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HIPPARCHUS GEOPOSITIONING MODEL: AN OVERVIEW Hrvoje Lukatela 33 Chancellor Way, Calgary, AB T2K 1Y3 Canada ABSTRACT This paper introduces a novel digital geopositioning model. It is based on computational geodesy in which direction cosines are used instead of the conventional -angular- ellipsoid normal representation, and eccentricity term expansions are replaced by iterative algorithms. The surface is partitioned by a spheroid equivalent of the Voronoi polygon network. The model affords seamless global coverage, easily attainable millimetric resolution, and data-density sensitive location indexing. Numerical representation of 0, 1 and 2 dimensional objects is in complete accordance with the unbounded, spheroidal nature of the data domain, free from any size, shape or location restriction. Efficient union and intersection evaluations extend the utility of the relational technique into the realm of geometronical systems with non- trivial spatial precision requirements. Digital modelling of orbital dynamics follows closely the numerical methodology used by terrestrial geometry. The HIPPARCHUS software package includes the transformations and utility functions required for efficient generation of transient graphics, and for the communication with systems based on conventional cartographic projections. Fig. 1: HIPPARCHUS ellipsoid surface partitioning scheme INTRODUCTION A numerical geopositioning model is an essential element of any system wherein a dimension of space enters into the semantics of the appli cation - and therefore into the software technique repertoire - in a fundamental way. It consists of location attribute data definitions 87
and computational algorithms, which allow position sensitive storage and retrieval of data, and provide a basis for evaluation of spatial relationships. (The term "spatial relationship" is used in this paper to describe the formal statement of any practical spatial problem which deals with positions of real or abstract objects on - or close to - the Earth surface. Their nature can vary; examples might include geodetic position computations, course optimization for navigation in ice-infested waters or determination of the most probable location of objects remotely sensed from a platform in the near Space.) If the location attributes of data elements in a computer system are used exclusively tor the generation of a small-scale analog map document, the demands made of a geopositioning model are few and simple. When the area of coverage is limited, and projection geometry, spatial resolution and partitioning of the data can be made directly compatible with same characteristics of all future required products, a single plane coordinate system is often employed. Such a system is usually based on one of the large-area conformal projections (e.g. Lambert, Gauss-Krueger, etc.), and provides adequate means to identify positions, partition the data, and construct a location index. The model may even allow limited spatial analysis. However, with the increase of the area of coverage and the functional power of information systems, the nature of the problem changes considerably. Precision requirements usually exceed the level of difference between planar coordinate relationships and the actual object-space geometry. In most cases, the generation of an analog map is reduced to a secondary objective. Location attributes are primarily used to support the evaluation of spatial relationships required by the application. Indeed, as the volatility and volume of data grows, it becomes increasingly common that a location-specific item enters a system, contributes to the evaluation of a large number of spatial relationships, and is ultimately discarded, without ever being presented in the graphical form. Even in systems used primarily to automate the production of analog documents, there is often a need to accommodate many different projection, resolution and data partitioning schemes on a continental or even global scale. A point is thus quickly reached where geopositioning model must satisfy very demanding functional requirements, yet any restriction on the data domain becomes unacceptable. From the application point of view, the mapping from an atomic surface fraction into a distinct internal numerical location descriptor must be global, continuous and conjugate. Faced with these requirements, manual spatial data processing resorts to a combination of two techniques. A set of multiple planar projection systems (e.g. UTM "zones") is used to achieve - seldom successfully - the global coverage. Initially simple calculations are cluttered with various "correction" terms in order to deal with differences between planar coordinates and true object geometry. A failure to understand the precise nature of spatial data (especially, by ignoring the profound conceptual difference between an analog map and the true data domain) often leads to a blind transplant of conventional cartographic techniques into a computerized system. 88
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Proceedings Eighth International Sy
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1987 by the American Society for Ph
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A NOTE ON THE FUTURE OF AUTO-CARTO
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Algorithms for spatial search or qu
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Research into electronic maps and a
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Sandhu, Jatinder 403 Shea, K. Stuar
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integration of the findings on tech
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departments of municipalities are p
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systems, similar cost reduction in
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exist here: it is rarely possible t
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REFERENCES Chris man, N. and Nieman
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THE USER PROFILE FOR DIGITAL CARTOG
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second is to reduce all lines to a
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OVERLAY PROCESSING IN SPATIAL INFOR
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digital terrain models, or magnetic
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(2-dimensional) or volumes (3-dimen
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whereas the lattice induced by spat
