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DEPTH SELECTION IN NAUTICAL CHARTS PRODUCTION Cartographic generalization is an collection of assemblies, which are used to transform the content of the cartographic originals to the content of derived cartographic presentation in a way that with needed reading possibility, both perceptually coresponds between each other and with reality. Cartography presents an very old scientific discipline and cartographic generalization is obviously that old as oldest cartographic presentation. In despite of mentioned facts, written notes on cartographic generalization are known only recently. Well known cartographic expert Mr. M. Eckert (1921) first noticed that essential of the generalization consists of selection and subcommunion, with a purpose of chart as its main factor, as well as a fact that , in order to reflect specific lines of the cartographic appearances,it is neccesary to posses an more deeper knowledge. Eckert also considered cartographic generalization as an subjective process dependable only on cartographers skill. Due to various factors an objective approach is necessary in cartographic generalization procedures. Subjective presentation is more specific for an art work. Cartographic presentation, as much as possible, must be objective both for an usable valuation of the chart and for operational use of the chart. Requirement for the objective approach in generalization process expressively appears if subject chart is devided in a sheets on which a few cartographic experts are involved ( chart composing ). An first scientific basement of the cartographic generalization goes to Imhof 1937. According to his statement, a larger scale charts are more objective than small scale charts. It is an overall goal of the cartographic generalization procedures and methods to design an new approach of the cartographic presentation which will allow reciprocal compatible mind flow of the users, that should follow to proper conception of the cartographic area. Word generalization is of a latin origin ( generalis ) meaning work of communion, subordination of something that is individual to something that is general, transrerring everything to one concept. Chart scale is intruding generalization as one tehnical necessity, and cartographic generalization is a fundamental principle of the cartographic originals processing. Cartographic generalization is not an steady (equally spreaded) content reduction that should lead out to mechanical reduction. Application of the steadiness principle in cartographic generalization would be a great mistake that should degrade (equally spreaded) generalizaton to a simple mechanical work, with a bad charts as a result. Principle of the objective presentation also requires detailed knowledge of the thematic processing by cartography. Generalization of the reality requires an differentiality from essential to unessential. One of the factors that devide cartographic from artistic presentation, considering generalization as scientific work of creation, is an objectivity of the presentation.

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Objectivity in full of the presentation should be acheived only by the carographic generalization concrete lawfulness placing. During first technical Conference ICA, 1962. in Frankfurt, Knorr stated an overall summary on cartographic generalization : As for the generalization, hereby I found that this is an creative and productive activity. Not subjective to any legalities. In his capital work Kartographische Generalisierung Töpfer, based on intensive research, very precisely defined certain legalities. But not even using these legalities, generalization process can not be automatic. CARTOGRAPHIC GENERALIZATION MATHEMATIC MODELLING PROBLEM IN

GENERAL Multiple need for the automatic processing of the cartographic original exists. Automatic processing of the cartographic originals should shorter time necessary for chart production. With that, charts should be cheaper and more available. Also, time necessary to charts upgrading should be shorter. Objectivity and quality of the cartographic presentation should not therefore depend only on knowledge, experience and conscience of the individual. Criterions would be exactly equal for any individual page of which chart or chart serial consists. Essential of the problem is impossibility to define mathematical model of the cartographic generalization. Cartographic generalization goes to empirical science category. Beside knowledge of geodesy, chartography, geography, geomorphology and subject problem (thematic and purpose), practical work experience is necessary. It is quite obvious that chart information quantity is going less proportionally to geometrical reducing of the deducing chart. Such a principle application A. Penck demonstrated back to the end of 19. century. He compared coastline lenght line of the Istria using charts with different scale, founding that lenght of the coastline together with associated scale are connected with function squared. In a sea nautical chart production, the most important attention goes to the generalization of the sea area content and its presentation. Basic cartographic originals for sea presentation on the sea nautical charts are hydrographic survey originals (hydrographic originals). Most regularly they are in a larger scale then those of the sea chart scale, with necessity to reduce it to a chart scale that is under construction. Basic rule to hydrographic originals content generalization is simple : it is necessary to present those depths to the chart user (navigator) in a way that these information should help solving navigational tasks and that user can safely navigate with his vessel. Nevertheless, the content generalization over certain sea area is an very difficult process.

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Contents generalization and deep sea with unspreaded relief bottom presentation is much more easy (Figure 1).

