NNINT

Description

Generates a raster image by interpolating image values obtained from the specified pixel locations using the natural neighbor interpolation method. This function uses the NNGRIDR code developed by Dr. D.F. Watson at the University of Western Australia.

Parameters

Name	Type	Length	Value range
Input: Input vector segment *	Vector port	1 - 1024
Output: Output interpolated image *	Raster port	1 - 1
Extrapolation	String	0 - 1	YES | NO Default: YES
Pixel X Size (m)	Integer	0 - 2
Pixel Y Size (m)	Integer	0 - 2
Field Name	String	0 - 1	Default: ATTRIBUTE

* Required parameter

Parameter descriptions

Input: Input vector segment

Specifies the input vector segment from which the attribute value or z-coordinate is used as the basis for interpolation.

The vector segment can specify an arbitrary number of structures.

Output: Output interpolated image

Specifies the output image channel to receive the interpolated results.

Extrapolation

Specifies whether to extrapolate the output data.

Pixel X Size (m)

Specifies the horizontal pixel size, in meters, for the output raster layer projection.

Pixel Y Size (m)

Specifies the vertical pixel size, in meters, for the output raster layer projection.

Field Name

Specifies the field name that contains the elevation values.

If this parameter is specified as ZCOORD, the actual z-coordinates of the vectors are used. Field names are not case-sensitive, and they do not need to be specified in complete form. If more than one match exists, the first name is used.

The Field Name (FLDNME) parameter is required only for vector layers that contain 3-D points or contours. For 3-D lines, the z-coordinates are automatically used. For 2-D layers, the elevation values are not specified.

The same name applies to all contour and 3-D point segments specified in the input vectors (DBVS) parameter. The segments that do not satisfy this requirement can be converted to the required format using ZVALTRNS.

If a field name other than ZCOORD is specified but is not found, this function attempts to use the z-coordinates of each vertex or point; this may, however, lead to unexpected results.

Details

NNINT uses the Natural Neighbor Interpolation method to read the gray-level values for an arbitrary number of pixel locations. The gray-level values are used to generate a raster image based on the interpolation obtained from the specified gray levels.

The gray-level values are read from either a GDB layer or a vector segment stored in the input file.

Algorithm

NNINT implements the Natural Neighbor Interpolation method and the NNGRIDR code developed by Dr. D.F. Watson at the University of Western Australia.

The Natural Neighbor coordinate was invented by Professor Robin Sibson, [Sibson 1980]. It can have more than one reference point. It is measured by the ratio of the area associated with one of the reference points to the total area surrounded by all of the reference points. For more information, see the Reference section.

The data from the input channel can be corrected then added to the Natural Neighbor Interpolation algorithm, which finds the natural neighbors and performs the interpolation.

The data becomes a natural neighbor when it is located on the circumference of a circle. Natural neighbors of a data set are found by laying down the least number of the largest possible circles that completely cover the convex hull of data with no data present within the circle. This is achieved by constructing each circle with exactly three data points, which form a Delaunay triangle.

Any position (x) inside the triangle formed by the three data points (the Delaunay triangle vertices) is interpolated based on the weight or distance between x and each point. The relevant circle is also determined by the three points.

The interpolated value of a location is based on the influence from all of the circles that it intercepts. The interpolated value equals the sum of the product of the Natural Neighbor's coordinate and the gray level of each data point.

For example:

          ___
  f(x) =  \   Nx(i) * f(P(i))
          /__ 
           i
  

References

Sibson, R. "A vector identity for the Dirichlet tessellation", Math Proc. Cambridge Philos. Soc., no. 87 (1980): 151-155.