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5.2 Overlay Operation One of the mo
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permit the determination of the len
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more about the quality of the avail
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of the user interface and would res
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FUNDAMENTAL PRINCIPLES OF GEOGRAPHI
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of continuous space (the model of A
Page 47 and 48: look like is transmitted through th
Page 49 and 50: (Sullivan and others, 1985). On the
Page 51 and 52: PRESCRIPTIONS To carry out the prin
Page 53 and 54: AN ADAPTIVE METHODOLOGY FOR AUTOMAT
Page 55 and 56: They reorganize available space and
Page 57 and 58: Global Filtering Basics: This filte
Page 59 and 60: If the geometry is determined throu
Page 61 and 62: SYSTEMATIC SELECTION OF VERY IMPORT
Page 63 and 64: Improvements The first improvement
Page 65 and 66: RESULTS ANALYSIS There are two test
Page 67 and 68: Figure 4. A TIN generated from VIP
Page 69 and 70: only or the most important one. Unt
Page 71 and 72: terrain surface, may have in corres
Page 73 and 74: Advantages of determining the Media
Page 75 and 76: egards points, only the endpoints o
Page 77 and 78: contours some measures of size and
Page 79 and 80: MEASURING THE DIMENSION OF SURFACES
Page 81 and 82: dimension of an entity, is constant
Page 83 and 84: terrain. In order to avoid a sampli
Page 85 and 86: APPLICATIONS TO DIGITAL ELEVATION M
Page 87 and 88: 1.20 1.16 • D I M 1.12 E N S 1.06
Page 89 and 90: Stability of Map Topology and Robus
Page 91 and 92: The 0-cells in the usual topologica
Page 93 and 94: Notice in Figure 1 that the interme
Page 95 and 96: Algorithm for computing robustness
Page 97: We may sum the forces by a straight
Page 101 and 102: The geopositioning model presented
Page 103 and 104: It should be noted that only the fr
Page 105 and 106: While Voronoi polygons have often b
Page 107 and 108: additional vector rotation about th
Page 109 and 110: inconsistency. The problem stems fr
Page 111 and 112: Chain Intersection Determining chai
Page 113 and 114: node(6,[h(l8),t(l9),t(24),h(21)]).
Page 115 and 116: Sliver Removal. We remove a sliver
Page 117 and 118: Little, J.J. and Peucker, T.K. 1979
Page 119 and 120: measured control points. In this pa
Page 121 and 122: TEST RESULTS For testing the above
Page 123 and 124: A SPATIAL DECISION SUPPORT SYSTEM F
Page 125 and 126: data by time period, by category, a
Page 127 and 128: BASIC version of the PLACE suite re
Page 129 and 130: procedural language. The classifier
Page 131 and 132: FIGURE 1: SOFTWARE COMPONENTS FOR S
Page 133 and 134: Realistic Flow Analysis Using a Sim
Page 141 and 142: TIN FORMAT VS. MATRIX FORMAT The pr
Page 143 and 144: One of the major challenges involve
Page 145 and 146: Because TINFLOW is a PC-based GIS,
Page 147 and 148: Art; I DitH ot twin 1.1610 Strew He
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RATIONALE Gridded surface data sets
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5. For each polygon, for each cell
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A mapping function was used to topo
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CONCLUSIONS This depression-finding
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Methods For spatial analusis The tw
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1. Sampling to determine the sample
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A simcle multiscale model . Instead
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Complex multiscale models. The one-
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Mandelbrot, B.B., 198E. The Fractal
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A number of authors have proved the
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Once having the Fourier-transf arm
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From the above listed aspects (2) i
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A considerably large number of labo
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Oliver,M.A., R.Webster (1936) Semi-
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model can be used as the basis for
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ts phase space by analogy to phase
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Figure 3. Classified 64 by 64 raste
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in the delimitation of domains in p
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Mark, D.M. and Aronson, P.B. 1984,
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To make decisions about this world,
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Limitations inherent to the modeliz
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operations delimiting rights to the
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Uncertainty absorption is very diff
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Minsky, M. L. 1965, Matter, Minds,
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data, covering extremely large area
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Figure 1. a) Test data set with, tr
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Figure 2. Four pyramids - line segm
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convenient to consider grids to be
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REFERENCES Davis, J.C., 1973, Stati
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the data element, in this case an a
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EXPERIENCE WITH R-TREES IN A CIS LA
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REFERENCES Guttman, A. 1984, R-Tree
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World Shoreline Vectors Shoreline v
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Table 4. Applications of gridded el
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classes desired for a given applica
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Table 6. The impact of block size o
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Jones, Christopher B. and Abraham,
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DISADVANTAGES OF A SINGLE COVERAGE
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faster and less complex than genera
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NOS detailed source data 20 meter r
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si '- /W^ ?f ? ( " ( I?
