  We introduce a numerical method for reconstructing a multidimensional surface
using the gradient of the surface measured at some values of the coordinates.
The method consists of defining a multidimensional spline function and
minimizing the deviation between its derivatives and the measured gradient.
Unlike a multidimensional integration along some path, the present method
results in a continuous, smooth surface, furthermore, it also applies to input
data that are non-equidistant and not aligned on a rectangular grid. Function
values, first and second derivatives and integrals are easy to calculate. The
proper estimation of the statistical and systematical errors is also
incorporated in the method.
