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In [[numerical analysis]], '''transfinite interpolation''' is a means to construct [[Function (mathematics)|functions]] over a planar ___domain in such a way that they match a given function on the boundary. This method is applied in [[geometric model]]ling and in the field of [[finite element method]].
The transfinite interpolation method, first introduced by William J. Gordon and Charles A. Hall,<ref name="Hall73"/> receives its name due to how a function belonging to this class is able to match the primitive function at a nondenumerable number of points.<ref name="Gordon82"/>
In the authors' words:
{{centered pull quote| We use the term ‘transfinite’ to describe the general class of interpolation schemes studied herein since, unlike the classical methods of higher dimensional interpolation which match the primitive function F at a finite number of distinct points, these methods match F at a non-denumerable (transfinite) number of points.}}
Transfinite interpolation is similar to the [[Coons patch]], invented in 1967. <ref name="coons">Steven A. Coons, Surfaces for computer-aided design of space forms, Technical Report MAC-TR-41, Project MAC, MIT, June 1967. </ref>
== Formula ==
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| journal = International Journal for Numerical Methods in Engineering
| volume = 7
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| pages = 461–477
| year = 1973
| doi=10.1002/nme.1620070405
| bibcode = 1973IJNME...7..461G
}}▼
}}
</ref>
<ref name="Gordon82">{{cite journal
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| pages =171–233
| number = 10
| url =
| doi = 10.1016/0096-3003(82)90191-6
| volume=10–11}}
</ref>
<ref name="Dyken2009">{{cite journal
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| last1 = Dyken
| first2 = Michael S.
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| volume = 1
| year = 2009
| pages =
| doi = 10.1016/j.cagd.2007.12.003
</ref>
</references>
[[Category:Interpolation]]
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