The history of geographic information systems invention and re invention of triangulated irregular networks

1. Proceedings, GIS/LIS'97, in press.
THE HISTORY OF GEOGRAPHIC INFORMATION SYSTEMS: INVENTION
AND RE-INVENTION OF TRIANGULATED IRREGULAR NETWORKS (tins)
David M. Mark
NCGIA, Department of Geography
University at Buffalo
Buffalo, NY 14261-0023
dmark@geog.buffalo.edu
http://www.geog.buffalo.edu/~dmark/
Abstract
The history of technical innovation in GIS appears to have many cases of real
or apparent multiple discovery. This paper reports on the history of the
invention and reinvention of Triangulated Irregular Networks (TINs) as
structures for representing topographic surfaces. Data for the paper has been
obtained from in-depth interviews with key innovators, as well as the literature.
Triangles were used as a basis for drawing contours from irregularly distributed
data points as early as 1964, but contouring solved as a two-dimensional
geometric problem. Triangles were used for topography in geomorphometry in
1969, but triangles were analyzed individually. The first known TIN as a
topologically-integrated triangulation, thought of as the upper surface of a
three-dimensional solid, was described by Thomas K. Poiker (then spelled
'Peucker') in 1973. By 1975, the TIN model was well established and several
articles had been published. However, triangulated structures were
independently invented in 1973 by an environmental consulting firm for
representing elevations and other attributes, and around 1975-76 by a geologist,
for representing underground geological surfaces. TIN was a key element in the
topological revolution in GIS.
1. Introduction
The history of scientific and technical innovation includes many cases of real or
apparent multiple discovery or invention (Lamb and Easton, 1984). GIS is no
exception, and documentation of the thought processes and experiences leading
up to innovations in as much detail as possible will help to identify common
sparks or inspirations, or to confirm truly independent discoveries. This paper
reports on the history of the invention and reinvention of Triangulated Irregular
Networks (TINs) as structures for representing topographic surfaces. Data for
the paper were obtained from in-depth interviews with key innovators, as well

2. as the literature. This research is part of The GIS History Project, which is
attempting to trace and document the history of this technology, and to conduct
a critical examination of developments in their social, institutional, and
technological context (http://www.geog.buffalo.edu/ ncgia/gishist). This paper
provides an early summary of innovation in the TIN case study, and documents
some aspects of the technical and institutional environments surrounding these
developments.
2. TIN-0: Precursors
Digital elevation models are important to a number of military and engineering
applications, and thus were one of the earliest areas of digital geographic
information to receive research attention and funding. In the 1960s, regular
grids were the conventional method for storing topography in computers. The
main alternative available at that time was digitized contours, but it was
becoming clear that contours, the most effective method to store and retrieve
precise elevation data on paper maps, were not an effective base for storing and
analyzing topography on computers. The main reason is that the topological
relations or nesting of the contours is visually obvious on graphic diagrams, but
difficult to store and manipulate on computers (see Mark, 1978a, 1979). A
paper by Boehm (1967) was seminal work comparing different methods for
terrain storage, concentrating on grids and digitized contours.
As early as 1964, triangles were used as a basis for drawing contours or other
isolines through irregularly distributed data points in two-dimensional spaces
(Bengtsson and Nordbeck, 1964). According to Davis (1975) IBM was using a
triangle-based approach to contouring in 1965, which Davis said could
"simulate the process of manual contouring" (IBM, 1965). Davis (1975) further
commented that triangulation is "the most obvious computer contouring
approach." Similarly, Gold (personal communication) reported that, as of 1970,
there was at least one other commercial contouring system using triangles,
developed for the oil industry (SCA, 1970). Such triangle-based contouring
itself seems to have been multiply 'invented,' but appears to have been solved
as a purely two-dimensional geometric problem--apparently, the triangles were
not thought of as representing a 3-dimensional, or 2.5 dimensional, surface.
The first known use of triangles to explicitly represent such a surface was in
1969, when German geomorphologist K. Hormann proposed a system of
triangles could be used to represent topographic surfaces for geomorphological
analysis (Hormann, 1969, 1971); however, Hormann's triangles were not
connected topologically, but were analyzed separately and the results summed.
3. TIN-1: Poiker's ONR Project

