# How Interpolate Shape (3D Analyst) works

The Interpolate Shape tool converts a 2D point, polyline, or polygon feature class into a 3D feature class by interpolating z-values for input features from a surface. The input surface can either be a raster, triangulated irregular network (TIN), or terrain dataset.

Attributes from the input are copied to the output.

The interpolation Method argument is used to specify the type of interpolation to use. When the input surface is a raster, the only option is bilinear. This uses a weighted average between the four closest cell centers surrounding the interpolation point. When the input surface is TIN or terrain, you may choose between linear, the default, natural neighbors, or one of four conflation options.

 Linear Uses a weighted average of the three nodes of the triangle containing the interpolation point. Natural Neighbors The natural neighbors option uses the Voronoi neighbors of the interpolation point. Conflate Z Min Obtains z from one of the TIN or terrain's natural neighbors of a query point. The z of the neighbor with the minimum height is used. Conflate Z Max Obtains z from one of the TIN or terrain's natural neighbors of a query point. The z of the neighbor with the maximum height is used. Conflate Z Nearest Obtains z from one of the TIN or terrain's natural neighbors of a query point. The z of the neighbor closest in x,y to the query point is used. Conflate Z Closest To Mean Obtains z from one of the TIN or terrain's natural neighbors of a query point. The z of the neighbor that is closest to the average height of all the neighbors is used.

The Sample Distance is a floating point value used by lines and polygons. The Sample Distance is used to control the frequency at which interpolation occurs along lines and polygon boundaries. Output vertices will be spaced no farther apart than this distance. Generally, the smaller the sample distance, the higher the frequency and the closer the output feature geometry conforms to the surface.

When the input surface is a raster, the default Sample Distance is set equal to the cell size. A smaller value can be specified, but it's recommended that you not go below one-half a cell size because it cannot provide any additional information, as the surface, constrained by its resolution, has no more detail to offer. Also, keep in mind, smaller sample distances require more resources. Switching from a one-cell sample distance to a half-cell sample distance can double the output vertex count with only slight improvement in accuracy. Larger distances can also be given, in which case less detail about the surface is captured.

When the input surface is a TIN or terrain, there is no default Sample Distance. With no sample distance specified, the tool will sample lines and polygon boundaries at their original vertex locations plus where these features cross triangle edges. Sampling at edge intersections is appropriate when using linear interpolation because it captures all detail available from the "linear" surface, where each triangle is a plane, without over- or undersampling.

When the input surface is a TIN or terrain and a Sample Distance is specified, the sampling strategy varies based on the chosen interpolation method. If natural neighbors is used, features will be sampled based on the sample distance plus where features cross hard breakline edges. If linear interpolation is used, features will be sampled based on the sample distance plus where features cross any triangle edges. As a general rule, a sample distance should be specified when using natural neighbors and should not be when using linear.

The following table gives insight into setting a sample distance based on the chosen interpolation method.

Setting interpolation methods and sample distances for input surfaces

Interpolation method

Sample distance

Description

TIN/Terrain Surface—Linear Interpolation Method

Interpolation focuses at the specified sample distance, as well as at the edge intersections.

TIN/Terrain Surface—Linear Interpolation Method

Left blank (off).

Interpolation densifies only at edge intersections. Not utilizing the sample distance is recommended for linear interpolation.

TIN/Terrain Surface—Natural Neighbors Interpolation Method

Interpolation focus is by the given sample distance, as well as hard edge intersections. When using a natural neighbors interpolation method, it is recommended that you set a sample distance.

TIN/Terrain Surface—Natural Neighbors Interpolation Method

Left blank (off).

Interpolation focus is at edge intersections.

Raster Surface—Bilinear Interpolation Method

Left blank (on).

Interpolation focus defaults to the cell size.

Raster Surface—Bilinear Interpolation Method