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Int roduct ion THE TRIANGULATED IRREGULAR NETWORK Thomas K. Peucker, Robert J. Fowler, James J. Little Department of Geography Simon Fraser University Burnaby, B.C., Canada, V5A 1S6 and David M. Mark Department of Geography University of Western Ontario London, Ontario, Canada For several years, our group has developed a Digital Terrain Model based on irregularly distributed points connected into a sheet of triangular facets. Our first motive for this research stems from problems with traditional terrain representations which were recognized as early as 1967 by Boehm. Topographic surfaces are non-stationary (Pike and R-ozema, 1975), i.e., the roughness of the terrain is not periodic but changes from one landtype to another. A regular grid therefore has to be adjusted to the roughest terrain in the mod'el and be highly redundant in smooth terrain. It is apparent that, if one is to model these non-stationary surfaces accurately and efficiently, one must use a method which adapts to this variation. The second principal motivation came from a realization This project has been supported by Co.ntract ONR No00014-75-C-0886, US Office of Naval Research. 96
that the purpose of the digital terrain system is the digital representation of terrain so that "real world" problems may be approached accurately and efficiently through automated means.In response to this problem it was decided that our digital terrain system should contain those features which are the natural units of analysis for the problems to be solved. This is an important current trend in general data base construction (Mark, 1978). These features and the boundaries between them are seen to have a higher "information content" than randomly located points on the surface. This is so both in the context of the analyses and from the standpoint of representing the surface with a minimum of storage. Like several other researchers (Gates, 1974, Bauhuber, et.al., 1975, Gold, 1977) we realized that one simple means of meeting these specifications is to model the surface as a sheet of triangular facets. We called our implementation of this approach a Triangulated Irregular Network or TIN (Peucker, et.al., 1975). There are two complementary approaches to the computer representation of a surface of triangular facets. One method gives primacy to the triangular facets themselves. Using that method,each triangle needs a total of six pointers to define the topology: three pointers to the nodes at its vertices (the point coordinates should be stored separately), and three pointers to the neighboring triangles. Since, by Euler's relations, there are 2N-B-2 triangular facets in a network with N nodes, B of which are on the boundary, a total of 12N-6B-12 pointers are needed. Alternatively the nodes can be regarded as the primary entities. This is the approach that is used in the TIN data structure. The topology is captured by allowing each node to point to a list of its neighboring nodes. The neighbor list is sorted in clockwise order around the node, starting at "North" in the local Cartesian coordinate system. Applying Euler's relations, the total number of neighbor pointers will be 6N-2B-6. Thus there is about fifty percent savings in storage by representing the topology as a TIN as opposed to using its graph dual. In this implementation, the surface has been mapped onto a topological sphere by the device of adding a dummy node to represent the "outside world" or 97
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'/1UTO QIRTO IV Proceedings of the
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SPONSORED BY: Proceedings of the Vo
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FOREWORD This is the fourth confere
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PREFACE The technical articles cont
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The Use of Computer Generated Maps
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Interactive Computer Mapping ......
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A Formal Model of a Cartographic In
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PHOTOGRAMMETRY SESSIONS Introductio
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William 0. Lucoff of Cal. State at
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widths may be varied at random from
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command codes to the minicomputer a
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Figure 2 Computer Controller EXPOSU
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— 1 X 0 u_ ABCDE M X ^ ^j to C£
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Figure 12 Portion of 48"X60" Chart
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3. THE GAS SYSTEM Chicago Aerial Su
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mode and guides the operator throug
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Figure 1 - Input Edit Figure 2 - Li
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Figure 7 - illegal Elevations Figur
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L Figure 11-Matching Between Models
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1. Street trees are defined as any
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exists between the calculated data
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Trom a conversation with Robert Lee
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II. The Alternatives Various conven
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With error correction as the final
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1. Introduction PRACTICAL EXPERIENC
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instruments with digital mapping te
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the patterns and stores the digital
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o Provides the capability to conver
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II.System Description Figure 1 is a
Page 61 and 62: Status signals are located on the m
Page 63 and 64: which have been digitized and recor
Page 65 and 66: Figure 4 Digitized/Recorded Image C
Page 67 and 68: IMAGE PROCESSING The Image Processi
Page 69 and 70: II. Background The work reported in
Page 71 and 72: coordinates from topographic maps.
