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REFERENCES precision in data handling. Maps are graphic communicators and clear and concise map mes sages result from easily read, clear rather than noisy maps. Communication via the map is not perfectly understood and there is need for continued research if we are to create more ef fective maps. 1. Petchenik, Barbara B., "A Verbal Approach to Characterizing the Look of Maps," The American Cartographer, vol 1, No. 1 (l97 iO» PP» 63-71. 2. Statistical maps are not necessarily products of statistical inference; rather many statistical maps are two-dimensional graphic representations of enumer ated data obtained by censual procedures. This paper is an abbreviated version of an oral paper presented at the Inter national Symposium on Computer-Assisted Cartography (Auto-Carto II), sponsored by the American Congress on Surveying and Mapping in cooperation with the Bureau of the Census. 3. The data presented in Table 1 and that used for other maps of Utah were taken from Utah Agricultural Statistics 1973> Salt Lake City: Utah State Department of Agriculture, pp. 86-7 Map makers frequently array these types of data in sequential order as a preliminary to processing the figures into categories for symbolization. ^. For a more sophisticated analysis of maps as communicative devices see: Robin son, Arthur H., and Barbara B. Petchenik, "The Map as a Communicative System," The Cartographic Journal, vol. 12, No. 1 (June 1975)? pp. 7-15. 5. Also see Robinson, Arthur H., and Randall D. Sale, Elements of Cartography, 3rd edition, New York: John ¥iley and Sons, 6. Dobson, Michael W. , "Symbol-Subject Matter Relationships in Thematic Carto graphy," The Canadian Cartographer, vol. 12, No. 1 (June 1975) > PP. 52-6? . 7. Areal standardization of data for choropleth maps is achieved by converting simple enumerated data to ratios. In the case of map B in Figure 5> the crop land area of each county was divided by its total land area to derive the ra tio, cropland as a percentage of total area. 8. Morrison, Joel, Method Produced Error in Isarithmic Mapping, Cartography Division Technical Monograph No. CA-5, Washington, D.C. : American Congress on Surveying and Mapping, 9. Arnheim, Rudolph, Art and Visual Perception, Berkeley: University of Califor nia Press, 1971, p. Ml. —————————— 10. These maps are taken from the unpublished Ph.D. dissertation research of Theodore Steinke at the University of Kansas. 60
ABSTRACT CHARACTER OF A MAP TOPOLOGICAL PRINCIPLES IN CARTOGRAPHY James P. Corbett A map may be described as a linear graph embedded in a orientable, two-dimen sional manifold. A manifold, aside from being a two-dimensional continuum, is locally flat, that is, each point of the manifold is contained in a neighborhood homeomorphic to a disk. A linear graph so embedded will, if it contains 1-circuits, delineate a number of simply connected domains. The collection of 0-cells and 1-cells of the graph, together with the 2-cells so delineated forms a two-dimensional complex, having the special property of local flatness. The structure of this two-dimensional complex is completely specified by a pair of relations among the cells. These are the oriented incidence relations between 0-cells and 1-cells, and those between 1-cells and 2-cells,, The local flatness condition implies that there is a form of symmetry, known as duality, between these two relations. A widely used model of this relational system, the DIME encoding, illustrates this symmetry in a perspicuous manner. This representation consists of a quadruple, or pair of ordered pairs of cell identifiers, a, bj c, d one such quadruple for each segment of the graph generating the map. The geometric interpretation of this model is as follows: a and b are interpreted as identifiers of the ordered pair of 0-cells, the initial and terminal points of the directed segment; c and d are interpreted as identifiers of an ordered pair of 2-cells, the right and left 2-cells separated by the segment. This latter interpretation is permissible only because of the local flatness condition of the manifold. The natural dualism is apparent from the DIME representation. Exchanging the first and second pair provides a representation of a dual segment which can be drawn in a canonical way on the same manifold. The dual elements and relation pairs are indicated below: 0-cells 2-cells 1-cells 1-cells boundaries coboundaries* The order relations on the oriented manifold are also expressed by the DIME representation. If we exchange the elements of the first pair, we obtain a repre sentation of a segment oppositely directed on the oppositely oriented manifold, and #The converse of the relation bounds is known as cobounds. 61
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sBuipaaoojd paj.sgsse-ja).nduioo uo
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of the international symposium on c
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PREFACE The. te.chnic.at oAticJteA
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Seminar on Statistical Mapping . .