3. The first known published description of a TIN as a topologically-integrated
triangulation thought of as the upper surface of a three-dimensional solid was
described by Thomas K. Poiker (formerly 'Peucker') in 1973, in the first-year
report of a project funded by the US Office of Naval Research. Poiker's
development of this structure had many earlier antecedents. An important step
in his thinking is shown in his essay, "Some thoughts on optimal mapping and
coding of surfaces," in which he proposed to represent terrain by an irregularly
distributed set of "surface-specific" points such as peaks and saddle points, that
would have higher information content per point and thus might require less
total data storage space and processing time (Peucker, 1969). However, the
story of the actual invention of TIN appears to have begun early in 1971, when
Poiker wrote an intervisibility program for William Wolferstan, a graduate
student at Simon Fraser University, to use in his research on coastal tourism
(Poiker, personal electronic communication, October 1996). Poiker used
regular grids of elevations as the data structure in that program, although he
was apparently aware of Bengtsson and Nordbeck's (1964) contouring by
triangulation approach, since Poiker cited their work in his 1972 AAG
monograph, "Computer Cartography" (Peucker, 1972).
Early in 1972, Poiker was visiting the University of Maryland, and a
government employee named Bob Mercready, whom Poiker had met earlier at
the Harvard Laboratory for Computer Graphics and Spatial Analysis, arranged
for Poiker to have lunch with Evelyn Pruitt, geography program officer at the
US Office of Naval Research (Poiker interview, March 18, 1997). Poiker
showed her his visibility maps, and Pruitt apparently expressed interest in
funding further research on the topic. Poiker was unhappy with grid DEMs,
having read Boehm's (1967) paper, and felt there must be a way to combine the
advantages of regular grids and contours. He also reported that he did not want
to get a grant simply to re-do something he had already done, but would prefer
to use a grant as an opportunity to do something innovative. In a March 1997
interview, Poiker reported that the idea to use triangles actually occurred to him
during that lunch with Evelyn Pruitt:
"I wanted to do this differently, and that's when the triangle came up, right at
that lunch. So, it [the TIN idea] must have been there, it must have been just
waiting" (Poiker, interview, March 1997).
Poiker wrote a proposal and received ONR funding later that year (1972) to
develop TIN. The TIN idea was well developed in the first year report of that
grant, submitted to ONR in December 1973 (Peucker et al., 1973). By 1975, the
TIN model was well established and several articles had been published (Mark,
1975; Peucker and Chrisman, 1975). Complete summaries of this TIN project

4. also were published (Peucker et al., 1978, 1979). A paper by Peucker and
Chrisman (1975) was a landmark in the maturation of topological data
structures for GIS, since that paper outlined both the TIN structure and the
POLYVRT structure for planar polygon maps. Being academics, Poiker and his
colleagues published early and often, and thus their version of TIN became the
best known in academic circles. The fact that it indeed seems to have been the
earliest incarnation of a topological TIN structure is almost a coincidence, since
if the following, slightly later TIN projects had happened a year or two earlier
than they did, they probably would not have been know to academics until long
after Poiker's version of TIN had been established.
4. TIN-2: ADAPT
A second invention of TIN as a topological data structure for topography
happened in a private sector environment. On May 3, 1973, programmers at
Engineering-Science, a consulting firm based in northern Virginia, came up
with the idea of representing topography by using triangles in an application
involving planning of sewer lines (Grayman, 1997). This key idea became
ADAPT (Areal Design and Planning Tool), a triangle-based GIS that used
triangle vertices for elevations and triangle faces to carry other attributes
(Grayman et al., 1975; Males, 1978). According to Grayman, the key
innovation was suggested in an evening session of an all day 'brain-storming'
meeting led by William E. Gates, looking for alternatives to regular grid-based
digital elevation models. "Several of the participants had experience in the
surveying field and someone suggested that since three points define a plane,
that a triangular based system was obviously the best way to store
topographical information" (Grayman, 1997). In December 1973, W. E. Gates
left Engineering-Science to form his own firm, and Grayman, Males, and the
ADAPT system moved with him to the new company. Males (email, 2 June
1997) states that none of the development team knew about other TIN projects
at the time that ADAPT was being developed; they only learned about Poiker's
TIN project during visits to the Harvard Lab later in the 1970s.
5. TIN-3: Gold's TINs
A triangulated structure was independently invented by geologist Christopher
Gold around 1975-76 for representing underground geological surfaces. In
email to David Mark on October 25, 1996, Gold told his recollections of how
he came up with the TIN idea. His dissertation involved attempting to
"reconstruct the subsurface glacial stratigraphy of the Cold Lake area, from
bore-hole data." The distribution of his data points was very uneven, yet he
needed and interpolation of surface reconstruction method that would exactly

