This tool can be used to interpolate a trend surface from a vector points file. The technique uses a polynomial, least-squares regression analysis. The user must specify the name of the input shapefile, which must be of a 'Points' base VectorGeometryType and select the attribute in the shapefile's associated attribute table for which to base the trend surface analysis. The attribute must be numerical. In addition, the user must specify the polynomial order (1 to 10) for the analysis. A first-order polynomial is a planar surface with no curvature. As the polynomial order is increased, greater flexibility is allowed in the fitted surface. Although polynomial orders as high as 10 are accepted, numerical instability in the analysis often creates artifacts in trend surfaces of orders greater than 5. The operation will display a text report on completion, in addition to the output raster image. The report will list each of the coefficient values and the r-square value. The Trend Surface tool can be used instead if the input data is a raster image.

Numerical stability is enhanced by transforming the x, y, z data by their minimum values before performing the regression analysis. These transform parameters are also reported in the output report.

## Function Signature

`def trend_surface_vector_points(self, input: Vector, cell_size: float, output_html_file: str, field_name: str = "FID", polynomial_order: int = 1) -> Raster: ...`

## Project Links

WbW Homepage User Manual Support WbW