How Spline with Barriers works
The Spline with Barriers tool applies a minimum curvature method, as implemented through a one-directional multigrid technique that moves from an initial coarse grid, initialized in this case to the average of the input data, through a series of finer grids until an approximation of a minimum curvature surface is produced at the desired row and column spacing.
At each grid refinement level, the current grid-based surface model is treated as an elastic membrane, and a convergent linear iterative deformation operator is applied repeatedly at each node to achieve an approximation to a minimum curvature surface that honors both the input point data and discontinuities encoded in the barriers. The deformation that is applied to each cell is calculated on the basis of a molecular summation (Terzopoulos, 1988) that compares the weighted summation of 12 neighboring cells with the current value of a central target cell to calculate a new value for the target cell.
References and further reading
Briggs, I. C., 1974. Machine contouring using minimum curvature, Geophysics, Vol. 39, pages 39–48.
Terzopoulos, D., 1988. The computation of visible-surface representations, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 10, No. 4, (July), pages 417–438.
Smith, W. H. F., and P. Wessel, 1990. Gridding with continuous curvature splines in tension, Geophysics, Vol. 55, No. 3 (March 1990), pages 293–305.
Zoraster, S., A surface modeling algorithm designed for speed and ease of use with all petroleum industry data, Computers & Geosciences, 2003, Vol. 29, No. 9, pages 175–182.