Therefore, in this "new" French design method, the normal runs of planks or ribbands, exhibiting double curvature, were transformed into design diagonals that are always straight in the body plan. These diagonals would be drawn first in the body plan without the use of any transverse templates. Curve offsets could then be directly plotted on these diagonals, thus making it possible to draw the shapes of all the design frames in one cross-sectional view—the body plan. However, in the sheer and breadth plans, the curves defined by these diagonals were still separated into their narrowing and rising components in order to show how these diagonal curves would actually appear on the hull in plan and profile.

This transition to graphic design was thus dependent on both the knowledge of the existing methods of quantifying curvature in ship design and advances in orthographic drawing methods in terrestrial art, architecture, and engineering. It is an intriguing possibility that this is exactly the mixing of ideas that occurred when terrestrial architects were brought to Toulon to teach the next generation of shipwrights drafting methods. Unfortunately, from the surviving historical evidence it is only known that this interaction occurred and not specifically what drawing methods were developed or how quickly or widely they were adapted. For example, the same François Coulomb, who drew the 1684 flute draft illustrating the method of geometric fairing with diagonals (Figure 7), wrote a description of the Mediterranean moulding method of design in 1683 (Lemineur 2007; Rieth 1998b). This manuscript presumably was meant to represent the current method of ship design since it was based on his lessons at the school for naval cadets in Toulon, where he was the head instructor since 1681. Although François Coulomb presents an innovative method of extending the design of the floor timbers to the ends of the hull, the basic method he describes is traditional Mediterranean moulding (Rieth 1998b).

Although such evidence indicates that this was a period of experimentation and transition in design, La Belle's archaeological remains clearly show that the new method of graphic design with diagonals was already effectively being used for the everyday construction of vessels by 1684. La Belle's example also concretely shows that this shift to graphic design allowed for both the predetermination of a larger percentage of the hull shape and greater flexibility in drawing the frame shapes.

Since in this design method the diagonals are drawn and the guide points defined without the use of any transverse templates, it is in theory possible to insert as many diagonals as is desired. With only one additional bilge diagonal added, it is still necessary to have some geometrical rules for joining the widely spaced guide points. With the introduction of more diagonals and thus with more guide points, such restrictions became increasingly unnecessary. NEXT