Page 73 and 74: polation techniques are available i
Page 75 and 76: egistrations. In all areas where re
Page 77 and 78: THE INTERACTIVE IMAGE SYSTEM FOR TH
Page 79 and 80: The operator may type in commands w
Page 81 and 82: input, each request being terminate
Page 83 and 84: The language elements invoke indepe
Page 85 and 86: IMAGE PROCESSING AND NAVIGATION FOR
Page 87 and 88: 4. Image Acquisition and Amplitude
Page 89 and 90: disc); - the satellite spin-speed w
Page 91 and 92: line start. These parameters are se
Page 93 and 94: PRACTICAL APPLICATIONS FOR DIGITAL
Page 95 and 96: need for early warning of impending
Page 97 and 98: In order to manipulate classes of f
Page 99 and 100: depends mainly on the density of fe
Page 101 and 102: A DATA STRUCTURE FOR A RASTER MAP D
Page 103 and 104: FIG. 2. A border with indicated max
Page 105 and 106: pointers associated with the max-po
Page 107 and 108: y-max 1 z \7 'x-min \x-max 3 x-min
Page 109 and 110: DIGITAL TERRAIN MODELS SESSIONS Int
Page 111: Their programs have been developed
Page 115 and 116: equirement for such a program is th
Page 117 and 118: equivalent to locating the lines of
Page 119 and 120: Brassel, K.,1974,"A Model of Americ
Page 121 and 122: It is not the intention of this pap
Page 123 and 124: One feature in this should be empha
Page 125 and 126: neighbouring data points to estimat
Page 127 and 128: Lawson, C.L., 1977. Software for C-
Page 129 and 130: EDIT SYSTEM HARDWARE The IPIN Edit
Page 131 and 132: Each edit terminal will also contai
Page 133 and 134: FIGURE 2. PLOT OF GEOMORPHIC DATA 1
Page 135 and 136: a 0° 0 0 + 0 o 0 FIGURE 4. SELECTE
Page 137 and 138: FIGURE 5. CONTOUR PLOT OF INTERPOLA
Page 139 and 140: absorbed in the merger if the diffe
Page 141 and 142: To an every-increasing degree, the
Page 143 and 144: potential storage volumes of depres
Page 145 and 146: Soil type sand, Vegetation trees -^
Page 147 and 148: References Brnjac, M; Carlsen, L; M
Page 149 and 150: is particularly important to allow
Page 151 and 152: (b) If Z-coordinate of the vertex B
Page 153 and 154: Figure 3a. TIN DTM Projection Figur
Page 155 and 156: URBAN MAPPING SESSIONS Introduction
Page 157 and 158: Norfolk, and Hampton Virginia. Part
Page 159 and 160: MAPPING SERVICES IN FAIRFAX COUNTY,
Page 161 and 162: If errors are detected they are res
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Some are only printed as the stocks
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URBAN MAPPING AND RELATED AUTOMATED
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tersection matching program was wri
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The selection of coding schemes wil
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cartography and are firmly committe
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main purpose of this paper. Five of
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The project was undertaken specific
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play and analysis. By breaking from
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The operating system environment is
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INTERACTIVE COMPUTER MAPPING* Thoma
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- By displaying variables in map fo
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with a start - head- and an end -ta
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Rovner, P.D and Feldman, J.A., 1968
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eading this complex type of map, (2
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y a law pertaining to persons 65 an
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So far the analysis has been concer
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enta separation to the family age g
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Mortality maps have been widely use
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1970 population values, growth rate
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CANCER MORTALITY BY CENSUS TRACT 19
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References Burbank, F., Epidemiolog
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Computer graphics is changing all t
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time to define the uses to which th
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tually complete - we had a meeting
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EXPLORATION AND UTILITY SYSTEMS SES
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AUTOMATED MAPPING AND FACILITIES MA
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turned out to be a boon for automat
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As an example, one utility had five
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suburb of Denver, is a group of eng
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Introduction CADAE * (COMPUTER AIDE
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using CADAE, but the convenience an
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fractions of an inch to 1/64 or in
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Now that the viability of CADAE has
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"LANDFORM" LAND ANALYSIS AND DISPLA
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(2) Information Display (3) Design
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scales, and perspective views can b
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ENGINEERING APPLICATIONS OF DIGITAL
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Once the Map Grids are complete, th
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TOPOLOGICAL MODELS FOR ARCHITECTURA
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dimension, may be oriented in two w
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1-cells, and the 0-cells on the bou
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IX. One and two-dimensional structu
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looking from c^ to c9 near side far
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Figure 4 File Layout for Model of a
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DATA BASES, SMALL SYSTEMS There wer
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The consistency requirements are se
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A 0-cell is A 1-cell is a A 2-cell
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is a 2-ditnensional surface, and pr
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Our Algorithm From the topological
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(a) graph \ (b) disk: node 5 lO (c)
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as earthquake damage assessment, lo
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data is relatively simple. Problems
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In theory, the structure of such a
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BASIS resides on a minicomputer ope
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DATA BASES, LARGE SYSTEMS SESSIONS
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Robert Haralick and Linda Shapiro o
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COMPUTER-ASSISTED ENVIRONMENTAL DAT
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System (GRIDS) and Calma Mapping Sy
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Results Space does not permit the r
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encoded data appear to be very sign
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NATIONAL OCEAN SURVEY—AUTOMATED I
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centered at NOS Headquarters, but r
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separately. There are also five of
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graphic, chart base, and labels may
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Introduction GEOMODEL - INTEGRATED
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ace, income, miles of bus-lines, or
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phrase pointer Figure Ib. 1-cell Fe
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Implementation The development plan
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ECQBASE OF BRITAIN: status report o
