in the context of optometry. Part 2: SurfacesW.F. Harris0Optometric Science Research Group, Department of Optometry, and Department of Mathematics and Statistics, University of Johannesburg, PO Box 524, Auckland Park, 2006This paper introduces the differential geom-etry of surfaces in Euclidean 3-space. The first and second fundamental forms of a surface are defined.   The  first  fundamental  form  provides a metric for calculations of length and area on the surface. The second fundamental form deter-mines surface curvature and, hence, concepts of importance in optometry such as surface power and sagitta. The principal curvatures at a point on a surface are obtained as solutions of a qua-dratic equation. The torus is used to illustrate the methods.https://avehjournal.org/index.php/aveh/article/view/246
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 2: Surfaces
African Vision and Eye Health
author_facet W.F. Harris
author_sort W.F. Harris
title Curves and surfaces in the context of optometry. Part 2: Surfaces
title_short Curves and surfaces in the context of optometry. Part 2: Surfaces
title_full Curves and surfaces in the context of optometry. Part 2: Surfaces
title_fullStr Curves and surfaces in the context of optometry. Part 2: Surfaces
title_full_unstemmed Curves and surfaces in the context of optometry. Part 2: Surfaces
title_sort curves and surfaces in the context of optometry. part 2: surfaces
publisher AOSIS
series African Vision and Eye Health
issn 2413-3183
2410-1516
publishDate 2006-12-01
description This paper introduces the differential geom-etry of surfaces in Euclidean 3-space. The first and second fundamental forms of a surface are defined.   The  first  fundamental  form  provides a metric for calculations of length and area on the surface. The second fundamental form deter-mines surface curvature and, hence, concepts of importance in optometry such as surface power and sagitta. The principal curvatures at a point on a surface are obtained as solutions of a qua-dratic equation. The torus is used to illustrate the methods.
url https://avehjournal.org/index.php/aveh/article/view/246
work_keys_str_mv AT wfharris curvesandsurfacesinthecontextofoptometrypart2surfaces
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