Duhamel du Monceau, writing in 1758, states that an experienced designer can join these points freehand while a novice may have to resort to bending small ribbands or splines as an aid (Duhamel 1758:241). Since bending splines does not involve any regular geometry or quantification, this is a major step toward freedom of design. In addition, Duhamel du Monceau states that the diagonals themselves can be oriented at various angles to the baseline of the equilateral triangle (Duhamel 1758:233). Changing the angle of these lines relative to the baseline allows for the altering of the nature of the diagonal's curve along its length, while still retaining a similarity of curvature with the other diagonals. The choice of these angles is completely at the designer's discretion without any additional rules or restrictions. Mungo Murray, who wrote a treatise on shipbuilding that includes a translation of Duhamel du Monceau's work, writes in frustration on the inability to formalize this method: "but as the artists leave us so much undetermined as to the angles that each diagonal is to make… when they are applied to the triangle, it will be very difficult to apply this method to practice." (Duhamel 1764:32; Murray 1765).

By the beginning of the nineteenth century this trend toward overcoming the restrictions inherent to geometric fairing methods results in a great conceptual leap—the almost complete abandonment of geometric fairing. The modern drawing of a hull adopted at about this time—the lines drawing—is conceptually the graphic equivalent of carving a model of the hull shape in wood. Unlike in geometric fairing, in which measurements are generated in order to draw fair curves, in this graphic version of optical fairing measurements for construction are taken from curves that have been drawn without any mathematical rules or restrictions. Thus the lines drawing offers complete freedom to define any shape desired.

With the development of the lines drawing method of hull design came the realization that the use of geometric fairing methods does not have any inherent connection with the performance of a hull shape. What they did offer through the centuries of their use was a method of standardizing and replicating hull shapes that were empirically determined to be desirable. It is important to keep in mind that the development of these geometric design methods predates the discovery and practical application of most scientific methods of reliably predicting hull performance (Ferreiro 2007; Phillips-Birt 1957:1–17). In addition, by predetermining frame shapes, these methods made it possible to build using a frame-first construction sequence that is both practical and economical.

I do not believe, however, that the development of design methods that enabled the predetermination of frame shapes for a frame-first construction sequence was a complete conceptual shift from the design principles involved in shell-first construction. NEXT