# Interpolated Surface Filter

The interpolated surface filter is a simple way for you to fit a surface to scatter data. What it actually does is to produce a regular grid that can be used with a Rectangular Grid plot style or an Iso Line plot style. to display the surface defined by those points. The way that it works if rather straightforward. You enter formulas for the x, y, and z values for the scatter points that are coming in. The output will be a regular grid and you can specify the range in x and y as well as the number of grid cells to use. For each point in the grid, the filter runs through all of the data points and makes a weighted average of them to give the z value at that location on the grid.

The trick is that you get to specify the way in which the data points are combined. The weight formula can use the variables x, y, and dist for the position of the grid point and the distance between that grid point and the scatter point it is comparing to. You can also use the other standard features of the formulas. The default formula gives a weight equal to the inverse of the distance of the grid point from the data point. Obviously, this formula has a problem if the grid point happens to land exactly on the data point. For this reason, there is also a check box allowing you to tell the filter to use the z value of the input point if it matches the grid point. There is also an option for setting the maximum distance to consider points from. If the value is negative, which is the default, then points are put into the average at all distances.

Because you get to set the weighting to whatever you want, you can also take into account things like error bars if you don't want to force the data to pass directly through the different points. A weighting function of a form similar to 1/(dist+v[3]), where v[3] is the error in a given point, will be forced to go very close to points with small errors and be further from those with larger errors.