3 Mapping of Spatial Data

(1)

3.1 Properties of Maps

3.2 Signatures, Text, Color

3.3 Geometric Generalization

3.4 Label and Symbol Placement

3.5 Summary

3 Mapping of Spatial Data

(2)

• Mapping (visualization) of spatial objects by

transforming them into representation objects (map objects)

• Map

– Generalized model in a reduced scale for representing selected spatial information

3 Mapping of Spatial Data

http://www.xerokampos.eu/

(3)

• Topographic map

– Geometrically and positionally

accurate

representation of landscape objects

drawn to scale

(topography, water network,

land use,

transportation routes)

3 Mapping of Spatial Data

http://www.wiedenbruegge.net/

(4)

• Thematic map

– Emphasis is on subject- specific

information (geological map,

vegetation map, biotope

map)

3 Mapping of Spatial Data

http://www.lbeg.niedersachsen.de/

(5)

• Challenges

– Projection of the 3D surface on two dimensions (paper, film, screen)

– Selection of the spatial objects and their attributes to be

displayed

– Generalization of geometric and

thematic properties (simplify, omit depending on scale)

– Exaggeration and displacement (e.g. river valley with roads and railway lines)

3 Mapping of Spatial Data

http://maps.google.de/

(6)

• Graticule

– Mapping the earth (sphere, ellipsoid) to a plane

– Two tasks

• Conversion of geographic coordinates (longitude

and latitude) to cartesian coordinates (x, y; easting, northing)

• Scaling of the map

3.1 Properties of Maps

www.klett.de

(7)

• Projections on

– Cone

– Plane

(azimuthal projection)

– Cylinder

3.1 Properties of Maps

[HGM02]

(8)

• Desired properties

– Length preservation: with plane maps only limitedly attainable (in certain directions or at certain points) – Equivalent (equal area): preserve area measurements

shape, angle, and scale may be

strongly distorted

3.1 Properties of Maps

http://www.informatik.uni-leipzig.de/~sosna/

(9)

– Conformal:

important for

navigation

in shipping and air

transport

3.1 Properties of Maps

http://flightnavigation.de/

(10)

• Areas and angles can not be preserved at the same time, therefore

– Compromise projections minimize overall distortion

3.1 Properties of Maps

http://support2.dundas.com/OnlineDocumentation/ WebMap2005/MapProjections.html

(11)

• The Gauss-Krüger coordinate system

– Used in Germany and Austria

– Cartesian coordinate system to represent small areas – Divides the surface of the earth into zones

• Each 3° of longitude in width

• The zones are projected onto a cylinder with the earths diameter

3.1 Properties of Maps

(12)

– Origin of the coordinate system:

intersection point of the central meridian and the equator

– X coordinate from the

origin positive towards east,

y coordinate from the origin positive towards north

– X and y values given in meters

3.1 Properties of Maps

http://www.gerhard-tropp.de/Troppo/gauss_krueger.html www.geogr.uni-jena.de/.../GEO142_3b.ppt

(13)

– To avoid negative x coordinates the central meridian is set to 500,000 m (false easting)

– Each projection zone (3°, 6°, ..., 177°) is identified by a number (1, 2, …, 59)

– This number is placed prior to the x value

– Example: the Gauss-Krüger coordinates

x: 3,567,780.339 and y: 5,929,989.731 refer to the following location

x: 67,780.339 m East of the 9° meridian y: 5,929,989.731 m North of the equator

3.1 Properties of Maps

(14)

• Transforming geographic coordinates into Gauss-Krüger coordinates

– Given geographic coordinates lon, lat (e.g. from GPS, reference ellipsoid: World Geodetic

System 1984 (WGS 84))

– Transformation into Cartesian coordinates x, y, z

3.1 Properties of Maps

https://www.univie.ac.at/

(15)

– 7 parameter Helmert transformation into Cartesian coordinates x’, y’, z’ referring to the Bessel ellipsoid

– Re-transformation into geographic coordinates – Transformation

into Gauss-Krüger coordinates

3.1 Properties of Maps

X Y Z

WGS84 gc 10.529 52.273 ---

cc 3845123.169 714709.117 5021445.455 Bessel cc 3844489.704 714681.311 5020993.750 gc 10.531 52.274 ---

Gauss-Krüger 3604481.733 5794379.689 ---

(16)

• The UTM coordinate system

– Similar to the Gauss-Krüger system

– Divides the surface of the earth into 6° zones

– Covers the area between 84° North and 80° South

3.1 Properties of Maps

https://www.e-education.psu.edu/

http://earth-info.nga.mil/

(17)