5. 'honor' all the data points. In the early 1970s, he was not able to locate a ready-
made program capable of doing a good job with data and objects of the type
that he had. He stated:
"I can still remember working at home with this one evening, and remarking to
[my wife] that what was needed was a structure that was adaptive to the data
distribution. Such as a set of triangles. Little did I know!" (Gold, email,
October 5, 1996).
Gold began implementing a triangle-based approach, and struggled with
various aspects of it. He eventually came up with a solution quite different from
those of Poiker's group or ADAPT: he (re)-invented methods for producing a
smooth surface across triangle boundaries, whereas both of the other groups
used linear interpolation within triangles, leaving breaks of slope along most
triangle edges.
Gold was not able to recall exactly when he came up with the triangle idea, but
the innovation presumably happened in the period 1972-1975. Gold first
presented the methods publicly in May 1976, first at a University of Alberta
symposium and later that month at to a Geological Association of Canada
conference. The next year, he had a paper on his method accepted for the 1977
SIGGRAPH meeting (Gold et al., 1977), and through submission of that paper,
began correspondence with Thomas Poiker and his TIN group. That connection
led Gold to present a paper in the fall of 1977 to the First International
Advanced Study Symposium on Topological Data Structures for Geographic
Information Systems organized by Harvard in October 1977 (Gold, 1978). That
was a pivotal meeting for the maturation of TIN and the conceptual integration
of the three main projects, as Richard Males also gave a paper there on TINs
(Males, 1978), as did several members of Poiker's ONR-funded research group
(Little, 1978; Mark, 1978b; Peucker, 1978).
6. Discussion
6.1 Multiple Invention?
TIN appears to be a case of genuine multiple invention. It seems clear that none
of the three groups discussed in this paper was aware of any of the others when
coming up with the idea of using triangles to represent topographic surfaces.
There are no particular common key papers or talks that provided inspiration.
However, both Poiker and Gold were aware of triangle-based contouring
programs, and both Poiker and the ADAPT group make reference to triangles
as being the way surveyors conceptualize terrain. All also were influenced to

6. varying degrees by the unfavorable trade-off between resolution and data
volume inherent in regular grids, and were looking for more efficient ways to
attain needed accuracy and resolution in critical areas.
Two themes have recurred in accounts of the invention of TINs. One involves
early triangle-based contouring programs, and another is based on the idea that
triangles are the 'natural' way for a surveyor to think of topography. Each of
these will be discussed briefly in the following sections.
6.2 Triangles in the Plane vs. A Triangulated Surface
In his monograph comparing TINs and gridded DEMs, Kumler begins his
discussion of the origins of TIN with a reference to Bengtsson and Nordbeck's
1964 paper on contouring using triangles (Kumler, 1994). But, how important
were these contouring programs? A key question is whether a triangle-based
program to draw isolines actually involves a 3-dimensional, or 2.5 dimensional
representation or data model. Did the programmers think of the data as a
surface? We will have to ask, if we can find them. However, the author's
intuition says that drawing contours or isolines through and around a set of
irregularly distributed points in the plane is not a 3-dimensional problem, but is
commonly approached as a strictly 2-dimensional problem. When doing this by
hand and eye, one identifies pairs of nearby points that straddle the isoline one
is drawing, and then use linear interpolation along the imaginary line joining
those points, to position the isoline. The mental process is very similar to
drawing bisectors, or constructing Thiessen polygons. No sloping surfaces or
hills or valleys are visualized.
Results of an informal survey posted to some relevant electronic news groups
appear to confirm the author's suspicions. Correspondents described in
considerable detail the process of interpolating along straight lines between
neighboring points, and did not mention 3-D visualization. If the triangle-based
contouring programs of the 1960s were developed and used along similar lines,
then the leap to topological triangles forming surfaces to bound a solid may
have been a greater innovation that it is given credit for today.
6.3 Surveyors Use Triangles
There is a belief among some GISers that surveyors think of topography as a
set of triangular planar facets. This belief was widely held in Poiker's ONR
project at Simon Fraser University, as reflected in Poiker's recent interview
comments:

