Mathematical Ship Lines and Surfaces

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Abstract
A mathematical spline, with mathematical ducks, is proposed for naval architecture as an alternative to the familiar draftsman's spline with its lead ducks. These mathematical tools are handled in virtually the same way that their traditional counterparts are used, as the hull form is developed line by line. A visual study of the curvature graph of the new spline substitutes for the naval architect's touch when testing for fairness. After the lines have been laid down and faired in, a mathematical surface is constructed automatically. Next, another new tool is applied: a graphic display of the Gaussian curvature of the whole hull is drawn at the designer's computer terminal. This display permits a visual evaluation of surface curvature, which is comparable to a model maker's test of surface fairness. Examples are given of lines laid down with mathematical splines and of the Gaussian curvature display.

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