Publication 1998 Issue No. 8 - August Abstract - A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids
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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
 ASCII Text x 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, August, 1998.
 BibTex x @article{ 10.1109/12.707591,author = {Riccardo Rovatti and Michele Borgatti and Roberto Guerrieri},title = {A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids},journal ={IEEE Transactions on Computers},volume = {47},number = {8},issn = {0018-9340},year = {1998},pages = {894-899},doi = {http://doi.ieeecomputersociety.org/10.1109/12.707591},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular GridsIS - 8SN - 0018-9340SP894EP899EPD - 894-899A1 - Riccardo Rovatti, A1 - Michele Borgatti, A1 - Roberto Guerrieri, PY - 1998KW - Computational multidimensional geometryKW - high-speed function generationKW - piecewise-linear interpolation.VL - 47JA - IEEE Transactions on ComputersER -

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.
Citation:
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