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CHARGE TO THE CONFERENCE William B.
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CONCLUSION Summing up, the introduc
Page 17 and 18: INTRODUCTION MAP DESIGN Arthur H. R
Page 19 and 20: Because it will help to emphasize a
Page 21 and 22: The main idea behind the communicat
Page 23 and 24: INTRODUCTION A CHALLENGE TO CARTOGR
Page 25 and 26: manner: The authors have attempted
Page 27 and 28: But just how new is the concept of
Page 29 and 30: Clearly the ability and the desire
Page 31 and 32: The third step is the DECISION stag
Page 33 and 34: He went on to call for the creation
Page 35 and 36: VISIONS OF MAPS AND GRAPHS William
Page 37 and 38: intution, rule of thumb, and a kind
Page 39 and 40: (Of course it might be that some ca
Page 41 and 42: How stable, for example, are the re
Page 43 and 44: Henry ¥ Castner and Arthur H. Robi
Page 45 and 46: General Session Papers Introduction
Page 47 and 48: WALP0 T08LER has been with the. Geo
Page 49 and 50: INTRODUCTION A GEOGRAPHIC AND CARTO
Page 51 and 52: In addition, numerous administrativ
Page 53 and 54: DELINEATION OF STATISTICAL AREAS Su
Page 55 and 56: which exist around the central citi
Page 57 and 58: distribution of school children by
Page 59 and 60: INTRODUCTION CONTEMPORARY STATISTIC
Page 61 and 62: tial relationships of cropland acre
Page 63 and 64: Figures 3 and k. At least part of w
Page 65 and 66: AESTHETICS AND MAP COMMUNICATION Th
Page 67: As a case in point, study the three
Page 71 and 72: epresents the operator composition
Page 73 and 74: Thus a contour lies between two of
Page 75 and 76: (2) From this table compute plane c
Page 77 and 78: 4: A Topogtuipkic. 1970 POPULRTION
Page 79 and 80: county map of the United States has
Page 81 and 82: If. D. Kendall, "Construction Of Ma
Page 83 and 84: By the way, graphs used for the var
Page 85 and 86: c. Suppose that maps are constructe
Page 87 and 88: Graph2: MEDIAN INCOME IN 1949 OF FA
Page 89 and 90: adults (see Yule and Kendall, 1950,
Page 91 and 92: original GRP, and a scale of tens h
Page 93 and 94: them (or in semi-logarithmic charts
Page 95 and 96: (iiaphll USA (1840, 1900, I960) Per
Page 97 and 98: ooooooooooooo< 4 DD 4 D 4 C 4 ooooo
Page 99 and 100: INTRODUCTION THE CHALLENGE OF MAPS
Page 101 and 102: Gilligan and Amendola here in the U
Page 103 and 104: handicapped will be better served b
Page 105 and 106: REFERENCES 1. Professor James F. Go
Page 107 and 108: INTRODUCTION MAP GENERALIZATION: TH
Page 109 and 110: map, symbols can be assigned and th
Page 111 and 112: that simplification of lines result
Page 113 and 114: Map 3a. .01 Map 3b. .30 Map 3c. .60
Page 115 and 116: 75,000
Page 117 and 118: As mentioned earlier, most surface
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exponentially with the number of po
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Panel Discussion on Experiences in
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C. GENE JOHNSON iA chie.fi ofi the.
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And in talking about the possibilit
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INTRODUCTION DECISION DAY FOR AUTOM
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THE ORDNANCE SURVEY This organizati
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AUTOMATED CARTOGRAPHY AT THE U. S.
