### Multivariable Curve InterpolationMultivariable Curve Interpolation

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 Author Ferguson, James Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1964 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract The problem of defining a smooth surface through an array of points in space is well known. Several methods of solution have been proposed. Generally, these restrict the set of points to be one-to-one defined over a planar rectangular grid $(\textit{X},$ $\textit{Y}-plane).$ Then a set of functions $\textit{Z}$ = $\textit{F}(\textit{X},$ $\textit{Y})$ is determined, each of which represents a surface segment of the composite smooth surface. In this paper, these ideas are generalized to include a much broader class of permissible point array distributions: namely (1) the point arrangement (ordering) is topologically equivalent to a planar rectangular grid, (2) the resulting solution is a smooth composite of parametric surface segments, i.e. each surface piece is represented by a vector (point)-valued function. The solution here presented is readily applicable to a variety of problems, such as closed surface body definitions and pressure envelope surface definitions. The technique has been used successfully in these areas and others, such as numerical control milling, Newtonian impact and boundary layer. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1964-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 11 Issue Number 2 Page Count 8 Starting Page 221 Ending Page 228

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Source: ACM Digital Library