Figure 1a : Part of the chart with scale 1 : 100 000 with unspreaded relief of the sea

bottom

Figure 1b. : Part of the chart with scale 1 : 100 000 with unspreaded relief of the sea

bottom

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Density and depth arrangement should create an impression of rather uniformed survey, which provide safety and confidence to chart user. DEPTH DENSITY DETERMINATION OVER UNSPREADED RELIEF SEA BOTTOM

AREA From the collection of all the depths registered within hydrographic survey, it is necessary to select depths representing surveyed area. Depths selection is necessery due to following three reasons: 1. Physically it is not possible to present on the chart all measured depths (geometrical condition), 2. Presentation of all depths which could be geometrically positioned on the chart, should make chart illegible and practically unusable (condition of illegibility) and 3. Generalization is necessary not just because of technical circumstances (lack of pace),

characteristics and to general appearances of global interests ( scientific, the most but also due to item essence, to passover from individual lines to general important condition stated by chartography as science ).

RESULTS BY COUNTING RESULTS BY CALCULATION

1:250 000 1:300 000 1:250 000 1:300 000

8 8 11 9

11 13 12 9

23 21 24 18

Table 1

Tablee 1 presents resulting number of depths given by calculation on certain aquatorium by Töpfer procedure, as well as an real number of depths from same area on existing sea charts published by Croatian Hydrographic Institute in Split. Larger number of measurements are used to calculate medium distance between depths. In total 130 distances were measured.

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To calculate middle (medium) distance we are using simple arithmetic. It follows that on the sea nautical chart with scale 1: 100 000 an average distance between depths is 22,52 mm over area with unspreaded relief of the sea bottom. Generalization, in this case selection of depths, is an process of smaller number of depths extraction, out of a greater collection with an overall adequate sea bottom depths presentation. Density and arrangement of the depths must be so selected to provide psychological safety and confidence in using chart. Even this paper consider reletively deeper part of aquatorium with monotonous relief of sea bottom, depth density should not be too small so chart user should not feel any unsafety and distrust. Depths arrangement should not be patterned : efforts should be focused with depths not to follow contour of the coastline or hydrographic survey lines. Arrangement and density of depths should be selected in a way not to overload chart with other elements of chart content, making it illegible. Depths density is directly proportional to navigational weight of aquatorium.

During depths selection attention should be considered to depths with smallest values. Based on selected depths it is possible to reconstruct sea bottom configuration in global, which must corespond to physical reality. During depth selection it is necessary to understand position of the user in order to make decisions from that aspect.

Before depth selection start it is necessary to study in details a content of the hydrographic originals which will be used in sea nautical chart creation. In order to fulfill given task of hydrographic originals content generalization (depths), beside knowledge of chartography, it is necessary to have certain knowledge about the sea, seamanship, navigation and geomorphology, as well as to have some experience in solving such a tasks. Such knowledge completition is certainly an prerequisite for successful construction of the sea nautical chart. Depths on the chart must also support other characteristics .

SEA DEPTH SELECTION ALGORITHM ON AREA WITH UNSPREADED RELIEF OF THE SEA BOTTOM

Given value of the medium (middle) distance between depths could be interpreted as follows : average distance of 22 mm between depths can be obtained by depths placing into the peaks of the square network of 19 mm ( Figure 2). Distance between depths using diagonal of the square is about 27 mm.

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Figure 2

Sum of all the distances is 180 mm, middle distance is 180 / 3 = 23 mm.

This middle distance is in accordance with calculated middle distance between depths (22,52 mm).

However, such arrangement of depths is not possible in practice and would be not in compliance with mentioned roules on arrangement of the sea depths. Same density and depths arrangement could be given by placing depths in the center of the square of mentioned network (Figure 3).

Figure 3

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Following this an conclusion is that within area of unspreaded relief of the sea bottom, one of each depth will be on every 500 mm x 500 mm, on the chart with scale

1 : 100 000. Depths density interpreted on such a way provides possibility that depths should not be fixly pointed to a certain place (top or center of the square). Such conclusion is in accordance with real arrangements of the sea depths, and could be prooved also visually.