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REFERENCES Aronson P. and Morehouse
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with the purpose of optimizing geom
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purposes, the value 1/e may be thou
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V describing points/ / y/ B / /•*
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clarity, the number of describing p
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ACKNOWLEDGMENTS The author wishes t
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INTRODUCTION In any application of
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7T 0 — 7T X Hay River Figure 1: A
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0 — 7T Alluvial fan contour Figur
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Peucker, 1973) can be used here; th
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Mark, D. M., 1985, Fundamental spat
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•©—e—©—e- Figure 1.1: Spl
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SLAU- 9/1000 Figure 1.5: Results of
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t-0 I.I 7.4 /.6 1.8 2.0 Figure 2.1:
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THE TIGER STRUCTURE Christine Kinne
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to another tail record. There are f
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Since records are fixed length, a n
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areal data is stored, but additiona
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KEY TO SUBFILE ABBREVIATIONS (CONTI
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TOPOLOGICAL ENTITIES Corbett's topo
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TOPOLOGICAL RULES The preceding def
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File and the new linear feature ref
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Encoding and Referencing (TIGER) Sy
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of the boundary are found and corre
Page 280 and 281:
CONCLUSION The GTUB routines have b
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SELECTION OF EQUIPMENT The least ef
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operations. The site and staff for
Page 286 and 287:
RESULTS Table one shows the numeric
Page 288 and 289:
would no longer have to determine a
Page 290 and 291:
THE DATA BASE ADVANTAGE Most of the
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SUMMARY AND CONCLUSIONS The major d
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the complexity o-f I/O processing.
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is on one and only one topological
Page 298 and 299:
•features represented in the data
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intersection is -found -for this -f
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An easy implementation o-f spatial
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organisations most precious asset -
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no reason why we should not model t
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- A VERTEX identifies a unique spat
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to the organisation and indexing of
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the retrieval of data from the disp
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original goals, through design, and
Page 316 and 317:
Contents and Queries Each geographi
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number of tables required. On the o
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generic, db-internal read/write/del
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we are guaranteed that each occurre
Page 324 and 325:
The db bottlenecks we found were, f
Page 326 and 327:
Bibliography [1] Date, C.J. 1983 -
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model is an object-oriented extensi
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SPECIALIZATIONS FOR SPATIAL DATA Th
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for each x in S, for each y in S if
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entity IMAGE PIXELS(IMAGE) - set of
Page 336 and 337:
Orenstem, J.A. 1984, "A Class of Da
Page 338 and 339:
understand the data model on which
Page 340 and 341:
Internally, KGIS is implemented on
Page 342 and 343:
AREA > 10; Spatial relationships be
Page 344 and 345:
Once established, a GEOVIEW remains
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___________, 1985, THE USE OF SPATI
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• the cross sections, profiles an
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• Rigid and homogeneous ores can
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Borehole data \ Geologist's ^^ know
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Figure 3 : A Portion of the Ore Bod
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REFERENCES Baumgart, E.G. (1975) -
Page 358 and 359:
This paper is organized into five s
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yields the resulting table: Poly* 1
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tightly bound to the map; there is
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A partial example of the relational
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REFERENCES Chrisman N. and Niemann,
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GEOGRAPHIC DATABASE TOPOLOGY SPATIA
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of a coordinate in n-space, usually
Page 372 and 373:
Airport refines Aviation; — This
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THE dbmap SYSTEM Donald F. Cooke Ge
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procedurally, like Pascal, FORTRAN
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een lassoed (and line-segments in o
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Figure 4 Result of Lasso Operation
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The goal of a DSS is to help decisi
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chosen structure must provide a mea
Page 386 and 387:
First, a general schema diagram is
Page 388 and 389:
Hopkins, L.D., and Armstrong, M.P.