7. "you've got to realize that the triangle is something that's... there are a lot of
people outside who would immediately think of triangles, because that's they
way surveyors measure terrain, and a lot of people think in these terms. I think
what we did was we added topology to it." (Poiker, interview, March 1997)
This author contributed to the dissemination of that idea. In a paper on
conceptual views of topography and their reflection in data models for
elevation data, I stated:
The surveyor's approach involves a polyhedral solid which approximates the
terrain, and adapts in density to the complexity of the topography. This view
can be accommodated by the 'triangulated irregular network' (TIN) approach"
(Mark, 1978a, p. 28)
Surveyors certainly triangulate. But do they really think of
triangular facets approximating the terrain surface? Twenty years later, my
intuition on this had changed, and so I asked some surveying engineering
professors, and again posted a query on Usenet. The academics were
unanimous in saying that surveyors use triangulation only to fix locations in the
two-dimensional plane. Elevations are determined independently of the
triangulation. Furthermore, since triangle edges traditionally have been sight
lines for instruments, they must lie entirely above the surface, rather than
approximating it! And furthermore, the triangles need not even form a
tessellation--they can overlap or have gaps, as long as each surveyed point is
tied to control points by a set of triangles. An analogy is to a stick figure, all of
whose points sit on the terrain, but whose sticks must stay above the terrain.
"Stick figures only, from my experience. The line-of-sight notion in these
triangles is so strong, that I have never thought myself about the plane,
although we always point out how closely related the concept is to DTMs"
(Email from a survey science academic, May 30 1997)
Surprisingly, the word from practicing land surveyors was quite different.
Practice in the late 1990s seems to be to survey terrain by selecting points in
the field based on the field worker's knowledge of the software that will be
used to interpolate, model, and contour later! If the above views from surveyors
trained at a much earlier time are true, the existence of the TIN model seems to
have changed field practice in topographic surveying! And the effect of the
change is to bring field survey practice and the data model much closer
together than we suspect they were in the early 1970s. Apparently, in this case,
life imitates art, or at least, life imitates software. This makes the idea that

8. surveying practice inspired TINs in the early 1970s even more interesting, and
worthy of further study.
6.4 Conclusions and Future Work
The TIN data model as a basis for computerized storage, retrieval, and analysis
of topography, appears to have been independently invented in North America
at least three times in the early 1970s. The environments for the TIN innovation
were very different. One was in an academic geography department by a
cartographer with a geography background; one was by engineers working on
environmental consulting in the private sector; and one was by a geologist
working in academia on data that did not readily fit existing programs. There
were few common factors, except a dissatisfaction with existing data models
and software, especially regular square gridded digital elevation models. Use of
triangles in surveying (two cases) or finite elements calculations (one case)
may have been factors contributing to the innovation, as may have been
programs to draw isolines in the plane based on a triangulation of control
points. Academic conferences eventually provided a forum for exchange of
ideas among the three groups and others, and by the end of the 1970s, a single
unified TIN model was a standard way to represent topography in GIS and
other software.
This paper has dealt very little with institutional and societal factors in these
three projects. Poiker's project was funded by the Office of Naval Research, a
part of US Department of Defense, at a Canadian University, beginning in
1972, a time of campus unrest and anti-War and anti-US sentiment among
many Canadian university students. The political context of the funding source,
and any influence that DoD funding may have had on the project, must be
investigated further. The other two projects appear to have been carried out in
less politicized contexts, related to non-military applications. The entire social
and political context of the invention of TIN will require critical examination as
part of placing GIS technology in general in its societal and historical context.
The fact that, within a few years in the early 1970s, at least 3 groups came up
with the same solution probably means that triangles were an obvious, natural,
and practical way to represent topography. This must emerge from some
combination of the characteristics of topography, of early 1970s computing,
and of human cognition and society. Why then was TIN not invented about a
decade earlier? Perhaps computing environments were unfavorable, or perhaps
alternative approaches such as grids had to be developed for some minimum
period of time that would allow the need for something different to become

9. evident. Future work will attempt to address this question, as well as the others
raised above, both for TIN and for other elements of GIS
7. Acknowledgments
I am especially grateful to Thomas Poiker, Richard Males, Christopher Gold,
and Walter Grayman for consenting to be interviewed by electronic mail and
(in Poiker's case) in person, and providing with with their memories and
insights regarding the early days of their TIN projects. Discussions with other
members of the GIS History Project have influenced my approach to this
research, and also are acknowledged. This paper is part of The GIS History
Project (http://www.geog.buffalo.edu/ ncgia/gishist), which in turn is part of
Initiative 19, The Social Implications of How People, Space, and Environment
are Represented in GIS, of the National Center for Geographic Information and
Analysis (NCGIA). Initial stages of the project have been funded by the
NCGIA's NSF grant, SBR-8810917; support from NCGIA and NSF is
gratefully acknowledged.
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