You can constrain the gridded area (and hence the contours) to the area inside the convex hull of the data by choosing to assign a NoData value to the grid outside the convex hull of the data during the gridding process. You can use this option in the user interface and via automation in a script.

To do this in the user interface:

1. Click Home | Grid Data | Grid Data.
2. In the Grid Data - Select Data dialog, click Browse in the Dataset 1 field, select the data file and click Open.
3. Assign the X, Y, and Z data columns.
4. Click Skip to End.
5. On the Output page of the Grid Data dialog, check the box Assign NoData outside convex hull of data. This automatically assigns the NoData value to the area outside the convex hull of the data points.  

Surfer Grid Data dialog with Assign NoData outside convex hull of data option enabled

If you are using a script in Surfer 13 or higher, you can use the BlankOutsideHull parameter of the GridData3 method:

    SurferApp.GridData3(DataFile:=SurferApp.Path + "\samples\Demogrid.dat", BlankOutsideHull:=True, InflateHull:=-1, OutGrid:="c:\temp\Demo3.grd")

If you wish to constrain the gridding inside an even tighter boundary around your data than the convex hull, you can use one of these methods:

1.  Assign NoData to the grid outside the data limits.

Beginning with Surfer 17, this process can be done directly inside the Grid Data dialog on the Output page. First, create a vector boundary file (BLN, SHP, DXF, etc.) defining the outline of your data points. After the boundary file is created, grid your data as normal by clicking Home |  Grid Data | Grid Data, select the data file and specify any gridding parameters you wish. On the Output page, select your polygon boundary, toggle NoData Outside, and click Finish. Create a BLN boundary file or other vector file defining the outline of your data points.

Assign a NoData polygon boundary to your grid file during gridding in Surfer

In Surfer 16 and earlier versions, the assign nodata process has to be completed after the grid is created. First, create a vector boundary file (BLN, SHP, DXF, etc.) defining the outline of your data points. After the boundary file is created, grid your data as normal by clicking Home |  Grid Data | Grid Data, select the data file and specify any gridding parameters you wish (a rectangular grid will be created). Next, click Grids | Edit | Assign NoData, select the grid file, select boundary file, and save the output grid to a new name.

If you are using Surfer 13 or earlier, a BLN file is required to Blank or Assign NoData to a grid. Please see: Create a NoData Polygon or BLN file in Surfer or, if you have our MapViewer or Didger software packages, you can easily do this by importing your data points, selecting them and using the Convex Hull command to create a polygon of the convex hull around the data points, and then click File | Export to export the polygon to a BLN file.

 2.  Use a fault file to define your data limits.

Create a BLN boundary file that defines the outline of your data points and use it as a fault file during gridding. Click Home |  Grid Data | Grid Data, select your data file and specify any gridding parameters you wish. On the Options page of the Grid Data dialog (Advanced Options in Surfer 16 and earlier versions), expand the Faults section, and specify the BLN as a fault file.

Apply a fault file in Surfer's Grid Data Options to limit interpolation to only the data area.

Only some gridding methods support faults. Kriging does not, but Minimum  Curvature (very similar to Kriging) does.  See the article Available advanced options for each gridding method in Surfer for additional information.

3.  Grid the data and specify a reduced search radius. 

Click Home |  Grid Data | Grid Data, select your data file and specify any gridding parameters you wish. On the Options page of the Grid Data dialog (Advanced Options in Surfer 16 and earlier versions), Expand the Search Neighborhood section. Remove the check mark from the None (use all data) box if necessary, and specify the Radius 1 and Radius 2 values.

Apply a limited search radius to your data interpolation in Surfer's Grid Data dialog

The default Kriging method offers the Search option. Other methods that offer it include Inverse Distance, Modified Shepard's Method, Nearest Neighbor, Radial Basis, Moving Average, Data Metrics, andLocal Polynomial.

Some gridding methods do not have this option, including Minimum  Curvature, Natural  Neighbor, Polynomial  Regression, and Triangulation with Linear Interpolation. See the article Available advanced options for each gridding method in Surfer for additional information.

Related articles: Create a irregular-shaped map in Surfer

Updated November, 2019