– The diameter of the transverse cylinder is slightly smaller than the

diameter of the Earth

 secant projection with two lines of true scale (about 180 km on each side of the central

meridian)

3.1 Properties of Maps

https://www.e-education.psu.edu/

(18)

• Common mapping errors

3.1 Properties of Maps

interchanging of x- and y-

coordinates

no transformation into Cartesian coordinates

ignoring the negative direction of the canvas`

y-axis

(19)

• Structure of maps

– Body of the map

presentation of the actual map

– Map margin contains name, map, scale,

legend

– Map frame borders map, contains numbering of the

respective coordinate system

3.1 Properties of Maps

http://www.apat.gov.it/

(20)

• Graphical design elements of maps are

– Symbols

(signatures) for

• Points

• Lines

• Areas

– Text

3.2 Signatures, Text, Color

http://lehrer.schule.at/Ecole/

(21)

• The use of point, line, area symbols depends on

– Spatial scale of a map – Purpose of the map – Convention

• Point signatures

are (composite) symbols for the

representation of spatial objects with point geometry

3.2 Signatures, Text, Color

[HGM02]

(22)

• Line signatures represent objects

with line geometry

• Area signatures

represent objects with area geometry

• Texts are needed in various fonts for the labeling of maps

3.2 Signatures, Text, Color

[HGM02]

(23)

• Color

– Important design element – Additive mixture

• Most relevant for displaying maps on screen

• Common color space: RGB

– Subtractive mixture

• Most relevant for printing maps

• Common color space: CMYK

Spatial Databases and GIS – Karl Neumann, Sarah Tauscher– Ifis – TU Braunschweig 236

3.2 Signatures, Text, Color

http://www.horrorseek.com/http://academic.scranton.edu/

(24)

– There exist

various color tables

Example:

color table for the official

German real estate map 1:1000

3.2 Signatures, Text, Color

(25)

• For maps and map series the signatures on-hand, fonts, and colors are specified in signature

catalogs and color tables

– Example:

topographical map 1:25.000 (TK25)

3.2 Signatures, Text, Color

http://www.lgn.niedersachsen.de/

(26)

• Signature catalog "SK25" describes how the TK25 is derived from the "digital landscape model" (digitales

Landschaftsmodell 1:25.000, DLM25)

• The catalog consists of derivation rules and signatures (about

300 forms)

• Some derivation

rules:

3.2 Signatures, Text, Color

(27)

• Some signatures:

3.2 Signatures, Text, Color

(28)

– Example:

real estate map 1:1000

• The ALKIS project (official property cadastre information system, Amtliches Liegenschaftskataster Informationssystem) specifies a signature library and derivation rules

• Approximately 670 signatures

• Approximately 850 derivation rules

3.2 Signatures, Text, Color

(29)

• A signature specification:

3.2 Signatures, Text, Color

(30)

• Section of a real estate map

3.2 Signatures, Text, Color

(31)

• The direct geometric derivation (coordinate transformation) of map objects from spatial

objects works only with large-scale maps (e.g. real estate

map)

• For small-scale maps there are

too many details

3.3 Geometric Generalization

http://www.geobasis-bb.de/GeoPortal1/

(32)

• Generalization simplifies map content for the

preservation of readability and comprehensibility

• Replacement of scale preserving mappings through simplified mappings, symbols, and signatures

• Select and summarize information

• Maintain important objects, leave out unimportant ones

3.3 Geometric Generalization

http://www.kartographie.info/

(33)

• Eight elementary operations

– To simplify – To enlarge – To displace – To merge

3.3 Geometric Generalization

(34)

– To select

– To symbolize

– To typify

– To classify

3.3 Geometric Generalization

www.ikg.uni-hannover.de

(35)

3.3 Geometric Generalization

Base map 1:5000 Topographical map 1:25.000

[HGM02] [HGM02]

(36)

3.3 Geometric Generalization

Topographical map 1:25.000 Topographical map 1:50.000

[HGM02] [HGM02]

(37)

3.3 Geometric Generalization

Topographical map 1:50.000 Topographical map 1:100.000

[HGM02] [HGM02]

(38)

• Typical operations for generalization (alternative view)

3.3 Geometric Generalization

[SX08]

(39)

• Smoothing of polylines by means of a simple low-pass filter:

y(n) = 1/3(x(n)+x(n−1)+x(n−2))

