document: In this work we develop a new approach to DEA suitable for modelling three-dimensional problems. The present DEA methods rely on the fact that one can easily parametrise the boundary of the region being modelled, and then apply an orthonormal basis approximation over the resulting boundary phase space coordinate system. In two dimensions this is simple as the boundary may be parametrised along its arc-length and the associated momentum (or direction) coordinate taken tangential to the boundary. The basis can be any suitable (scaled) univariate basis in both position and momentum, such as a Fourier basis [8] or Chebyshev polynomials [9]. Defining a suitable parametrisation for the spatial coordinate in three-dimensions becomes much more difficult. In momentum space spherical polar coordinates may be employed and so these problems do not arise.
extractive_keyphrases: boundary phase space coordinate system chebyshev polynomials dea fourier basis orthonormal basis approximation parametrise the boundary of the region spherical polar coordinates univariate basis
abstractive_keyphrases: arc-length dea methods develop a new approach to dea suitable for modelling three-dimensional problems modelling three-dimensional problems momentum (or direction) coordinate