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******* DATABASE IDENTIFICATION AND
Page 392 and 393:
Because of these limitations, furth
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cannot share the data. A minicomput
Page 396 and 397:
Historically the whole orientation
Page 398 and 399:
To reach the stated goal of this pa
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mapping techniques conceptualized a
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The future skill level, and trainin
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€6€ COMPUTER SCIENTIST ELECTRIC
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U* '^ OUTPUT \ / REVIEWIM. CORRECTI
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We may conceptually divide a VNA in
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most interest for transmitting navi
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necessary) in such a display. This
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ENHANCEMENT AND TESTING OF A MICROC
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make maximum use of the limited, lo
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I Text Display Window (Toggle On/Of
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as well, using the PLINK86 Plus ove
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AN INTEGRATED PC BASED CIS FOR INST
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RAW DATA INPUT DATA BASE MAPh ANALY
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Figure 3. Example of output from SH
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Figure 8. CONTOUR of elevation on v
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Figure 11. COLOR map on printer of
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IDRISI : A COLLECTIVE GEOGRAPHIC AN
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felt to be negligible compared to t
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Although the IDRISI system was prim
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data file, and a second backwards t
Page 440 and 441:
TABLE 1 : IDRISI PROGRAM MODULES IN
Page 442 and 443:
CLASSLESS CHOROPLETH MAPPING WITH M
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polygon. The process of selecting s
Page 446 and 447:
There are a number of places where
Page 448 and 449:
COMPUTER-ASSISTED TERRAIN ANALYSIS
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2. Input. A digitizing tablet to al
Page 452 and 453:
terrain analysis data. Items 3. and
Page 454 and 455:
Database Structure Currently, DMA-p
Page 456 and 457:
RESULTS OF THE DANE COUNTY LAND REC
Page 458 and 459:
E. G.
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section maps of tax parcels maintai
Page 462 and 463:
Public Land Survey System (PLSS) co
Page 464 and 465:
Sheets, Proc. ACSM, 1:153-161. Chri
Page 466 and 467:
von Meyer, N.R. 1984b. Westport Ine
Page 468 and 469:
While meeting the above criteria pr
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oundary line. An example of the sam
Page 472 and 473:
Four groups of approximately thirty
Page 474 and 475:
LEGEND MULTIPLE BOUNDARIES STATE, C
Page 476 and 477:
TABLE 2 shows that more respondents
Page 478 and 479:
What features are considered when d
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position is insignificant. Thus, th
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ASSESSING COMMUNITY VULNERABILITY T
Page 484 and 485:
Yale University was selected for st
Page 486 and 487:
distribution of hazardous materials
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»++ 0000000001000OCCCOOOOOOCOOOOCO
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44* 444 444 ICO 9 CO 9CO to CO ECO
Page 492 and 493:
IMPROVEMENT OF GBF/DIME FILE COORDI
Page 494 and 495:
Establishment of Control Points In
Page 496 and 497:
transformation parameters for a par
Page 498 and 499:
of using a fixed set of transformat
Page 500 and 501:
vertex coordinates into exact corre
Page 502 and 503:
Friedman, J., Baskett, F. and Shust
Page 504 and 505:
and small freehold land. It does no
Page 506 and 507:
The next step in the planning proce
Page 508 and 509:
TSO on UNB's IBM 3090 mainframe com
Page 510 and 511:
3. Kettela, E.G. 1975. Aerial spray
Page 512 and 513:
The integration of developing techn
Page 514 and 515:
and photographic processes are used
Page 516 and 517:
Figure 4 EXAMPLE OF PUBLISHED FIRM
Page 518 and 519:
EXAMPLE OF COMPUTER-GENERATED FIRM
Page 520 and 521:
BIBLIOGRAPHY Federal Emergency Mana
Page 522 and 523:
more detailed introduction to exper
Page 524 and 525:
MAPEX is a rule-based system for au
Page 526 and 527:
discrimination nets, Click et al (1
Page 528 and 529:
example, FES (Goldberg et al, 1984.