3.3 Geometric Generalization

(40)

• Electronic filter that passes low-frequency signals but attenuates high-frequency signals

• Further common filter types

– High-pass – Band-pass

– Band elimination

3.3 Low-pass Filter

(41)

• Passive electronic realization

– Simple circuit consists of a resistor and a capacitor (RC filter, first order filter)

– More advanced circuit with additional inductor (RLC filter,

second order filter)

3.3 Low-pass Filter

http://upload.wikimedia.org/

http://ecee.colorado.edu/~mathys/

(42)

• Active electronic realization

– For example RC filter with an operational amplifier – An operational amplifier has a high input impedance

and a low output impedance

– Voltage gain is

determined by resistors R

₁

, R

₂

3.3 Low-pass Filter

http://www.electronics-tutorials.ws/

(43)

• Digital filters are realized as

– Finite impulse response filter (FIR)

• Impulse response lasts for n+1 samples and settles to zero

• Output is a weighted sum of the current and a finite

number of previous values of the input

– Infinite impulse response filter (IIR)

3.3 Low-pass Filter

(44)

• A moving average filter is a very simple FIR filter

– All n filter coefficients are set to

¹

/

_n

– Realization by means of

• Delay units

• Ring buffer

3.3 Low-pass Filter

http://blog.avangardo.com/wp-content/

(45)

• In offline mode (no real-time constraints) a moving average filter results in a simple loop

3.3 Low-pass Filter

x[1...n] input values y[1...n] output values

for (int i=2; i<n; i++) {

y[i] = 0.333*(x[i-1]+x[i]+x[i+1]);

};

y[1] = x[1];

y[n] = x[n];

(46)

• Adaptation of simple low-pass filter to two-dimensional geometry

x ′

_i

= ⅓(x

_i−1

+x

_i

+ x

_i+1

) y ′

_i

= ⅓(y

_i−1

+y

_i

+ y

_i+1

)

+ very efficiently to compute

− coordinates are changed, no reduction of points

3.3 Geometric Generalization

(47)

– Example (polyline with 41 points):

3.3 Geometric Generalization

(48)

– Example (polyline with 41 points):

3.3 Geometric Generalization

(49)

– Example (polyline with 41 points):

3.3 Geometric Generalization

(50)

– Example (polyline with 41 points):

3.3 Geometric Generalization

(51)

– Example (polyline with 41 points):

3.3 Geometric Generalization

(52)

• Simplification of polylines

– Reduction of points

– No change of coordinates

• Douglas/Peucker algorithm [DP73]

– Given: polyline L, threshold g

– g is very small: L remains unchanged g is very large: L is changed to

one single line

3.3 Geometric Generalization

(53)

• Douglas/Peucker algorithm

1. given: polyline L, threshold g

2. determine line between the start and end point of L,

3. determine the point of L that is furthest from the line segment

4. if distance > g then the point is

significant, repeat procedure for both sub-lines,

otherwise remove all the points between the start and end point of L

3.3 Geometric Generalization

(54)

Examples:

3.3 Geometric Generalization

(55)

3.3 Geometric Generalization

(56)

Properties:

+ simple base operation: distance measurement − runtime of naive implementation: O(n

²

)

+ runtime of optimized implementation: O(n log n), using two convex hulls

+ good results even with a strong reduction of points + extendable for polygons

− "outliers" are not eliminated

3.3 Geometric Generalization

(57)

• Polygon to polyline conversion

– Presentation of rivers and roads – Text placement within polygons

3.3 Geometric Generalization

http://www.almenrausch.at/bergtouren/ http://www.naturathlon2006.de/

(58)

• Schoppmeyer/Heisser procedure [SH95]

1. Given: elongate polygon P

2. Determine the longitudinal axis of P

3. Drop the perpendicular from all edge points to the longitudinal axis

4. Determine the intersection points of the extended perpendicular lines

5. Determine the centre of the resulting axes 6. Connect adjacent centers

7. Determine suitable start and end segment

3.3 Geometric Generalization

(59)

Example

1. Given: elongate polygon P

2. Determine the longitudinal axis of P

3.3 Geometric Generalization

(60)

3. Drop the perpendicular from all edge points to the longitudinal axis

4. Determine the intersection points of the extended perpendicular lines

3.3 Geometric Generalization

(61)

5. Determine the centre of the resulting axes

6. Connect adjacent centers

3.3 Geometric Generalization

(62)

7. Determine suitable start and end segment

Result

3.3 Geometric Generalization

(63)