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1. Coastlines (high water mark) inc
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much statistical data, e.g. , from
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Figure 1 Scale of digitisation of p
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I. Introduction A DATA STRUCTURE FO
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One obvious division of the state i
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Figure 2 illustrates this structure
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Raster or grid form is another form
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For each type of spatial data struc
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The following questions are possibl
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4. Freeman, H., "Computer Processin
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also be generalized to remove exces
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Figure I. On the left, a map of zon
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The other important role the error
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REFERENCES Corbett, J. (1975). "Top
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The fundamental building block of a
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discussed previously are of the COD
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[2] Bonczek, R. H.; Holsapple, C. W
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REFERENCE BASE REFERENCE LINES NAP
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Polygon data, in contrast, results
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An alternative to grid resampling i
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Should this table already contain a
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Murray, F. W. (1968) A_ Method of O
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ships between units, and thereby fe
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ture, encode, reduce, edit, format,
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could be assigned to each 40-acre g
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more on chain encoding rather than
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RIDS-CURRENT TECHNOLOGY IN RESOURCE
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The RID system is designed to overl
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Data Input Once the relevant data h
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Data Manipulation Timber Contour Cu
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THE DEVELOPMENT OF A NATIONAL SMALL
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III. The National Small-Scale Data
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cally-structured data base is under
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Appendix A: HAWAII: Hydrography U>
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INTERACTIVE CARTOGRAPHY, SMALL SYST
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options but it also extends our res
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sis techniques) information not pre
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media forming input to the system i
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D. CIS Data Base Limitations There
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input space into a set of 8 x 8 sub
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esolution of the system and the num
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impractical to use this terminal fo
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and heat from power plants into wat
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The present and future Low-resoluti
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Development of GIMMAP at the Kansas
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The second area of development is a
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GROUP Fig. 1
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MOVING INTERACTIVE THEMATIC MAPPING
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directives. Both map and data files
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Parameters are commonly of the form
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7. Conclusions In the s:!x months C
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INTERACTIVE CARTOGRAPHY, LARGE SYST
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developed at LBL has been particula
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printed at a common scale and forma
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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
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V. Production Sequence The most imp
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1. Introduction MULTIPLE SYSTEM INT
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measurements during map compilation
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Photogrammetric —— > Digitizer/
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intersections. These are a few exam
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Introduction ENERGY ANALYSIS BY MEA
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enabled us to undertake runs consit
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Cost (k $) (D CD M M
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which seek to incorporate powerful
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ELECTRON BEAM RECORDERS FOR AUTOMAT
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data files are supplied as an 8 Bit
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signals representative of map featu
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composite photograph prepared to sh
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Figure 5 16 AAIPS Approach Charts R
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Figure 8 - LANDSAT Image Recorded i
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AUTO-CARTO IV STAFF AND COMMITTEES
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University of Kansas Mike Hogben A'
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Efi Arazi, President Sci-Tex Corp.,
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Peter F. Bermel Chief, Eastern Mapp
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Sherry K. Brown Princeton Universit
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Steven D. Clark Petroleum Informati
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Richard Davis NOAA, NOS 6001 Execut
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John Durkin Suiranagraphics 35 Bren
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E. Porrest A-E-C Automation Newslet
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Barry J. Glick Middlebury College M
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Jim Hargis M & S Computing Co. 14 I
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Howard C. Hopps Dept. of Pathology
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Lee P. Johnston GeoGraphic Decision
Page 467 and 468:
Herbert Kressler Defense Mapping Sc
Page 469 and 470:
D. Richard Lycan Center for Pop. Re
Page 471 and 472:
Robert K. McKinney Weyerhaeuser Co.
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Joel L. Morrison Dept. of Geography
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David Osiecki 83 Gerber Rd. South W
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A.D. Poole Phillips Petroleum Co. 2
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Dirck L. Rotty USDA Forest Service
Page 481 and 482:
Craig L. Shafer NFS 18 & C Street,
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Bobby Staudt M & S Computing 406 Au
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Laure Thompson George Mason Univers
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D.J. Walker Image Graphics 107 Ardm
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Alberta Auringer Wood Chairperson,
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AUTHOR INDEX - VOLUME II Allam, M.
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Schmidt, Warren E. ...............
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