ArcGIS Tutorial: 3D Surface Basics (i)

The 3D surface model is a digital representation of elements (true or imaginary) in three-dimensional space. Several simple examples of the 3D surface include the surface, urban corridor, underground gas deposits, and a network of deep wells used to measure the depth of the groundwater level. These are examples of real-world features, but the surface can also be derived or hypothetical. The degree of contamination of a particular bacterium in each well is an example of a derived surface. These levels of contamination can also be plotted as 3D surface maps. A hypothetical 3D surface can often be seen in video games or computer simulation environments.

You can often use specially designed algorithms to get or calculate 3D surfaces that sample point, line, or polygon data and then convert it to a digital 3D surface. ArcGIS can create and store four types of surface models: rasters, triangulated irregular networks (tins), terrain datasets, and LAS datasets.

These surface models can be created from a variety of data sources. The two main methods for creating surface models are interpolation and triangulation. There are a number of interpolation methods for creating raster surfaces, such as inverse distance weighting, spline function, kriging, and natural neighborhood methods. You can build a triangle polygon by creating a TIN, terrain dataset, or Las DataSet. You can also convert between these surface models.

Raster, TIN, terrain, and LAS datasets all belong to the functional surface type. A functional surface is a field of contiguous values that vary in values at each point. For example, points in an area of the Earth's surface may differ in elevation values, proximity to features, or concentrations of a particular chemical. Any of these values can be represented on the z-axis of a three-dimensional x, y, z coordinate system, so they are often referred to as Z-values.

Surface models can be used to store surface information in a GIS. Because the surface contains countless points, it is not possible to measure and record the z-values for each point. However, by sampling the values at different points on the surface and interpolating between these points, the surface model can be approximated as a surface.

A surface model showing the concentration of chemical substances in an area is shown. Where the dots indicate the concentration of the sample location.

　　

　　Grid

GIS data is generally divided into two main types: raster data and vector data. Vector data is defined by points, lines, polygons, and the association relationships between them to form geospatial data. Real features and real surfaces can be represented as vector data stored in GIS. Raster data is a rectangular matrix of raster cells, expressed as rows and columns. Each raster cell is used to represent a defined square area on the Earth's surface whose value remains constant throughout the raster cell range. The surface can be represented by raster data, and each raster cell in the data represents a value for the actual information. The value can be elevation data, pollution level, groundwater level height, etc.

Raster data can also be subdivided into categories, such as thematic data, picture data, or continuous data. A surface represented by raster data is a form of continuous data. Continuous data also refers to field data, non-discrete data, or surface data. This can be expressed by a continuous surface: each position on the surface can be used to measure the concentration level, and it can also be used to measure the relationship between a point and a fixed point in space or with a transmitting source.

An elevation model is an example of this raster surface model. Fixed points may be elevation points that are derived from photogrammetry, and interpolation between these elevation points will help build a digital elevation model (DEM). Because raster surfaces are typically stored in a grid format that is evenly spaced between raster cells, the smaller the raster cells, the higher the grid's positional accuracy. The following example compares a higher-precision grid (left) to a lower-precision grid (right).

　　

The location of each feature (for example, the peak) is directly related to the size of the grid cell. In the example above, a very coarse elevation surface data is used to depict a surface model in a two-dimensional planar view. You can also create a raster surface from another image source in a 3D perspective and create a surface model, such as a high-resolution DEM with Hillshade (shown).

　　

A raster surface is a field of contiguous values that vary in values at each point. For example, points in an area may differ in elevation values, proximity to features, or concentrations of a particular chemical. Any of these values can be represented on the z-axis of a three-dimensional coordinate system of x, Y, z, so that a continuous 3D surface can be generated.

Raster surface data represents the surface as a grid of raster cells of the same size, while the attribute values for each raster cell represent Z-values and x, y position coordinates.

When working with the ArcGIS 3D Analyst extension, many raster datasets are likely to be consumed or created. Understanding how raster datasets are represented in 3D Analyst is critical when working with Rasters.

　　TIN

TIN represents surface morphology digitally, and the GIS community has used this approach for years. A TIN is a form of vector-based digital geographic data that is constructed by composing a series of vertices (points) into a triangle. Each vertex is connected by a series of edges, resulting in a triangular network. There are many kinds of interpolation methods for forming these triangles, such as Delaunay triangulation or distance sequencing. ArcGIS supports the Delaunay triangulation method.

The resulting triangulation satisfies the Delaunay triangle criterion, which ensures that no vertices are located inside any circumscribed circle of the triangle in the network. If any position on the tin conforms to the Delaunay criterion, the smallest inner angles of all triangles are maximized. This avoids the formation of narrow triangles as much as possible.

Each side of a TIN can form a continuous triangular polygon that is not superimposed, and can be used to capture the position of a linear feature that plays an important role in the surface, such as a ridge line or a river channel. In the following two images, the left image shows the nodes and edges of the tin, and the right image shows the nodes, edges, and faces of the tin.

　　

Because the nodes can be placed irregularly on the surface, the TIN can have a higher resolution in areas where the surface is fluctuating or where more detail is required, whereas in areas with smaller surface fluctuations it can have a lower resolution.

The input features used to create the tin are in the same position as the nodes or edges in the tin. This allows the TIN to model the values between known points while preserving all the precision of the input data. You can introduce precisely positioned features (such as peaks, roads, and rivers) on the surface by using them as input features for tin nodes.

The available range of TIN models is not as extensive as the raster surface model, and is more time-consuming to build and process. The cost of obtaining good source data can be high, and because of the complexity of the data structure, the processing of tins is less efficient than processing raster data.

Tins are typically used for high-precision modeling of smaller areas, such as in engineering applications, where tins are useful because they allow the calculation of planar area, surface area, and volume.

ArcGIS Tutorial: 3D Surface Basics (i)