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A related but distinct device is the "flexible curve", which can be molded by hand and used to design or copy a complex curve. Unlike a spline, the flexible curve does not have significant tension, so it maintains a given shape, instead of minimizing its curvature between point. The equivalent device
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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
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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.
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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.
455:"Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae"
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168:, 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.
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By 1946, mathematicians had begun to devise mathematical formulae to serve a similar purpose, and ultimately created efficient algorithms to find piecewise
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Rheault, W.; Ferris, S.; Foley, J. A.; Schaffhauser, D.; Smith, R. (1989). "Intertester reliability of the flexible ruler for the cervical spine".
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382:. Fowler, F. G. (Francis George), 1870-1918. (100th Anniversary ed.). Oxford: Oxford University Press.
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Spline devices have been used to designs shapes for pianos, violins, and other wooden instruments. The
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gave the spline function its name after its resemblance to the mechanical spline used by draftsmen.
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The Oxford
English Dictionary finds the first recorded usage in the 18th century in
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Proceedings of the
National Academy of Sciences of the United States of America
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of the spline material combined with the constraint of the control points, or
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were employed by designers drawing by hand. To draw curves, especially for
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505:. Vol. 38, no. 4. Society for Industrial and Applied Mathematics
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The concise Oxford dictionary of current
English : 1911 first edition
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Long flexible batten used to produce a fair curve through a set of points
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Proceedings of the Centre for
Mathematics and Its Applications
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Canoe and Boat
Building: A Complete Manual for Amateurs
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The
Journal of Orthopaedic and Sports Physical Therapy
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49:. Unsourced material may be challenged and removed.
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378:Fowler, H. W. (Henry Watson), 1858-1933. (2011).
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526:"Spline Functions and the Problem of Graduation"
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496:"The Extensive Use of Splines at Boeing"
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222:Other curve drawing tools
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325:"A draftman's [
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955:Cutting and abrasive
791:Laser measuring tool
271:Spline (mathematics)
198:Mathematical splines
43:improve this article
696:and alignment tools
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548:1964PNAS...52..947S
901:Thread pitch gauge
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160:-like shape). The
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99:February 2012
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60: –
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58:"Flat spline"
55:
54:Find sources:
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38:
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32:This article
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26:
21:
20:
1032:Shipbuilding
891:Tape measure
876:Straightedge
866:Steel square
861:Spirit level
856:Speed square
831:Radius gauge
796:Lesbian rule
766:French curve
760:
756:Feeler gauge
711:Beam compass
628:
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507:. Retrieved
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465:(1): 45–99.
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437:. Retrieved
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336:. Retrieved
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259:Lesbian rule
253:French curve
237:lesbian rule
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146:shipbuilding
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41:Please help
36:verification
33:
1005:Woodworking
781:Laser level
761:Flat spline
542:: 947–950.
182:East Anglia
1021:Categories
906:Try square
896:Theodolite
841:Set square
826:Protractor
816:Micrometer
811:Meterstick
721:Chalk line
612:required.)
439:2020-05-09
338:2012-02-24
309:1360838279
278:References
204:polynomial
162:elasticity
69:newspapers
821:Plumb-bob
694:Measuring
645:0190-6011
503:SIAM News
481:0033-569X
406:cite book
398:706025127
186:splinter.
960:Forestry
950:Cleaning
886:T-square
716:Calipers
653:18791322
576:16591233
247:See also
125:A spline
985:Masonry
975:Kitchen
926:Wiggler
871:Stencil
846:Skirret
731:Compass
544:Bibcode
208:splines
83:scholar
995:Mining
965:Garden
881:Square
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567:300377
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509:May 9,
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241:Lesbos
154:lathes
131:spline
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1027:Tools
1000:Power
836:Ruler
606:
538:(4).
499:(PDF)
166:knots
150:laths
90:JSTOR
76:books
970:Hand
916:Vise
649:PMID
641:ISSN
572:PMID
511:2020
477:ISSN
416:link
412:link
394:OCLC
384:ISBN
304:ISBN
158:duck
62:news
776:Jig
633:doi
562:PMC
552:doi
467:doi
327:sic
45:by
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