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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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3
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
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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
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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
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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
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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
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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
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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
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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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