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Two steps of choropleth mapping hav
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The identification subsystem will u
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AUTOMATED CARTOGRAPHY IN THE NATION
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GEODETIC CONTROL MAPS The National
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SEMINAR ON STATISTICAL MAPPING This
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INTRODUCTION STATISTICAL ACCURACY A
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was purposely conventional. The low
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F;VL - FIVE 7 FIVE 9 FIVE M FIVE 16
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classes tended to smooth out the bl
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TABLE III. OVERALL ACCURACY OF THE
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epresentation of statistical relati
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7. G. Jenks and F. Caspall, "Error
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7. A -6eo£con oft the. UrUte,d Sta
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3. Two boie map* pAepaAed tfoA paAt
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Figure 5 are generalizations of the
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City Selection The twenty largest m
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Dot distribution maps are used for
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plate. Pages with isopleth maps and
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THE URBAN ATLAS PROJECT: HISTORICAL
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The feasibility of such a project,
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SCALE Since the primary purpose of
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LINE-WEIGHT The line-weight of the
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SEMINAR ON MAP REAPING ANV PERCEPTI
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perception using the. basic oAAumpt
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an attempt to reach a re.atistic mo
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Census of Agriculture, the Census B
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maps. Research cartographers have m
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Five shades in black and white or c
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Ve selected this scheme for use in
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The important shift that has occurr
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For a good many years, researchers
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So far cartographic research in map
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This will be a difficult order, eve
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This is equally true of many aspect
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AN ANALYSIS OF APPROACHES IN MAP DE
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the clues that you get in the visua
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take immediate action to correct th
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• BASE MAPS PLANIMETRIC TOPOGRAPH
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as the one in the front of the room
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INTRODUCTION CURRENT RESEARCH IN TA
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D.B.RH. NEIGHBORHOOD MAP Key ;to m
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3. GENERAL REFERENCE MAP OF THE UNI
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tions were noted for both practiced
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for the single lines, ranging from
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INTRODUCTION THE OPTIMAL THEMATIC M
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eye comes to rest for at least 2/10
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The 20 reconstructed maps were then
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307 302 Figure. 10. TkeAe. two tKLc
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~i 12. The^e, dote -6how the. locat
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INTRODUCTION THE MAP IN THE MIND'S
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VALUE OF RETAIL TRADE SURPLUS LOCAT
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has a prominent role in goal specif
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the subjects some elements are domi
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a sound explanation for it. A secon
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Finally, one of the most interestin
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INTRODUCTION IN PURSUIT OF THE MAP
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producing a personal image fictitio
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individuals chosen appear from the
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screen gray area and its perceived
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There are a number of questions whi
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Note, first, that the four areas wi
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18. Stevens, S.S. (Geraldine Steven
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PER CAPITA INCOME: 1 970 3.
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MICROFILM OUTPUT This film is a typ
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ANAHEIM-SANTA ANA- GARDEN GROVE, CA
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ANAHEIM-SANTA ANA- GARDEN GROVE, CA
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NUMBER OF AMERICAN INDIANS COUNTIES
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HOUSING UNITS BUILT BEFORE 1950 - W
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NESTED CATEGORIES EMPHASIS ON EXTRE
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Seminar on Uses of Color Introducti
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In theJji pne*entation f "Tke- Sele
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INFORMATION PROCESSING AND RECALL T
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The great 19th century physicist Ja
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general, there is a tendency for a
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THE SELECTION OF COLOR FOR THE U.S.