Using the result for text placement

3.3 Geometric Generalization

(64)

Properties:

+ relatively short runtime

+ quite good results with "good-natured" polygons − determining the start and end segment

− procedure fails for

non-elongate polygons

3.3 Geometric Generalization

(65)

• Procedure for arbitrary polygons Petzold/Plümer [PP97]

1. given: Polygon P (set of points S) 2. determine Voronoi diagram of S

3. determine intersection points of the Voronoi edges and the polygon edges

4. consider resulting Voronoi skeleton:

5. choose an appropriate sequence of edges Voronoi diagram:

assigns each point P

_i

∈ S the points of the plane that are closer to P

_i

, than to each P

_j

∈ S, i≠j.

3.3 Geometric Generalization

(66)

Example

1. given: Polygon P (set of points S)

2. determine Voronoi diagram of S

3.3 Geometric Generalization

(67)

3. determine intersection points of the Voronoi edges and the polygon edges

4. consider resulting Voronoi skeleton:

5. choose an appropriate sequence of edges

3.3 Geometric Generalization

(68)

Properties:

− computation of the Voronoi diagram

− selection of an appropriate polyline from the skeleton

+ results for

more polygon classes

3.3 Geometric Generalization

(69)

Example (polygon with 2000 points):

3.3 Geometric Generalization

visualization tool: [Me11]

(70)

• Procedure with rasterization, thinning, and re-vectorization

1. given: polygon P (set of points S) 2. rasterization of P

3. topological thinning of P (building a skeleton)

4. line following and re-vectorization 5. determine the longest path

6. line simplification

3.3 Geometric Generalization

(71)

Example

1. given: polygon P (set of points S)

3.3 Geometric Generalization

(72)

2. rasterization of P

3.3 Geometric Generalization

visualization tool: [Bu11]

(73)

3. topological thinning of P

3.3 Geometric Generalization

(74)

4. line following and re-vectorization

3.3 Geometric Generalization

(75)

5. determine the longest path

3.3 Geometric Generalization

(76)

6. line simplification

3.3 Geometric Generalization

(77)

• Simplification of polygons

– Low-pass filter

• Coordinates are changed

• No reduction of points

• Shapes might be drastically changed

3.3 Geometric Generalization

(78)

– Douglas/Peucker (adapted)

• Decompose polygon P into two polylines L

₁

, L

₂

e.g. at the points P

_L1

, P

_L2

∈ P, with maximum distance between each other

• Simplify L

₁

and L

₂

• Recombine

resulting polylines at P

_L1

and P

_L2

3.3 Geometric Generalization

(79)

• Example

3.3 Geometric Generalization

(80)

• Example

3.3 Geometric Generalization

(81)

• Example

3.3 Geometric Generalization

(82)

• Further example

3.3 Geometric Generalization

(83)

3.3 Geometric Generalization

• Cartographically desired

generalization

• Results with

Douglas/Peucker (adapted)

(84)

• Douglas/Peucker reduces the number of polygon points

• Characteristic shapes are preserved (within certain limits)

• Good results with "natural" geometries (bogs, lakes, forests)

• Less satisfactory results with polygons with predominantly right angles (buildings), therefore modification to preserve right angles and long edges (e.g. [NSe01])

3.3 Geometric Generalization

(85)

• Geometric generalization (and displacement) of building sketches is a challenging task

• Convenient results achieved by programs

• E.g. CHANGE, PUSH, TYPIFY [Se07]

3.3 Geometric Generalization

(86)

• Placement of all texts (labels) in the same way

results with high probability in overlappings (poor readability)

• Therefore, it is necessary to move, scale down,

rotate, or omit texts

• In the general case this is

a NP-hard optimization problem

3.4 Label and Symbol Placement

http://www.laum.uni-hannover.de/ilr/lehre/Isv/

(87)

• Objectives of labeling

– Easily readable

– Unambiguity: each label must be easily identified with exactly one graphical feature

– Same facts are represented in the same way – Different facts are represented differently – Important facts are emphasized

– Important objects are never covered

– No uniform pattern

(avoidance of raster effect)

3.4 Label and Symbol Placement

(88)

• Text or label placement is divided into

– Point labeling

• Positions to the right are preferred to those on the left

• Labels above a point are preferred to those below

• E.g. cities with a horizontal label

– Line labeling

• Labels should be placed as straight as possible

• E.g. rivers with names

– Area labeling

• It must be clear what the total area is

• E.g. forest areas containing their names

3.4 Label and Symbol Placement

http://www.sprachkurs- sprachschule.com/

(89)

