Available with Geostatistical Analyst license.

## Summary

Uses one of five basis functions to interpolate a surfaces that passes through the input points exactly.

## Usage

The smooth search neighborhood is only available for the Inverse multiquadric function.

For all methods except the Inverse multiquadric function, the higher the parameter value, the smoother the surface. The opposite is true for the Inverse multiquadric function.

## Syntax

RadialBasisFunctions(in_features, z_field, {out_ga_layer}, {out_raster}, {cell_size}, {search_neighborhood}, {radial_basis_functions}, {small_scale_parameter})

Parameter | Explanation | Data Type |

in_features | The input point features containing the z-values to be interpolated. | Feature Layer |

z_field | Field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input features contain z-values or m-values. | Field |

out_ga_layer (Optional) | The geostatistical layer produced. This layer is required output only if no output raster is requested. | Geostatistical Layer |

out_raster (Optional) | The output raster. This raster is required output only if no output geostatistical layer is requested. | Raster Dataset |

cell_size (Optional) | The cell size at which the output raster will be created. This value can be explicitly set under Raster Analysis from the Environment Settings. If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250. | Analysis Cell Size |

search_neighborhood (Optional) | Defines which surrounding points will be used to control the output. Standard is the default. The following are Search Neighborhood classes: SearchNeighborhoodStandard and SearchNeighborhoodStandardCircular. Standard - majorSemiaxis—The major semiaxis value of the searching neighborhood.
- minorSemiaxis—The minor semiaxis value of the searching neighborhood.
- angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
- nbrMax—The maximum number of neighbors that will be used to estimate the value at the unknown location.
- nbrMin—The minimum number of neighbors that will be used to estimate the value at the unknown location.
- sectorType—The geometry of the neighborhood.
- ONE_SECTOR—Single ellipse.
- FOUR_SECTORS—Ellipse divided into four sectors.
- FOUR_SECTORS_SHIFTED—Ellipse divided into four sectors and shifted 45 degrees.
- EIGHT_SECTORS—Ellipse divided into eight sectors.
Standard Circular - radius—The length of the radius of the search circle.
- Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
- nbrMax—The maximum number of neighbors that will be used to estimate the value at the unknown location.
- nbrMin—The minimum number of neighbors that will be used to estimate the value at the unknown location.
- sectorType—The geometry of the neighborhood.
- ONE_SECTOR—Single ellipse.
- FOUR_SECTORS—Ellipse divided into four sectors.
- FOUR_SECTORS_SHIFTED—Ellipse divided into four sectors and shifted 45 degrees.
- EIGHT_SECTORS—Ellipse divided into eight sectors.
| Geostatistical Search Neighborhood |

radial_basis_functions (Optional) | There are five radial basis functions available. - THIN_PLATE_SPLINE —Thin-plate spline function
- SPLINE_WITH_TENSION — Spline with tension function
- COMPLETELY_REGULARIZED_SPLINE — Completely regularized spline function
- MULTIQUADRIC_FUNCTION — Multiquadric spline function
- INVERSE_MULTIQUADRIC_FUNCTION —Inverse multiquadric spline function
| String |

small_scale_parameter (Optional) | Used to calculate the weights assigned to the points located in the moving window. Each of the radial basis functions has a parameter that controls the degree of small-scale variation of the surface. The (optimal) parameter is determined by finding the value that minimizes the root mean square prediction error (RMSPE). | Double |

## Code sample

##### RadialBasisFunctions example 1 (Python window)

Interpolate point features onto a rectangular raster.

```
import arcpy
arcpy.env.workspace = "C:/gapyexamples/data"
arcpy.RadialBasisFunctions_ga(
"ca_ozone_pts", "OZONE", "outRBF", "C:/gapyexamples/output/rbfout", "2000",
arcpy.SearchNeighborhoodStandard(300000, 300000, 0, 15, 10, "ONE_SECTOR"),
"THIN_PLATE_SPLINE", "")
```

##### RadialBasisFunctions example 2 (stand-alone script)

Interpolate point features onto a rectangular raster.

```
# Name: RadialBasisFunctions_Example_02.py
# Description: RBF methods are a series of exact interpolation techniques;
# that is, the surface must go through each measured sample value.
# Requirements: Geostatistical Analyst Extension
# Import system modules
import arcpy
# Set environment settings
arcpy.env.workspace = "C:/gapyexamples/data"
# Set local variables
inPointFeatures = "ca_ozone_pts.shp"
zField = "OZONE"
outLayer = "outRBF"
outRaster = "C:/gapyexamples/output/rbfout"
cellSize = 2000.0
rbf = "THIN_PLATE_SPLINE"
smallscaleParam = ""
# Set variables for search neighborhood
majSemiaxis = 300000
minSemiaxis = 300000
angle = 0
maxNeighbors = 15
minNeighbors = 10
sectorType = "ONE_SECTOR"
searchNeighbourhood = arcpy.SearchNeighborhoodStandard(majSemiaxis, minSemiaxis,
angle, maxNeighbors,
minNeighbors, sectorType)
# Check out the ArcGIS Geostatistical Analyst extension license
arcpy.CheckOutExtension("GeoStats")
# Execute RadialBasisFunctions
arcpy.RadialBasisFunctions_ga(inPointFeatures, zField, outLayer, outRaster,
cellSize, searchNeighbourhood, rbf, smallscaleParam)
```

## Environments

## Licensing information

- Basic: Requires Geostatistical Analyst
- Standard: Requires Geostatistical Analyst
- Advanced: Requires Geostatistical Analyst