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mixes for CIA with the formulas on
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Red Cyan Yellow Other Color Agrocli
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Red Cyan Yellow Other Color Rural P
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Administrative Divisions, p. 58 —
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spaced in hue, such as this sequenc
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THE ORGANIZATION OF COLOR ON TWO-VA
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diagonal. (See Figure 18, page 265
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CONCLUDING COMMENTS Finally, there
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Seminar on Automation in Cartograph
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The. majoA tkAaAt o& the. TopogAaph
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Subcontracted work has until now ge
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Software development before 1970 di
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INTRODUCTION INTERACTIVE CARTOGRAPH
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Our system assumes that automated c
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can be taught to correct some, at l
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this, very little attempt has been
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The vast increase in speed (about t
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Data Management System 1100 (now us
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APPENDIX B: A BRIEF DISCUSSION OF H
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CO-ORDINATE SYSTEMS AND TRANSFORMS
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A digital data bank comprises colle
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The second advantage is particularl
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The production of maps, however, re
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Things become more complicated with
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For less high quality we plan to el
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One of the most important facts in
Page 340 and 341:
SEMINAR ON AUTOMATION IN CARTOGRAPH
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pAoje,ct at the. LaboAatoAy fioA Co
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Master Enumeration District List (M
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as seen in Figure 1. The resulting
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(X). Implicitly this problem is ide
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6. Fou/i data. po^ntA loc.at
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F-tgote 7. Cteecf and open Thxte64e
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INTRODUCTION TOPOLOGICAL INFORMATIO
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Topological notation emphasizes the
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NEW PROCEDURES In particular, many
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-INTRODUCTION CONTOURING ALGORITHMS
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The second step is the estimation o
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1111 T ? ^ ? Weighting Function F-c
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obtainable. An algorithm which fait
Page 369 and 370:
Seminar on Land Use Mapping Introdu
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de.veJtopme.nt and availability ofi
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Image. pAocessing te.chniqu.eA oAig
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INTRODUCTION LAND UNIT MAPPING WITH
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MANAGEMENT COMPONENTS • Highly de
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SOURCE MAP CHARACTERISTICS WRIS has
Page 381 and 382:
Polygon boundaries to be digitized
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less than 10 minutes. This speed wi
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6. Diello, Joseph, (1970), The Evol
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the map is only peripheral at prese
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THE NATURE OF PROPERTY TAXATION TAX
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The maps are actually parts of an i
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5. Commonwealth of Massachusetts, D
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LANDSAT image, a stereoscopic pair
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The climate of the area is moderate
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The developed formula of peak runof
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This coordinate system is shown on
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The drainage basin maps show the ac
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BLOCK #24-21 (continued) 3. 153 Del
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SQUARE 2 1 ^ i 7 2 —— ~1T ~6^ 8
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24-21 msv -Co 75° 12' 40° 38' X =
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24-21 75°I2' 40°38' X = 1851968.7
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24-21 75° I2 1 40°38 X= 1851968.
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BRIEF ANALYSIS OF THE USERS The req
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6. Halasi-Kun, G. J. (1975), "Water
Page 420 and 421:
SEMINAR ON IWTERACTIl/E MAP EPITING
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0/ES SHEPHERD o$ the. U.S. Amy Engi
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Youngmann (1972), Peucker (1973)> a
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developed in other areas, to the so
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7. Christian!, E. J., et al., 1973>
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NEIGHBORHOODS MAP EDITING USING A T
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FUTURE RESEARCH Every field in a DI
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3. "Hie fiundanuintal noA.Qkbonhood
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7. Tkn dua£ $fw.pk aA.ou.nd ueA^ex
Page 438 and 439:
INTRODUCTION GDIS VS. CUE: A LOOK A
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3. Douglas County Auto Title/Regist
Page 442 and 443:
3. The lack of broad based local go
Page 444 and 445:
that intergovernmental cooperation
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2. Inquiry by address - The fields
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cities throughout the United States
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REQUEST 1 DIME FILE RECORD U P D A
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REQUEST 3 DIME RES P 0 N S E S C R
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REQUEST 7 DIME RE S P 0 N S E S C R
Page 456 and 457:
INTRODUCTION AN INTERACTIVE GBF CRE
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equiring a GBF in a slightly differ
Page 461 and 462:
Seminar on Urban Information System
Page 463 and 464:
1/ICT0R PA I/IS oi the. Ci£y ojj A
Page 465 and 466:
INTRODUCTION ANALYTICAL MAPS FOR SC
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coordinates (referred to as rectili
Page 469 and 470:
The map of Figure 3 shows the bound
Page 471 and 472:
Figure 4 BLACK STUDENT ASSIGNMENTS:
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Maps based on student-allocation mo
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housing development per every stude
Page 477 and 478:
COMPUTER MAPPING AND ITS IMPACT ON
Page 479 and 480:
the shades. Digit 5 is a coded numb
Page 481 and 482:
The most frequent use of computer m
Page 483 and 484:
\ \ / ,.L5_i / /hjgj-->-»• VJ1 .
