Sandbox Visualization

Overview and Objective:

This lab is a continuation of the first lab that involved creating a survey grid to survey a sandbox. The objective for this lab was to use the data that was collected in the survey to create a 3D model of the sandbox environment. The X,Y and Z values were compiled into a spreadsheet; a process known as data normalization. Each X,Y and Z value in a row corresponds to 1 point on the survey grid. A secondary objective was to gain an understanding of different interpolation methods and use different methods to create each model. Interpolation is the process of a computer program calculated the estimated value of areas in between points on a grid.

Fig 1.0
Normalized Data in Excel Spreadsheet

Methods:

In this lab five interpolation methods were used to create a 3D model using ArcMap and ArcScene software. The methods used are as follows. The descriptions are based on those provided by ESRI


Spline- The Spline interpolation method uses a mathematical function to estimate values in-between given points and provide a smooth surface. The spline method is best used when a data set has a large number of sample points. Because a spline surface passes directly through the points, the more points there are the smoother the surface will be.

Kriging-This interpolation method uses an advanced equation to investigate the spatial correlation between data points to estimate a surface. Kriging works well with scattered data.

Natural Neighbor- Finds closest subset of input samples to a point and applys weights based on proportionate areas to interpolate a value. An advantage of this method is that it can work with equally or irregularly spaced data

IDW- Also known as inverse distance weighted, estimates cell values by averaging values of sample points in neighboring cells. IDW works better with closely grouped data.

TIN-Interpolates by triangulating sets of vertices. A surface is generated from non-overlapping triangles. More triangles are generated in areas with more surface variation, such as a slope that changes in elevation.

After collecting the data, the values were placed into a spreadsheet, which may be seen in figure one. Each X,Y and Z value represents one point. This Excel document was then placed imported a geodatabase in Arc GIS software. Then, using the add XY data function, a grid of the data points was generated. Interpolation tools were then used on the grid to generate a terrain model. These were transformed 3-D models using the Z-coordinate values with Arc Scene software. Elevation surfaces were set to float on a custom surface. The models were oriented with north being at the top of the image. To represent scale I drew a straight line at the base of the model created a label that displayed the overall length. It is important to include the scale and orientation because when doing an experiment or exercise the process needs to be repeatable  Once the scenes were generated they were exported as JPEG images. These images were then loaded into an Adobe Illustrator document along with map elements from ArcMap to create a final map.

Results

The end result of this exercise was a map showing the 3-D terrain model for each interpolation method. These may be seen below.

Kriging

The Kriging method did not do an adequate job  modeling the terrain. The major features are shown, however several smaller depressions are not shown in this model but are in models generated using different interpolation methods. On a positive note, the surface generated by the Kriging method looks more realistic.

Figure 2
Map with Kriging Interpolation

Natural Neighbor

I believe that the natural neighbor interpolation does a nice job of representing the contours of the sandbox surface. Smaller ridges and depressions may be seen which do not appear in other models. The smooth surface in between features is accurate as to what the sandbox actually looked like. 

Figure 3
Surface Model using Natural Neighbor Interpolation

IDW

The IDW interpolation method is not the best method to use. Because of the way the points are weighted, small bumps in the sand box look peaked. The depressions on the surface are more difficult to make out as well with this model.

Figure 4
Model using IDW interpolation

Spline

The spline interpolation method proved very useful in showing small changes in the terrain. For example, in the center of the map there are three depressions that form a triangle. The depression at the top is actually two smaller depressions, which was harder to make out in the other models. One aspect of this model that should be changed would be the color ramp. The contrast between red and blue accurately shows changes in elevation, however the highest points and lowest points are both represented as black, which may be confusing

Figure 5
Surface Model Using Spline Interpolation

T.I.N

The Tin model did a great job visualizing changes in elevation. This can especially be seen on the slope in the northeast corner. one downside to this map is that it looks more computer generated and not as "pretty" as the other models.

Figure 5
T.I.N model

Overall the Spline and Natural neighbor interpolation methods produced the best terrain models. All of the models included a very small amount of variance between what was actually in the sandbox and what was generated in the model. This could be due to measurement error. The initial exercise was done in single digit temperatures and it's possible this contributed to human error when measuring.

Conclusion

The overarching goal of this exercise was to understand the fundamentals of data creation by gathering data in the field and importing the data into a geodatabase in order to generate a model. The survey we performed was very similar to professional surveys in that we divided an area of land into smaller, equally sized sections to map it. The differences include the scale of the project and the tools used. Because we were in a sandbox, hand measuring tools were fine. In the field professional survey equipment needs to be used in order to insure accuracy. The grid pattern we used is ideal for relatively flat land. This can be seen in the landscape of the rural mid-western United States. In other areas, such as the east coast, the different terrain was not conducive to a grid like survey system. 

Interpolation may be used in many different ways besides those in this exercise.  For example, bi-linear interpolation is used in remote sensing to resample images.