# ModelMuse: Interpolation in ModelMuse

Video Transcript

## Detailed Description

This video illustrates differences among the various interpolation methods in ModelMuse.

## Details

Image Dimensions: 800 x 600

Date Taken:

Length: 00:06:34

Location Taken: US

## Transcript

The letters "USGS" and the words "Science for a Changing World" appear in green and fade to black.
This video illustrates the interpolation methods in ModelMuse.
ModelMuse allows you to assign values to two dimensional data sets by interpolating among points.
There are several different interpolation methods.
They are all documented in the help.
Of the seven interpolation methods, five use only point data.
With them, objects with more than one vertex are treated as a series of disconnected points.
The five methods that only use point data are
Nearest Point, Triangle Interpolation, Fitted Surface, Natural Neighbor, and Point Inverse Distance Squared.
The methods that take into consideration the lines connecting the vertices of an object are Nearest, and Inverse Distance Squared.
Let's go through what each of these does.
This model has three objects that are used to set the elevation of the top of the model by interpolation.
They've been carefully positioned to show each of the interpolation methods in their worst light.
This object as the value of 3.
This one has a value of 2.
This one has a value of 1.
Right now, the interpolation method of the Model_Top dataset is set to Nearest Point.
We'll color the grid with the Model_Top dataset.
If you look down here you can see the value of the grid cell underneath the cursor.
If I move it back up here notice that thevalue of this cell which is on the middle line having a value of 2 gets a value of 1.
That's because the Nearest Point method ignores the lines connecting the vertices and this point at this cell is closer to this object with the value of 1 than it is to either this or this point which have values of 2.
If we change the interpolation method to Nearest like this the results are more like what we might expect.
This is because the Nearest Point method ignores the lines connecting the vertices whereas those lines are taken into account in the Nearest method.
However, the Nearest Point method is quite a bit faster than the Nearest method.
We'll talk about that more later.
The next method will look at is Triangle Interpolation.
In this method, a triangulation of all the points is created.
The values assigned inside any the triangles is calculated by passing a plane through the values of three points of the triangle.
For points outside all the triangles, the value of the nearest edge of the nearest triangle is assigned.
If you don't have any long narrow triangles, this generally works well.
I set up this model so that there would be some long narrow triangles.
For example there would be a long narrow triangle from here to there and there and back.
And another from here to here and here and back.
You can see some abrupt changes in the assigned values at the edge of this long narrow triangle.
Another method you can try is Fitted Surface.
As its name implies, it fits a curved surfaced to the data values to assign interpolated values.
As with the triangle interpolation, long narrow triangles can cause problems.
In addition, the interpolated values can be higher or lower than any of the data points.
In this example, the maximum data value of the data point is 3 in the object right here that we can't see right now.
But if you look down here the cell gets a value of 6.
The Natural Neighbor interpolation  interpolates among the points in the neighborhood of the point where an interpolated value is required.
It usually performs well inside the convex hull of the data points but may perform or poorly outside that zone.
Now, let's looking at a Point Inverse Distance Squared.
The value assigned to any point is a weighted average of all the points.
The weight is the square of the inverse of the distance from the data point to the location where a value is assigned.
Notice that the lines connecting the vertices are ignored in this method.
If ignoring the lines isn't acceptable, then use the Inverse Distance Squared method.
The downside of the Inverse Distance Squared method is that it is quite a bit slower than any of the other methods.
In the help, there is a chart that shows that the speed test of each of the different interpolation methods with different numbers of points.
Nearest Point is fastest.
Inverse Distance Squared is slowest.
In the Data Sets dialog box, the interpolation methods are listed in order from fastest to slowest.
Interpolation is a useful way of assigning values to data sets.