The surface method defines how z or elevation values are determined when exporting a surface or comparing control points to a surface. Each surface method implements a different way of interpolating elevations from LIDAR points. The following describe the surface methods in more detail.

**Triangulation (TIN)**

TIN (Triangulated Irregular Network) partitions a surface into a set of contiguous, non-overlapping, Delaunay triangles. The heights or elevations between each triangle vertex are interpolated as definitions of planes and thus together construct a surface. Each triangle has a normal vector which points perpendicular out from the face of the triangle. The normal vector is used to calculate derived attributes of a surface such as slope, aspect, and hillshade or brightness (Berg 2000).

**Point Insertion**

Point Insertion examines only the points that fall within each defined cell and assigns a value to the cell based on the Surface Attribute being exported. The Point Insertion methods are calculated as follows:

*Intensity* selects the intensity value of the closest point to the center of the cell and assigns that value to the cell.

*dz Images* measures the elevation difference between points with the highest and lowest elevation having different overlapping Point Source ID in the cell and assigns the difference as the cell value. If there is no overlap of the LAS data in the pixel output, then the intensity of the LAS point that has the highest elevation is set as the pixel value.

*Density* measures the number of points in a given cell, divided by the area of the cell, and designates that number as the cell value.

**Inverse Distance Weighted (IDW)**

IDW defines a surface using a linearly weighted combination of LIDAR points. The weight used in this interpolation is distance. Points closer to the location of interpolation have more influence on the interpolated elevation than points further away.

There are two ways to control the characteristics of an IDW surface: power and radius. The power shifts focus of the interpolation from local to global. A large power results in less influence from surrounding points (nearby data has more influence) resulting in more detail (less smooth). Small power values will result in a smoother surface and gives points further away more influence in the interpolation (ArcView™ 3.2 Help System).

There two methods for defining the radius: fixed radius, and minimum number of points, The fixed radius option uses a fixed radius to search for points or neighbors to be used in the interpolation. In theory, larger radii will use more points in the surface calculation than would a smaller radius. However, gaps in the data (ponds, lakes, etc.) larger than the fixed radius will result in no data points towards the center of the gaps. The second option uses a minimum number of points or neighbors to define the radius used in the interpolation. Using a minimum number of points increases the radius until the number of points criteria is achieved, thus eliminating the effect of the gaps in the data.

In some cases, you may be allowed to input a maximum search distance that limits the search area when using a minimum number of neighbors. This prevents processes from “bogging” down on areas with large gaps and increases the completion time of those processes.

Because IDW is a distance weighted average interpolation, elevations cannot be greater or less than the LIDAR point elevations used in the surface. Thus, IDW cannot create ridges or valleys, and are also not ridge or valley preserving due to the symmetrical influence (isotropic) of the interpolation (Burrough, 1998).

**References:**

ArcView™ 3.2 Help System

Berg, Mark de, Marc van Kreveld, Mark Overmars, Otfried Schwarzkopf. Computational Geometry. Springer, 2nd Edition, 2000.

Burrough, Peter A., Rachael A. McDonnell. Principles of Geographic Information Systems. Chapter 5, “Creating Continuous Surfaces from Point Data”. Pages 98-131. Oxford. 1998.