Original Research

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

W.F. Harris
African Vision and Eye Health | South African Optometrist: Vol 65, No 1 | a246 | DOI: https://doi.org/10.4102/aveh.v65i1.246 | © 2006 W.F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 19 December 2006 | Published: 19 December 2006

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

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Abstract

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.

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