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A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids
August 1998 (vol. 47 no. 8)
pp. 894-899

Abstract—An algorithm for the linear interpolation of multi-input functions sampled on rectangular grids is presented. A geometric approach is adopted and the mathematics is thoroughly developed. We show that the algorithm is optimum. In fact, when the number n of inputs grows to infinity its computational requirement is ${\cal O}(n {\rm\ log}\ n),$ which is the same as the lower-bound on the cost of continuous linear interpolation procedures.

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Index Terms:
Computational multidimensional geometry, high-speed function generation, piecewise-linear interpolation.
Riccardo Rovatti, Michele Borgatti, Roberto Guerrieri, "A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids," IEEE Transactions on Computers, vol. 47, no. 8, pp. 894-899, Aug. 1998, doi:10.1109/12.707591
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