Page 530 and 531:
Pereira, L.M., P. Sabatier, and E.
Page 532 and 533:
e flexible enough to address a wide
Page 534 and 535:
intermediate hypotheses are "posted
Page 536 and 537:
All cited rules become part of the
Page 538 and 539:
The Geographic Information System L
Page 540 and 541:
geographic knowledge system applies
Page 542 and 543:
In view of this it is not suprising
Page 544 and 545:
placement, the main area of cartogr
Page 546 and 547:
EXPERT SYSTEM INTERFACE TO A GEOGRA
Page 548 and 549:
ASPENEX automates the analysis of s
Page 550 and 551:
Rule-Base Creation SYSTEM OPERATION
Page 552 and 553:
the rulebase created by the aspen e
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AUTOMOBILE NAVIGATION IN THE PAST E
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oadside equipment to provide equipp
Page 558 and 559:
algorithm and provides step-by-step
Page 560 and 561:
DRIVER INPUTS • DESTINA1ION • R
Page 562 and 563:
Vehicular Technology Conference, 35
Page 564 and 565:
Map retrieval is also crucial to na
Page 566 and 567:
elative coordinate accuracy is very
Page 568 and 569:
destination does not require knowin
Page 570 and 571:
PRESENTATION The extremes of styles
Page 572 and 573:
REFERENCES Ashkenazi, V. 1986, Coor
Page 574 and 575:
decision-making, learning, and natu
Page 576 and 577:
that these travellers felt that wri
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e weak, if present at all. Since ma
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Figure 2: An example of a distorted
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directions were produced in real ti
Page 584 and 585:
Figure 1. Concept of an Automatic V
Page 586 and 587:
AVL COMPONENTS AND THEIR FUNCTIONS
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OUTPUT FACILITIES V7MIC1Z «IflT KA
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need extensive customizing. This cu
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PRACTICAL EXPERIENCE WITH AVL 2000
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ACKNOWLEDGEMENT This research has b
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separate AVL system is needed (spec
Page 598 and 599:
Sources Two plausible sources of a
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o t=z ATTRIBUTE RELATIONSHIP ENTITY
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(a) optimal route between the pair
Page 604 and 605:
REFERENCES Cooke, D.F., Vehicle Nav
Page 606 and 607:
THE BBC DOMESDAY SYSTEM: A NATION-W
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which are not commonplace: it permi
Page 610 and 611:
Geochenrstrj Climate VNater fiature
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(ii) measure area and distance in m
Page 614 and 615:
Rhind D.W. and Mounsey H.M. (1986).
