Difference between TRN (Triangulated Regular Network) and TIN (Triangulated Irregular Network)

There are two methods of how survey points are connected and interpolated. They are TIN (Triangulated Irregular Network) and TRN (Triangulated Regular Network). The definition, differences, accuracy and other essential details are explained in this article. 

What is TIN and TRN? #

	TIN (Triangulated Irregular Network	TRN (Triangulated Regular Network)
Interpolation of Meshing Network	Interpolated directly from survey points	Interpolated based on fixed interval
Terrain Output	Terrain is fixed, solely depend on the survey points	Terrain is not fixed, it depends on the interval of the meshing

Output Difference Between TIN and TRN #

Difference of Meshing Shape
TIN (Triangulated Irregular Network)	The meshing are directly connecting between survey points. Cyan = Imported Survey Points White = Meshing Strings
TRN (Triangulated Regular Network)	The meshing is done independent of the surveyor point distribution; it is done so that the element size and shape are as similar to one another as possible. Cyan = Imported Survey Points White = Meshing Strings

Difference of 3D view
TIN (Triangulated Irregular Network)	Sparsely connected mesh elements, as they connect within survey points, as explained above
TRN (Triangulated Regular Network)	The meshing are connected, as the survey points are triangulated mesh.

Note that in 3D view, on the parts where there is a lack of surveyor points, TIN will look like a land of sparsely connected mesh elements, whereas TRN will look the same as the rest. In other words for TRN,  in 3D view, you can’t tell which parts of the ground level are lacking of surveyor points, and which part is not. 

The difference between ‘actual surveyor points’ and ‘interpolated surveyor points’  #

The difference between TRN and TIN is manifested most dramatically in terms of the interpolated surveyor points and actual surveyor points; for TIN, the z value of the actual surveyor points are always the same as the interpolated surveyor points, where as for TRN, it may not be necessarily so. 

To illustrate, please download this project. Note that in this project, we are using TRN. 

1. To check your ‘actual surveyor points’, you may go to Survey Points > Edit >  Spread Input (as you can see as per image below):

2. The actual surveyor points are listed in the Z  (m) column.
3. As for the interpolated height (Z, mm). As the cursor moving around the surveyor points

4. For further understanding, you may refer to the image below. You can see that the real Z value is 43.48 m, but however at the ‘status bar’ the value of Z is 46.332 m (interpolated value).

In TIN, there is no such problem; as you can find when you switch the meshing method from TRN to TIN.

How can we improve the accuracy of TRN? #

To ensure a faithful representation of the Ground Level, here are a few options you can adjust.

The Controlled by Size Method (TRN). #

The way this works is like this.

1. The program will generate a mesh of the whole terrain, bound by the surveyor points.
2. The program will divide the mesh into different elements, based on the “Element Count”. The higher this number is, the more elements will be created, and thus more accurate. (Options > Project Parameters > Earthworks > Analysis > Element Count)

3. For the points on the elements, the program will interpolate the z value based on the “interpolation technique.”

So, usually, the mesh produced by this method is always smoother, even when the surveyor point is scarce. However, because the program takes the whole surveyor points and does the interpolation, and the mesh point may not be the same as the surveyor points, there might be some height difference between the surveyor points and mesh points.

To increase the accuracy of this method, you can do the following:

MiTS 1 Parameter Settings

MiTS 2 Parameter Settings

1. You can increase the Grid Cluster (MiTS 1)/Element Count (MiTS 2) to a bigger value ( such as 5,000,000). Grid Cluster/Max. Survey Points determines how many surveyor points to be used in the program. The higher the grid cluster value is, the more surveyor points used.
2. You can also increase the Mesh Element Size/Element Count to a bigger value ( such as 120). The higher this value is, the finer the mesh is.
3. You can also change the Meshing Method to “TIN” to ensure the most exact interpolation. See below for more information.

