Flat spline
Encyclopedia
A spline or the more modern term flexible curve consists of a long strip fixed in position at a number of points that relaxes to form and hold a smooth curve passing through those points for the purpose of transferring that curve to another material.
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 lath
s, not to be confused with lathe
s). 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.
Splines are more recently referred to as flexible curves and perform much of the original function. The main difference between splines and flexible curves is that the control points of flexible curves are entirely internal in their housing. This has one advantage over splines: whereas the draftsman had to first set up the spline and control points before moving the object to be marked to the spline in that order only, with flexible curves the draftsman can also set up the flexible curve before carefully moving the flexible curve to the object to be marked.
One can recreate an original 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.http://www.cs.wisc.edu/~deboor/draftspline.html
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
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 elastomer
ic materials.
Spline devices help bend the wood for pianos, violins, violas, etc. The Wright brothers
used one to shape the wings of their aircraft.
Before computers were used for creating engineering designs
Computer-aided design
Computer-aided design , also known as computer-aided design and drafting , is the use of computer technology for the process of design and design-documentation. Computer Aided Drafting describes the process of drafting with a computer...
, drafting tools
Technical drawing
Technical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or has to be constructed.Drafting is the language of industry....
were employed by designers drawing by hand. To draw curves, especially for shipbuilding
Shipbuilding
Shipbuilding is the construction of ships and floating vessels. It normally takes place in a specialized facility known as a shipyard. Shipbuilders, also called shipwrights, follow a specialized occupation that traces its roots to before recorded history.Shipbuilding and ship repairs, both...
, draftsmen often used long, thin, flexible strips of wood, plastic, or metal called splines (or lath
Lath
A lath is a thin, narrow strip of some straight-grained wood or other material, including metal or gypsum. A lattice, or lattice-work, is a criss-crossed or interlaced arrangement of laths, or the pattern made by such an arrangement...
s, not to be confused with lathe
Lathe
A lathe is a machine tool which rotates the workpiece on its axis to perform various operations such as cutting, sanding, knurling, drilling, or deformation with tools that are applied to the workpiece to create an object which has symmetry about an axis of rotation.Lathes are used in woodturning,...
s). The splines were held in place with lead weights (called ducks because of their duck
Duck
Duck is the common name for a large number of species in the Anatidae family of birds, which also includes swans and geese. The ducks are divided among several subfamilies in the Anatidae family; they do not represent a monophyletic group but a form taxon, since swans and geese are not considered...
-like shape). The elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
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.
Splines are more recently referred to as flexible curves and perform much of the original function. The main difference between splines and flexible curves is that the control points of flexible curves are entirely internal in their housing. This has one advantage over splines: whereas the draftsman had to first set up the spline and control points before moving the object to be marked to the spline in that order only, with flexible curves the draftsman can also set up the flexible curve before carefully moving the flexible curve to the object to be marked.
One can recreate an original 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.http://www.cs.wisc.edu/~deboor/draftspline.html
In 1946, mathematicians started studying the spline shape, and derived the piecewise polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
formula known as the spline curve
Spline (mathematics)
In mathematics, a spline is a sufficiently smooth piecewise-polynomial function. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher...
or spline function. This has led to the widespread use of such functions in computer-aided design
Computer-aided design
Computer-aided design , also known as computer-aided design and drafting , is the use of computer technology for the process of design and design-documentation. Computer Aided Drafting describes the process of drafting with a computer...
, especially in the surface designs of vehicles. I. J. Schoenberg
Isaac Jacob Schoenberg
Isaac Jacob Schoenberg was a Romanian mathematician, known for his discovery of splines.He studied at the University of Iaşi, receiving his M.A. in 1922. From 1922 to 1925 he studied at the Universities of Berlin and Göttingen, working on a topic in analytic number theory suggested by Issai Schur...
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 elastomer
Elastomer
An elastomer is a polymer with the property of viscoelasticity , generally having notably low Young's modulus and high yield strain compared with other materials. The term, which is derived from elastic polymer, is often used interchangeably with the term rubber, although the latter is preferred...
ic materials.
Spline devices help bend the wood for pianos, violins, violas, etc. The Wright brothers
Wright brothers
The Wright brothers, Orville and Wilbur , were two Americans credited with inventing and building the world's first successful airplane and making the first controlled, powered and sustained heavier-than-air human flight, on December 17, 1903...
used one to shape the wings of their aircraft.