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Pythagorean-hodograph curves on isothermal surfaces. (English) Zbl 0959.65033

Cripps, Robert (ed.), The mathematics of surfaces. VIII. Proceedings of the 8th IMA conference held in Birmingham, GB, August and September 1998. Winchester: Information Geometers. 339-353 (1998).
Summary: Polynomial or rational isothermal surfaces are offset-rational surfaces. There are isothermal surfaces on which the curves are Pythagorean-hodograph (PH) curves. Weierstrass’s formula allows us to construct isothermal minimal surfaces; one of which is Enneper’s minimal surface. This surface is a offset-rational polynomial surface and all the image curves of the straight lines in the parameter space of the surface are PH space cubics. We also construct principal, asymptotic and triangular patches bounded by PH space cubics on such surfaces.
For the entire collection see [Zbl 0938.00014].

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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