As we continue the study of building good 3D models, the edge or external limit of the TIN is very important to analyze for correctness.

I am going to be using a term that needs definition for clarity.  The word is Link.  This is the term that I use for one side of a triangle in a TIN.  The link connects two 3D points.  Other software programs or trainers may use a different word to describe one side of a triangle in a TIN.

One of the files that I have built to get the student or model builder to consider the issue is field cross-sections taken along an alignment.  The particular file is one that I created, but displays real life issues that must be considered when building models.

The setting is an alignment, curves and tangents in a digital file.  This could be the centerline of a roadway or a subdivision road.

Then along this alignment, cross-sections were taken approximately every 50 feet.  Real world stuff, huh.  The points are 3d, point number, northing, easting, elevation, and descriptor.  These are points that would traditionally be taken by the field crew or created by roadway design software.

In the zoomed in figure, you will notice that there are individual points collected along the alignment.  For instance the points would be centerline, edge of pave, edge of shoulder, centerline of ditch, top of ditch and ground shots.  Hopefully, the points would have descriptors so you would know what the point is to locate.

Now, we are ready to explore the edge or limits of the TIN.

As you notice, the triangles are all over the place.  They are linking across the road, jumping from edges at the bends, etc.  This example really exaggerates the issue, but it should make you think about the possible bogus triangles that can be formed along the edge of your DTM. 

Where the triangles exist, a real DTM is formed.  The problem is any surface where these bogus triangles exist will form an improper surface.  You can compute volumes, cut profiles and sections, and even view in 3D.  But those surfaces are wrong; at least you cannot prove they are correct.  There is no valid 3D data other than the cross-section field shots.  Anytime the TIN triangles extend past the edge where valid data exists a questionable surface is formed.

Most software packages that build 3D DTMs that are TINs have some form of setting that will help you limit the length of the triangle or link.  Since the sections were every 50 feet, a length of 85 feet as a limit is a good place to start.  If you set the length to 50 feet, a problem would occur in the bends.  The distance between the points on the outside of the bend is longer than 50 feet and probably would not link up.

Just by changing the length setting for triangle link the TIN looks like it is completely finished.  NOT QUITE!  That would have been too easy.  Now, is time to zoom in and move around the entire perimeter of the TIN to make sure all of the links are correct.

Ron’s definition of Flat Angled Triangle, occurs when one of the angles is great than 160 degrees for instance.  This usually occurs when a link connects to a point that is past the nearest point on the edge of the TIN.  The only way to dig these problems out is to zoom in and move along the edge of the TIN from beginning to end.

The problem linking usually occurs when there is a significant bend or irregularity in the edge of the TIN.

Some software packages allow the angle limit to be set, so that the flat angle triangles are automatically removed as shown above.

Most software packages will allow the user to apply an edge or wrapper around the limits of the TIN.  The reason for this is later in the project a new TIN may be formed that requires a different triangle link length and angle setting.  The edge should anchor each on TIN that is formed so when the settings are adjusted no changes occur to the wrapped TIN.

In conclusion, the process covered in this article deals with the DTM edge when using TINs.

The TIN formation routine in most programs just does it automatically.  It does not always and cannot consider all the issues regarding the edge of a TIN.  Again the responsibility falls upon the person building the TIN to assure its accuracy.  You can’t say to the client the devil made me do it (software or programmer, though many times you would like to blame them).  You are responsible!

Having bogus areas in the TIN can cause problems down the road (no pun intended).  Your client may just assume since there is a surface there then it can be used or trusted.

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