Triangulated Irregular Network History

Parent Category: Columns

Written by Ron Ciccarone, LS

Created on Saturday, 03 April 2010 01:00

Before I begin this article, I would like to reference a document as recommended reading from my last article.  The late Joseph Dracup wrote an excellent history of US surveying from the 1800’s forward.  This is an excellent research of surveying in the US.  It is located at the following NGS website:

Http://www.ngs.noaa.gov/PUBS_LIB/geodetic_survey_1807.html

Triangulated Irregular Network or TIN as most people know it has become a very well known term in surveying and civil engineering.  Interestingly, it is not a new concept, but it was not used much until the late 1980s give or take a couple of years.  The TIN is the basis used by most programs supporting 3D modeling in the surveying, engineering and construction industry.

I began surveying in the mid 60s, before total stations, data collectors, hand held calculators (except for Kurta and Monroe hand cranked), desktop/laptop computers,  CADD systems (computer aided design and drafting) and Al Gore had not developed the internet.  This list could keep going, I feel old as dirt.

The surveying crew would throw a set of muddy field notes on my desk in the evening and I would stare at the notes the next morning hoping everything was there (cell phones did not exist either).  I would get a sheet of velum drafting paper, a larger paper protractor, a scale and plot all of the ‘topo’ shots, labeling the description and elevation (did not need point numbers).

Once the notes were plotted, I would connect all of the geographic features located such as centerlines, edge of pave, curb lines, power lines, streams, etc.  I would also write a lot of notes or questions for the fieldcrew on this drawing, since this was the working drawing. 

Soapbox, in the current day of CADD, the art of the working drawing is lost.  Putting notes on a CAD layer about why you made certain decisions is critical.  You could get run over by or drink a beer truck tonight and no one would know the rationale behind some of your decisions when you did not show up the next day.

Anyway, I would then begin analyzing the elevation points.  I would create imaginary lines between the points and interpolate where the contour lines would cross this line.  Some people would use proportional dividers (and yes you can find them on the web), or a scale to do the interpolation.  Then, they would connect all the appropriate dots to form the contour.  Experienced staff would simply draw the contours through the approximate interpolated locations without drawing the interpolation lines and be done with it.

Interestingly, this was a hand drawn form of a TIN.  I was connecting the points with lines (probably not drawn but implied) and hashing the contour crossings, then connecting the dots.  I did not even realize that I was making a TIN at that stage in my career.  See Fig. 1

In 1934, a Russian mathematician named Boris Delaunay developed the triangulated network and the algorithm is referred to as the Delaunay Triangulation.  A rule in the Delaunay algorithm is that circumcircles would be drawn through the three points of the triangle (remember our geometry class, any 3 points not in a straight line could form a circle), but also no other points of adjacent triangles be contained in the circle.  This rule uses the smaller interior angles to form the triangle and minimize the elongated skinny triangles.  Most current CADD systems use this method as the basis for their TIN DTM creation.   See Fig. 2

The scenario today in the office would be much different.  The field crew would be using a total station and data collector (DC).  At the end of the job, they would download the DC file and send a notification.  They might even download the file and send it through their cell phone to the companies FTP site.  The DC raw data file would be processed through the CADD system; the raw data would be reduced to NEZ points and plotted in the CADD file.  If point descriptors were used, the CADD probably has an automated feature generation routine and draws all of the topographic features collected and labels them.  The TIN and contours can be generated and shown in the CADD file.  All of this is done in a matter of minutes, when in pre-CADD it took hours.  But, the office technician is not finished.  Don’t forget the quality control; you still need to review the entire site to be sure things are correct.  Computers are not all that bright; they only used what they are given.  I appreciate my roots in surveying, but would not want to go back.

Using the TIN rather than a GRID for DTM has some real values.  The grid is made from equal distant points.  Topographic features do not fit this layout.  The TIN allow the points to be random.  When the ground is relatively flat or even grade less points are required.  If the relief is more significant, the points can be as dense as needed.  For random features such as streams, roadways, curblines, buildings, etc. all the points needed to properly define graphically these features can be used in the TIN.

When you get to the proposed design, the same rules would apply.  As the site is developed, a TIN would be produced to properly reflect all of the site grading and features to be constructed.  A second TIN may be produced to sub-grade.  These files could be downloaded to the data collector and the fieldcrew would be ready to stake-out any features need.  These same files could be used by the automated machine control equipment employed by the contractor.

I have covered some of the origins of the digital age as related to surveying, civil engineering and CADD.  My next articles will go in-depth into some of the issues that should be address when making an accurate TIN DTM.

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