# Flat spline: Wikis

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# Encyclopedia

A spline.

A spline consists of a long strip fixed in position at a number of points that relaxes to form a smooth curve passing through those points.

Before computers were used for creating engineering designs, drafting tools were employed by designers drawing by hand. To draw curves, especially for shipbuilding, draftsmen often used long, thin, flexible strips of wood, plastic, or metal called splines (or laths, not to be confused with lathes). The splines were held in place with lead weights (called ducks because of their duck-like shape). The elasticity of the spline material combined with the constraint of the control points, or knots, would cause the strip to take the shape that minimized the energy required for bending it between the fixed points, this being the smoothest possible shape.

One can recreate a draftsman's spline device with weights and a length of thin stiff plastic or rubber tubing. The weights are attached to the tube (by gluing or pinning). The tubing is then placed over drawing paper. Crosses are marked on the paper to designate the knots or control points. The tube is then adjusted so that it passes over the control points[1].

In 1946, mathematicians started studying the spline shape, and derived the piecewise polynomial formula known as the spline curve or spline function. This has led to the widespread use of such functions in computer-aided design, especially in the surface designs of vehicles. I. J. Schoenberg[1] gave the spline function its name after its resemblance to the mechanical spline used by draftsmen.

The origins of the spline in wood-working may show in the conjectured etymology which connects the word spline to the word splinter. Later craftsmen have made splines out of rubber, steel, and other elastomeric materials.

Spline devices help bend the wood for pianos, violins, violas, etc. The Wright brothers used one to shape the wings of their aircraft.

## References

1. ^ I. J. Schoenberg, Spline Functions and the Problem of Graduation PNAS 1964 52: 947-950 pdf