Label | Explanation | Data Type |

Input point features | The input point features containing the z-values to be interpolated into a surface raster. | Feature Layer |

Z value field | The field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input point features contain z-values. If the regression type is Logistic, the values in the field can only be 0 or 1. | Field |

Output raster | The output interpolated surface raster. It is always a floating-point raster. | Raster Dataset |

Output cell size (Optional) | The cell size of the output raster that will be created. This parameter can be defined by a numeric value or obtained from an existing raster dataset. If the cell size hasn't been explicitly specified as the parameter value, the environment cell size value will be used if specified; otherwise, additional rules will be used to calculate it from the other inputs. See the usage section for more detail. | Analysis Cell Size |

Polynomial order (Optional) | The order of the polynomial. This must be an integer between 1 and 12. A value of 1 will fit a flat plane to the points, and a higher value will fit a more complex surface. The default is 1. | Long |

Type of regression (Optional) | The type of regression to be performed. - Linear — Polynomial regression is performed to fit a least-squares surface to the set of input points. This is applicable for continuous types of data.
- Logistic — Logistic trend surface analysis is performed. It generates a continuous probability surface for binary, or dichotomous, types of data.
| String |

Output RMS file (Optional) | File name for the output text file that contains information about the RMS error and the Chi-Square of the interpolation. The extension must be .txt. | File |

Available with Spatial Analyst license.

Available with 3D Analyst license.

## Summary

Interpolates a raster surface from points using a trend technique.

## Usage

As the order of the polynomial is increased, the surface being fitted becomes progressively more complex. A higher-order polynomial will not always generate the most accurate surface; it is dependent on the data.

For the Logistic option of Type of regression, the z-value field of input point features should have codes of zero (0) and one (1).

The Output cell size can be defined by a numeric value or obtained from an existing raster dataset. If the cell size hasn’t been explicitly specified as the parameter value, it is derived from the Cell Size environment if it has been specified. If the parameter cell size or the environment cell size have not been specified, but the Snap Raster environment has been set, the cell size of the snap raster is used. If nothing is specified, the cell size is calculated from the shorter of the width or height of the extent divided by 250, in which the extent is in the Output Coordinate System specified in the environment.

If the cell size is specified using a numeric value, the tool will use it directly for the output raster.

If the cell size is specified using a raster dataset, the parameter will show the path of the raster dataset instead of the cell size value. The cell size of that raster dataset will be used directly in the analysis, provided the spatial reference of the dataset is the same as the output spatial reference. If the spatial reference of the dataset is different than the output spatial reference, it will be projected based on the selected Cell Size Projection Method.

The optional RMS file output contains information on the RMS (root mean square) error of the interpolation. This information can be used to determine the best value to use for the polynomial order, by changing the order value until you get the lowest RMS error. See How Trend works for information on the RMS file.

Some input datasets may have several points with the same x,y coordinates. If the values of the points at the common location are the same, they are considered duplicates and have no effect on the output. If the values are different, they are considered coincident points.

The various interpolation tools may handle this data condition differently. For example, in some cases, the first coincident point encountered is used for the calculation; in other cases, the last point encountered is used. This may cause some locations in the output raster to have different values than what you might expect. The solution is to prepare your data by removing these coincident points. The Collect Events tool in the Spatial Statistics toolbox is useful for identifying any coincident points in your data.

For data formats that support Null values, such as file geodatabase feature classes, a Null value will be ignored when used as input.

## Parameters

arcpy.ddd.Trend(in_point_features, z_field, out_raster, {cell_size}, {order}, {regression_type}, {out_rms_file})

Name | Explanation | Data Type |

in_point_features | The input point features containing the z-values to be interpolated into a surface raster. | Feature Layer |

z_field | The field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input point features contain z-values. If the regression type is Logistic, the values in the field can only be 0 or 1. | Field |

out_raster | The output interpolated surface raster. It is always a floating-point raster. | Raster Dataset |

cell_size (Optional) | The cell size of the output raster that will be created. This parameter can be defined by a numeric value or obtained from an existing raster dataset. If the cell size hasn't been explicitly specified as the parameter value, the environment cell size value will be used if specified; otherwise, additional rules will be used to calculate it from the other inputs. See the usage section for more detail. | Analysis Cell Size |

order (Optional) | The order of the polynomial. This must be an integer between 1 and 12. A value of 1 will fit a flat plane to the points, and a higher value will fit a more complex surface. The default is 1. | Long |

regression_type (Optional) | The type of regression to be performed. - LINEAR —Polynomial regression is performed to fit a least-squares surface to the set of input points. This is applicable for continuous types of data.
- LOGISTIC —Logistic trend surface analysis is performed. It generates a continuous probability surface for binary, or dichotomous, types of data.
| String |

out_rms_file (Optional) | File name for the output text file that contains information about the RMS error and the Chi-Square of the interpolation. The extension must be .txt. | File |

### Code sample

This example inputs a point shapefile and interpolates the output surface as a TIFF raster.

```
import arcpy
from arcpy import env
env.workspace = "C:/data"
arcpy.Trend_3d("ca_ozone_pts.shp", "ozone",
"C:/output/trendout.tif", 2000, 2, "LINEAR")
```

This example inputs a point shapefile and interpolates the output surface as a Grid raster.

```
# Name: Trend_3d_Ex_02.py
# Description: Interpolate a series of point features onto a
# rectangular raster using a trend technique.
# Requirements: 3D Analyst Extension
# Import system modules
import arcpy
from arcpy import env
# Set environment settings
env.workspace = "C:/data"
# Set local variables
inPointFeatures = "ca_ozone_pts.shp"
zField = "ozone"
outRaster = "C:/sapyexamples/output/trendout02"
cellSize = 2000.0
PolynomialOrder = 2
regressionType = "LINEAR"
# Execute Trend
arcpy.Trend_3d(inPointFeatures, zField, outRaster, cellSize,
PolynomialOrder, regressionType)
```

## Environments

## Licensing information

- Basic: Requires 3D Analyst or Spatial Analyst
- Standard: Requires 3D Analyst or Spatial Analyst
- Advanced: Requires 3D Analyst or Spatial Analyst