Highlights:

• N-dimensional interpolation, any N
• accurate and efficient algorithms; efficient MEX-file implementation
• convenient array indexing syntax with fractional indices
• optional extrapolation, derivatives, etc.
  
• N-dimensional inverse function evaluator
• interpolation on general non-uniform ("non-plaid") coordinate maps

Description:

ZipInterp comprises two companion software packages: ZipInterp-1, the “forward interpolator”, performs multidimensional interpolation on a uniform, rectangular sampling grid; and ZipInterp-2, the “inverse interpolator”, computes an interpolator’s functional inverse. The two packages can be used in conjunction to perform interpolation on a general non-uniform, multidimensional coordinate map. (Although they are designed to be used conjunctively, ZipInterp-1 and ZipInterp-2 can also be used independently. Neither one requires the other.)

The forward interpolator, in essence, enables multidimensional array indexing with fractional indices. Three algorithms are supported: multilinear and two variations of cubic. The algorithms are designed for high efficiency and optimum accuracy performance, and an optional “bias compensation” procedure neutralizes residual systematic error in the interpolation function. Additional options are provided, for example, to enable extrapolation and to compute the interpolation function’s gradient. ZipInterp-1 would typically be used to create an N-dimensional fast function evaluator (e.g. for real-time metrology or global optimization applications), and the optional derivative computation would be useful for numerical inversion or optimization algorithms.

ZipInterp-2 is specialized to efficiently interpolate a functional mapping between N-dimensional real vectors, taking advantage of sparse dependency relationships in the functional map. It also includes an inverse function evaluator, which combines an efficient global seed search with a Newton’s-method iterative solver. ZipInterp-2 and ZipInterp-1 can be used in conjunction to perform N-dimensional interpolation on a general, non-uniform coordinate map. (The coordinate map need not have a "plaid" form, as required by MATLAB's interpn function.)