Description of the surfit gridding algorithm

surfit uses originally developed gridding method called CMOFS (consecutive minization of functionals sequence). The CMOFS method described below, allows to strictly determine the influence for each data, used for gridding. To process data with CMOFS algorithm it is necessary to create so-called "gridding rule". Gridding rule is a functional that describes how to use data in gridding. The order of gridding rules defines the priority levels for each data. For example, we can think, what data given in scattered points is most precise and must be taken first. Information about the resulting surface behavior between scattered points is less reliable and we should use it at the last step.

To build resulting surface with CMOFS algorithm surfit determines values in the cells of equidistant grid:

\[ u(x,y) = \sum_{i=1}^N \sum_{j=1}^M u_{i,j} \phi_{i,j}(x,y), \]

where $u_{i,j}$ are cell values, $\phi_{i,j}$ - set of step basis functions:

\[ \phi_i \left( x \right) = \left\{ 1,x \in \left[ih + a - \frac{h} {2},(i + 1)h + a - \frac{h} {2}\right) \qquad 0, x \notin \left[ih + a - \frac{h} {2},(i + 1)h + a - \frac{h} {2}\right) \hfill \right. \]

Here is the breif scheme of CMOFS algorithm:

Then minimizing i-th functional, two situations are possible:

surfit: gridding and contouring software.