Increasing both should allow you a more accurate representation of the terrain, at the expense of computing time

What is the most exact interpolation technique? Answer: TIN Method! #

The most exact interpolation technique is always the TIN method (Meshing method=”TIN”), this is because the TIN method is using the surveyor point itself as the element point to construct the mesh, unlike “Controlled By Size/TRN” method.

This means at the surveyor points, the interpolated and the actual height value will always be the same for TIN method.

You can also increase the grid cluster/max. Survey points, when using the TIN method in order to increase the accuracy of the interpolation. The bigger this grid cluster value is, the more surveyor points will be used in TIN, so, more accurate!

MITS 1 Parameter Settings

MiTS 2 Parameter Settings

The drawback of TIN method is that,

1. For surveyor points that are sparse, the interpolated surface may not be smooth, because all the points on the mesh are coming from the surveyor points.
2. If there are a lot of surveyor points, TIN method can be slow, as the mesh can be very, very fine. Yes, it is more accurate, but it can be slow.
3. If some surveyor points are wrong ( i.e. : the points are very different from other nearby surveyor points), then the cross section may look discontinuous and very ugly and also downright wrong ( other methods will still give wrong cross section, but the error is not so glaring). It is the user’s responsibility to seek out the offending surveyor points and delete them. To verify that there is no wrong surveyor point, or wrong surveyor point doesn’t matter, please make sure that all the cross section existing level looks smooth.

How to check/increase the accuracy of the interpolation? #

Option 1: Compare against tracing contour #

If your tracing file has contour, then you can compare the contour generated by the program with the tracing file contour, by clicking on the “string/contour” icon, change the Show Contour to Yes, and compare the superimposing of the tracing file contour and the Program contour.

MiTS 1 Settings

For MiTS 2 setting, click Terrain tab  (on the Right-hand Side) > Tick Show Contours

MiTS 2 Settings

Bear in mind that these are all estimations, so it is not possible to get 100% match of the original contour and the generated contour.

However, with TIN method and a big enough grid cluster value, you can expect to get a 100% match of z value at most of the surveyor points.

Option 2: Visually inspect the generated terrain mesh.  #

One can manually inspect the generated terrain mesh by clicking on “Strings/Contours”, and then set the “Show String lines=Yes”, as shown below, to visually inspect the generated terrain mesh.

MiTS 1 Setting

MiTS 2 Setting

As a rule, the more the element meshes, the more faithfully the terrain ground levels are being represented. You can always increase the “Grid Cluster” or the “Mesh Element size” and observe how it affects the generated terrain ground level.

Tips to increase the accuracy: #

To verify that there is no wrong surveyor point, or wrong surveyor point doesn’t matter, please make sure that all the cross section existing level looks smooth in TIN method

How to know which value of “Mesh Element Size” and “Grid Cluster” and which Meshing Method is good enough for my project? #

This is very project dependent, the only way is to experiment; if you increase the parameters, to a stage whereby the cut/fill volume doesn’t change much, then the value you pick is good enough. Increasing them further will only increase computing time with very little improvement in accuracy.

If TRN is not accurate enough for cutfill volume calculation, then what is it good for? #

It’s good for qualitative study and smooth 3D view visualization.

1. Because TRN first construct a uniform mesh network before generating the z levels, the 3D view is always smoother than the TIN, resulted in better visualization ( accuracy notwithstanding)
2. For slope classification purposes, one values the visualization and smoothness of the slope classification over all else. In this case, TRN is an acceptable meshing method.  
3. TRN can interpolate well within the convex hull of the surveyor points ( not to be confused with extrapolation that happens outside of the convex hull, which both TRN and TIN can’t do), so consultants can use this feature to ask the surveyor to obtain accurate spot levels at those areas. Consultants can either say to the surveyor ”according to my software, this is the elevation value at this spot, can you confirm?” , or “According to my gut feeling, this is the elevation value at this spot, can you confirm?” Surveyors are far more likely and motivated to respond well to the first question rather than second, because the general perception is that computer results are more accurate than mere gut feeling.