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

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.