Natural neighbor interpolation estimates the value at the center of each raster cell by exploiting the unique properties of a Voronoi tessellation of the source data points. A Voronoi tessellation or Voronoi diagram is a network of non-overlapping polygons that enclose each input data point such that the polygon boundaries are equidistance between the closest points. As a result, any location within a polygon region will always be closer to the enclosed input point in that region than to any other point in the dataset. Moreover, each polygon exerts a natural area of influence around its enclosed point. The method can be used to create surface models from data that is clustered, dense in some areas and sparse in others, or data with linear spatial distributions.
The natural neighbor technique does not extrapolate the raster cell values beyond the range of the input values so there is very little overshoot or undershoot at the minimum and maximum data values. Natural neighbor interpolation uses an area-weighting technique to determine a value for every raster cell.
As illustrated in the figure below, a natural neighbor region is first generated for each input data point. Then at every raster cell node a new natural neighbor polygon is generated by inserting the raster cell point location into the Voronoi diagram of the input points. This insertion creates a new polygon which effectively borrows area from various portions of the surrounding natural neighbor regions defining each of the closest input points. The value assigned to the raster cell is then calculated as the average of the surrounding point values, proportionally weighted by the borrowed area taken from each surrounding region.
Figure above shows the natural neighbor regions around a set of input points as well as a region (shaded) which represents the “borrowed area” that would be taken from the original Voronoi diagram by inserting a raster cell coordinate into the diagram. The shaded areas of each “borrowed area” which overlap with the original Voronoi polygons represent the area weightings that are then applied to weight each of the closest data points to derive a new value for the raster cell in the output surface.
Natural Neighbor Method Options
- Parameter Unit
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Specifies whether spatial parameters are defined in cell units or distance units. The units should be supported by MapInfo Pro, for example, the options for Distance unit include: US Survey feet, yards, rods, chains, miles, nautical miles, millimeters, centimeters, meters, inches, links and kilometers. If you choose Distance, you need to select a distance unit from the Distance Unit drop-down list.
- Maximum Search Distance
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The maximum distance allowed between a grid cell and the neighboring input data points that will be considered when computing its value. The distance value determines whether these points are considered in the distance weighing average. The Maximum Search Distance must be greater than 0, and specified in Parameter Units type.
Click More Options to open the following advanced options.
- Gaussian Distance Weighting
- When enabled applies a Gaussian based distance weighting to input data point vales that are found within the search radius. Data point values closest to the source raster cell being interpolated will be assigned higher weights than points further away
- Auto Gaussian Range
- Automatically defines the distance over which Gaussian weighting will be applied to the data points. By default this is set to half of the Maximum Search Distance. If you clear this check-box you can manually specify Gaussian Range.
- Gaussian Range
- The distance over which Gaussian weighting will be applied to the data points. Points closest to source raster cell being interpolated will have more influence on the output raster cell value than points further away.
- Smoothing Method
- Apply smoothing on the gridded data to produce smoother surface.
- Clipping
- The Clipping control provides options to limit the extents of the interpolated raster, so it more closely approximates the distribution of the input data. Enabling this option can improve the appearance of the output raster when interpolating irregularly spaced input data, where the interpolation methods has interpolated across large gaps in the input data.
- None - No clipping is applied to the raster cells.
- Near Only - The Near value represents the maximum distance from a source input data point for which an interpolated raster cell will be created. Cells in the raster which lie at a distance greater than the Near distance will be assigned a null value. This method has the same effect as applying a distance buffer to the source data points equal to the near distance.
- Near/Far - Interpolated cells in the output raster will be clipped to the near distance if no other data point is found within the Far distance that meet the angular search constraints. Applying both Near and Far clipping can be useful to constrain the interpolated raster to a required distance from the source points. It also allows the larger gaps to be interpolated across in irregularly spaced data.
- Polygon - You can provide a TAB file of polygon(s) to clip the output raster to the polygon boundaries. You can specify whether to clip a region outside or inside the raster bounds. However, it does not support polygons with holes.
Coincident Points Method
The Coincident Points drop-down list controls the handling of multiple data points at the same location. For more information see, Coincident Point Methods.