Flat spline

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A spline consists of a long strip fixed in position at a number of points whose tension creates a smooth curve passing through those points, for the purpose of transferring that curve to another material.^[1]

Before computers were used for creating engineering designs, drafting tools were employed by designers drawing by hand.^[2] 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).^[1] 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.^[3]

One can recreate an original draftsman's spline device with weights and a length of thin plastic or wood, flexible to bend enough without breaking. Crosses are marked on the paper to designate the knots or control points. The spline is placed on the drafting paper, and weights are attached to the shaft near each knot so that the spline passes through each one. Once adjusted to the satisfaction of the drafter, a line may be traced along the shaft, creating a template for a smooth curve.^[1][3]