An network with page of 20 mm should be constructed (round off middle distance between depths Dsr=22,52 mm) using transparent leaf. Then, leaf should be lay down on the chart on area of the unspreaded relief of the sea bottom, here on the area for which density were calculated. Network should be turned off and translated over area until each of the depths is placed in each square. Figure 4 is an clear proof illustrating that supposition is correct.

Figure 4

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This fact can be used in a reverse process: to cover hydrographic original with square network and by some rule to select one of each depth in every square (Figure 5).

Figure 5

It is necessary to select one depth, in each square, with minimal value. To select minimum depth, in each square by computer is an problem that can be solved by software. However, result of selected depths does not satisfy so far mentioned criterion, as shown on Figure 6.

Namely, with this selection, appearances of condensing density and empty spaces were shown, which is not in compliances with required criterion that in any square one of each depth with minimal value should be presented. It is certainly necessary to involve one more parameter, which should assure that depths in between each other will not be to close, that is, not closer then one up front dated distance. Logically, given parameter is to be connected with middle smallest distance between depths. By measurements, smallest distance is 12 mm, but maximum distance 35 mm. Middle distance by calculation is 22.

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Figure 6 Arithmetic middle of all measured distances between depths that are less then 22 mm is 17,4 mm, round number 17 mm. This parameter (D min) is limiting a minimal distance between depths to 17 mm. Maximal distance (Dmax) is to be defined by square diagonal in the network. Around each depth in a square it is to write an circle with radius r = Dmin = 17 mm. All depths that are falling inside of the circle with center in other depth, should be rejected. Figure 7 presents circles with centers in a decimal point of depth. All depths that are falling within circles of other depths are marked and should be rejected. Depths complying both criterions should rest: with minimum values in square, as well as that are, comparing to other depths, far away from calculated minimum distance (Dmin).

Applying both criterions a small amount of depths rests, that is, many network squares are now without any depth (Figure 8). These squares should be filled in with depths that are satisfying first condition and condition with minimal distance to depths already complying existing criterions. First condition should read as follows : to find next smallest value depth in a square with no depth at all. This geometrical construction is shawn on Figure 9. Around depths, smallest in value, circles are presented. From the depths that are out of this circles, it is to select a smallest one. In such a way, all squares should be filled in with depths. It is not possible

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to present all measured depths, so some of the squares might apparently be left without depth.

Figure 7

Figure 8

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Figure 9

It is possible to define algorithm as follows :

1. To cover hydrographic original with network of squares, 2. To find in each square a depth with smallest value, 3. To eliminate all depths which are mutually closer to minimal distance (Dmin), 4. From remaining depths to find depths with next smallest values and to join them to

adequate empty squares and 5. To repeat procedure from item 3. and 4. of the algorithm until each square contain

one depth. From the flow diagram we can see how program for automatic selection of depths works, using hydrographic originals for unspreaded relief of the sea bottom.

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START

DATA FILE NAME DEFININGIME_ORG.LINIME_ORG.TOC

DATA FILE OPENINGIME_ORG.LIN

CIRCLE SIZE DEFININGINTERDICTET FOR DEPTH

DMIN=0,7DGRID

SUBPROGRAM GRID CALL FOR COUNTING NUMBER OF ELEMENTS NETWORK NX, NY

K COLUMN INITIALIZATION OF

THE MATRIX MATDUB (I, J, K)

1

GENORG FLOW DIAGRAM PROGRAM

LOADING BY KEYBOARD1. NAME ORNUMBER OF FARE SHETS IME_ORG2.CHART SCALE MJE3. NETWORK ELEMENT SIZE DGRID4. ITERATION NUMBER NIT

LOADINGYMIN, XMIN

YMAX, XMAX

13

1

OPEN DATA BASEIME_ORG.TOC

WITH SEQUENTIAL APPPROACH

NR =1

READ IME_ORG.TOC

I=(YT-YMIN)/DGRID+1J=(XT-XMIN)/DGRID+1

NR=NR+1

MATDUB(I,J,K)=0

MATDUB(I,J,K)=0

3

YES

NO

K=1,5

2

14

3

CLOSE DATA BASEIME_ORG.TOC

I=1, NX

J=1, NY

6

YES

K1=0

YES

DATA BAZE ENDIME_ORG.TOC

OPEN DATA BASE IME_ORG.TOC

WITH DIRECT APPROACH

K=1,50

MATDUB(I, J, K)>0

2

5

4

NO

7NO

15

6

NT=MATDUB (I, J, K)