Page 485 and 486:
B g TM BT BSTH TER M B8TH TfH M SBT
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GRAFPAC Subroutines ADVANG - ADVANG
Page 489 and 490:
TABDVG - TABDVG initializes that pa
Page 491 and 492:
several decades increasing amounts
Page 493 and 494:
Automated Evolution of the Time Fac
Page 495 and 496:
It merits noting that operators and
Page 497 and 498:
So as to be consistent with the pre
Page 499 and 500:
INTRODUCTION GEOLOGICAL INFORMATION
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or values (weights) to the presence
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factors are depicted in shades of g
Page 505 and 506:
Proper use of UNIMATCH, however, fr
Page 507 and 508:
INTRODUCTION THE CONGRUENCE BETWEEN
Page 509 and 510:
By 1968 SACS had been conceptually
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in an engineering precision. Inhere
Page 513 and 514:
Seminar on Data Structures Introduc
Page 515 and 516:
*cheme* oft aggregation present and
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(Clement, 197*0> etc., have all bee
Page 519 and 520:
A line of n points can be subdivide
Page 521 and 522:
LINE GENERALIZATION The theory of t
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shortened to close to half by const
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DOUBLE LINE AND OTHER LINE SYMBOLS
Page 527 and 528:
INTRODUCTION APPLICATIONS OF LATTIC
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The computation of intersections is
Page 531 and 532:
CARTOGRAPHIC DATA BASE DESCRIPTION
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Cartographic data for the United St
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P/iopo-i ecf D M S Output Decimal S
Page 537 and 538:
BASE CATEGORY IV - TERRAIN SURFACE
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objectives of a specific data base.
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COORDINATE POINT DIRECTORY Coord. 4
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7\ POINTS Ident. (Name) CHAIN GROUP
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Some of the attributes of a topolog
Page 547 and 548:
Seminar on Automation in Cartograph
Page 549 and 550:
infrastructure, and human resources
Page 551 and 552:
negative and repel each other. This
Page 553 and 554:
THE GRIMAS SYSTEM APPLICATION softw
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GRIMAS SYSTEM FLOW: PLOT -CONTROL/
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All object classes have locational
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PROJECT BAR CHART TR M E S T E R RR
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To get a flexible system it was dec
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E. - Topography 80 Man-Hours F. - G
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The goal described above is further
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1. With respect to the dimensional
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561 BRRSIL FUNDRCRO I.B.G.E. DIRETO
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SPECIAL AND THEMATIC MAP SERIES The
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As to geodetics and topography, the
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THE AIR FORCE MINISTRY: ELECTRONICS
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URBAN AND RURAL, TECHNICAL AND FISC
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APPENDIX I AUTO-CARTO II STAFF AND
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Robert T. Aangeenbrug Department of
Page 584 and 585:
H. G. Barnum University of Vermont
Page 586 and 587:
Kurt E. Brassel Assistant Professor
Page 588 and 589:
James M. Collom Cartographer NOAA N
Page 590 and 591:
James F. Dixon Assistant Director G
Page 592 and 593:
John B. Fieser Program Specialist U
Page 594 and 595:
Terry W. Gossard U.S.D.A. Forest Se
Page 596 and 597:
Daniel E. Holdgreve 507 Kibler Circ
Page 598 and 599:
Olaf Kays Asst. Program Mgr.-RALI U
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Gary Lewis Graphics Coordinator Tet
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S. E. Masry Assoc. Professor Univer
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David C. Mowbray Head, Map Informat
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Thomas K, Peucker Assoc. Prof. , Si
Page 608 and 609:
William R. Roseman Vice President I
Page 610 and 611:
Lee Henry Slorp Miami University, D
Page 612 and 613:
G. L. Thornton Research and Develop
Page 614 and 615:
Dean P. Westmeyer Cartographic Edit
Page 616 and 617:
APPENDIX III AUTHOR AND TITLE INDEX
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Contemporary Statistical Map6: Evid
Page 620 and 621:
Martell, Alberto Torfer (Automation
Page 622:
Van Driel, Nicholas (Ge.ological In
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