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language expression. One of the mot
Page 618 and 619:
This process begins from a position
Page 620 and 621:
E(l(k)) be the expectation of I ( k
Page 622 and 623:
There are several approaches to con
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In this paper we will discuss preml
Page 626 and 627:
Table 2. Length of Sessions and The
Page 628 and 629:
Table 5. Fuzzy Membership Values fo
Page 630 and 631:
Table 7. Results of Zimraermann's M
Page 632 and 633:
Chamberlain, D.D. and R.F. Boyce. 1
Page 634 and 635:
ACCESSING LARGE SPATIAL DATA BASES
Page 636 and 637:
WORKSTATION #2 1 - IBM-AT; 640K, 20
Page 638 and 639:
RECORD 1 —— coordinates 1-256 f
Page 640 and 641:
Future developments include the pol
Page 642 and 643:
Once features of two coverages have
Page 644 and 645:
Figure 3a Partial street network co
Page 646 and 647:
Figure 3e Coverages aligned with 50
Page 648 and 649:
Solving the Feature Matching Proble
Page 650 and 651:
References Chen, Z. and A. Guevara,
Page 652 and 653:
determined that a conversion of dra
Page 654 and 655:
PAT GRP NUM 1 2 3 4 5 6 7 8 9 10 11
Page 656 and 657:
various raster and vector operation
Page 658 and 659:
Figure 4a - Portion of scan-digitiz
Page 660 and 661:
the set of points. This will introd
Page 662 and 663:
which represents the terrain by a t
Page 664 and 665:
leaf for 4 and 5). Chen and Tobler
Page 666 and 667:
fixed polynomial order for each run
Page 668 and 669:
RESULTS As noted above, the program
Page 670 and 671:
REFERENCES Chen, Z.-T., and Tobler,
Page 672 and 673:
Shortcomings in Existing Raster-to-
Page 674 and 675:
Template design parameters are base
Page 676 and 677:
RESULTS REPORT type RESULTS REPORT
Page 678 and 679:
Significance of the AFT Technology
Page 680 and 681:
REFERENCES Antell, R.E. (1983), "Th
Page 682 and 683:
Grid systems do not permit vertical
Page 684 and 685:
SCHEMA structures an urban model ar
Page 686 and 687:
The second data structure regards t
Page 688 and 689:
The resulting polygon "hole" is the
Page 690 and 691:
REFERENCES Brassel, Kurt E., and Do
Page 692 and 693:
The link between these two bodies o
Page 694 and 695:
The same technique of Fourier analy
Page 696 and 697:
The similarities between this and t
Page 698 and 699:
In many respects, a terrain model c
Page 700 and 701:
AN ALGORITHM FOR LOCATING , CANDIDA
Page 702 and 703:
The left and right boundaries of a
Page 704 and 705:
limits. The overall problem of gene
Page 706 and 707:
To find the cluster limits, the sim
Page 708 and 709:
next box. The entry (m = s) is ther
Page 710 and 711:
Figure 3.-Portion of test data set
Page 712 and 713:
PRACTICAL EXPERIENCE WITH A MAP LAB
Page 714 and 715:
£ X lfk = 1 k=1,2,...,K. (1) i If
Page 716 and 717:
Deleted Labels The optimization alg
Page 718 and 719:
Figure 2. Point Symbol Labels With
Page 720 and 721:
AUTOMATIC RECOGNITION AND RESOLUTIO
Page 722 and 723:
FUNCTION REQUIRED l)ls a point on a
Page 724 and 725:
distance by finding the square root
Page 726 and 727:
Proportional Radial Enlargement As
Page 728 and 729:
distribution). If the thresholds ar
Page 730 and 731:
CALCULATING BISECTOR SKELETONS USIN
Page 732 and 733:
Thiessen centroid than to any other
Page 734 and 735:
there are exactlv n boundary skelet
Page 736 and 737:
AREA MATCHING IN RASTER MODE UPDATI
Page 738 and 739:
THE AREA MATCHING PROCESS This proc
Page 740 and 741:
defaults are made of very short seg
Page 742 and 743:
POLYGONIZATION AND TOPOLOGICAL EDIT
Page 744 and 745:
If no label exists between the chai
Page 746 and 747:
these internal (non-boundary) chain
Page 748 and 749:
However, a cartographic database ne
Page 750 and 751:
"WYSIWYG" MAP DIGITIZING: REAL TIME
Page 752 and 753:
with tolerance circles such that it
Page 754 and 755:
CONCLUSION For many years a major i
Page 756 and 757:
implementation methodology and the
Page 758 and 759:
SPLIT SCREEN o o oo SIDE BY SIDE o
Page 760 and 761:
determined applicability aided by s
Page 762 and 763:
the 384 LPI resolution patch used t
Page 764 and 765:
TESTING A PROTOTYPE SPATIAL DATA EX
Page 766 and 767:
2. An Overview of MAPS The MAPS spa
Page 768 and 769:
containment tree can be used to eff
Page 770 and 771:
ROLE: BUILDING UNKNOWN MEDICAL CENT
Page 772 and 773:
and the segment direction within ea
Page 774:
seg : nodes: points south west: 20.
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