RB(K)=NT

RA(K))=ZT

K1=K1+1

MATDUB (I, J, K)=K1

MATDUB (I, J, K)>1

9

5 7

MATDUB (I, J, K)=1

2625

YES

NO

YES

NO

READ BATCH NTYT, XT, ZT

CONTINUE

16

K=1,K1

CONTINUE

NK=1, NIT

I=1, NX

J=1, NY

ISTAT=GENDUB (I, J, K)

ISTAT=1

MATDUB (I, J, K)=NT

9

25

26

4

27

27

29

MATDUB (I, J, K)=RB (K)

CALL SUBPROGRAMME

HEAP FOR SORTING

28 NO YES

17

11

Y0=GENDUB (I, J, 1)X0=GENDUB (I, J,2)

I1=I-1

M=1, 3

I1=0

J1=J-1

N=1, 3

J1=0

I1=JAND

J1=J

12

15

17

16

16

YES

NO

NO

NO

YES

YES

18

18

J1=J1+115

J1>NY

CONTINUE

I1=J1+1

I1>NX

CONTINUE

I1=1, NX

J1=1, NY

ISTAT=GENDUB (I1, J1, 4)

20

30

12

16

13

NO

NO

YES

YES

19

20

ISTAT=1

GENDUB (I1, J1, 4)=2GENDUB (I1, J1, 4)=NK

CONTINUE30

SELECTED DEPTHS CHARTING 1. ALL ITERATIONS 2. UP TO CERTAIN ITERATION 3. CERTAIN ITERATION ONLY

NIT=0

ONLY MINIMUM DEPTHS CHARTING(ZERO ITERATION)

DRAWNETWORK

CALL SUBPROGRAME GRID FOR NETWORK DRAWING

END

NO

YES

YES

YES

NO

NO

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C O N C L U S I O N

Based on geometrical interpretation of described algorithm it is quite possible to conclude that its selected depths, in a quantitive and a qualitive sences, as well as with the arrangement, are mostly satisfying established criterions. Computer software produced on a base of a flow diagram is flexible enough to provide selection of the chart scale, square page size and number of iteration. Selected depths density depend on square page size. Square page size is changable until satisfactory result is reached. Based on experiences so far , square page size of 25 mm is suitable for chart scale 1 : 100 000. With a same established criterions, software will select always a same depths. Software has automatical ending when each square selects one depth each. B I O G R A P H Y NAME AND SURNAME: Radovan Solariã NATIONALITY: Croat HOME ADDRESS: 21 000 Split, Njegoeva 3 DATE AND BIRTH PLACE: 10. January, 1946. WORKING POSITION : Hydrographic Institute of the Republic of Croatia, Deputy Director EDUCATION AND CERTIFICATION: Zagreb University, Faculty of Geodesy , Zagreb Post graduate study, Faculty of Geodesy, Master of Science, Technical science, Geodesy, Cartography English language, University ÐURO SALAJ, Split EMPLOYMENTS and DUTIES: - Hydrographic Institute 1973 1980: Marine nautical chart redactor - Hydrographic Institute 1980 1986: Marine nautical chart redactor in chief - Hydrographic Institute 1986 1990: Cartographic department head - Hydrographic Institute 1988 1990: Cartographic and Reproduction department head - Hydrographic Institute 1990 1992: Deputy Director - Hydrographic Institute 1992 1998: Assistent Director - Faculty of Geodesy University in Zagreb: Lecturer marine geodesy, marine cartography, - MBSHC (Mediteranean and Black Sea Hydrographic Conference), Conference organizer in

Split, Croatia MEMBERSHIP - Member Chart Standardisation Committee, International Hydrographic Organisation, Monaco, 1998 2003, - Member Chart Standardisationand Paper Chart Working Group, International

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Hydrographic Organisation, Monaco, 2003 tkill now - Member of Geodetic Society of Croatia - Member and Founder: Cartographic Society of Croatia Beside above mentioned items, author and coauthor of a few tens of special papers covering marine cartography and hydrography. Coauthor of the first Law act of Parliament on hydrographic activity, 1998. Project manager for various marine cartographic activities. Active creator and developer of the marine cartographic activities in Croatia since 1985. till now. Married, father of two children. Hobby : Mechanics, Do it by yourself, Photography, Sailing.

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