In order to effectively apply Poisson's equation to the problem of surface reconstruction, it is necessary to find a good discretization of the vector field V. The basic approach is to bound the data with a finite-difference grid. For a function valued at the nodes of such a grid, its gradient can be represented as valued on staggered grids, i.e. on grids whose nodes lie in between the nodes of the original grid. It is convenient to define three staggered grids, each shifted in one and only one direction corresponding to the components of the normal data. On each staggered grid we perform trilinear interpolation on the set of points. The interpolation weights are then used to distribute the magnitude of the associated component of n i onto the nodes of the particular staggered grid cell containing p i. Kazhdan and coauthors give a more accurate method of discretization using an adaptive finite-difference grid, i.e. the cells of the grid are smaller (the grid is more finely divided) where there are more data points. They suggest implementing this technique with an adaptive octree.