A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids

  • Authors:
  • Riccardo Rovatti;Michele Borgatti;Roberto Guerrieri

  • Affiliations:
  • Univ. of Bologna, Italy;Univ. of Bologna, Italy;Univ. of Bologna, Italy

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1998

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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.