• For the three classes there are many specialized algorithms, based on

– Greedy algorithm

• Labels are placed in sequence

• Each position is chosen according to minimal overlapping

• Acceptable results only for very simple problems

• Very fast

3.4 Label and Symbol Placement

(90)

• Example : placement of

75 city names

priorities for a single

placement:

3.4 Label and Symbol Placement

(91)

• Example : placement of

75 city names

priorities for a single

placement:

3.4 Label and Symbol Placement

(92)

• Example : placement of

75 city names

priorities for a single

placement:

3.4 Label and Symbol Placement

(93)

• Example : placement of

75 city names

priorities for a single

placement:

3.4 Label and Symbol Placement

(94)

• Example : placement of

75 city names

priorities for a single

placement:

3.4 Label and Symbol Placement

(95)

• Example : placement of

75 city names

priorities for a single

placement:

3.4 Label and Symbol Placement

(96)

– Local optimization

• The labels are checked several times

• On each pass a single label is repositioned an tested

• The position is kept, if the overall result improves

• Stop, if a local optimum is reached

• Suitable only for maps

which relatively few labels

3.4 Label and Symbol Placement

(97)

– Simulated annealing

• Similar to local optimization, however yielding better results

• A placement of a label can be kept even though it (initially) downgrades the overall result

• At first "high temperature", thus leaving local optima is possible

• Later on ("low temperature") only small changes are possible

• Challenges: a good evaluation function, and a good annealing schedule

3.4 Label and Symbol Placement

(98)

• Name and inspiration from annealing in metallurgy:

controlled cooling of a material until it changes from liquid to solid

• Structure of the solid depends on „the cooling schedule“

– Fast cooling results in

• Unordered solid

• Internal stresses

– Slow cooling results in

• Ordered solid

• Low internal energy

• Macroscopic crystal lattice

3.4 Simulated Annealing

http://webuser.hs-furtwangen.de/~neutron/

(99)

• Example: SiO

₂

– Short range order: tetrahedron – Crystalline form: Cristobalit

– Without long range order: Silica glass

3.4 Simulated Annealing

Si

O

(100)

• Elements

– Initial solution (liquid)

– Modifications (vibrations of molecules)

– Cooling schedule: change

of temperature over time

• Initial temperature

• Freezing point

– Weighting function (internal energy)

3.4 Simulated Annealing

(101)

• Pseudocode:

– Usually the temperature is decreased after multiple changes

3.4 Simulated Annealing

T = initialTemperature;

currentSolution = InitialSolution;

while (T > freezingPoint){

newSolution = CHANGE(currentSolution);

if (ACCEPT){

currentSolution = newSolution;

}

ANNEAL(T);

}

(102)

– Decision if the new solution is accepted

• A better solution is always accepted

• Probability of accepting a worse solution depends on the temperature and its cost

• Boltzmann factor: e

^-E/k*T

; k = 1,3806504(24) · 10

⁻²³

3.4 Simulated Annealing

ACCEPT{

Δ = EVALUATE(newSolution)

– EVALUATE(currentSolution) if((Δ < 0) or RANDOM(0,1) < e

^-Δ/T

)){

return true;

} return false;

}

(103)

• Example: label placement

3.4 Simulated Annealing

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.2327

(104)

• Initial solution: random label placement

• Weighting function

– Number of covered (or deleted) labels

– Consideration of cartographic preferences by weighting of possible positions for point labels

• Modifications

– Move an arbitrary or covered label to a new position – If cartographic preferences are considered an

arbitrary label should be moved

3.4 Simulated Annealing

2 4 1 5 6

8 7 3

(105)

• Cooling schedule:

– Initial temperature ca 2,47 → the probability of

accepting that a solution whose cost are 1 higher is accepted is 2/3, i.e.: e

^-1/T

= 2/3

– T = 0,1 * T

– T is decreased as soon as more than 5*n new

solutions have been accepted (n is the number of objects)

– Search ends

• As soon as T has been decreased 50 times

• If none of 20*n new solutions in a row has been accepted

3.4 Simulated Annealing

(106)

• Result

3.4 Simulated Annealing

(107)

• Result

3.4 Simulated Annealing

(108)

• Result

3.4 Simulated Annealing

(109)

• Symbol placement (point signatures) is just as complex as text placement

• In the following two examples for special cases

– Displacement and placement of tree symbols in TK25-like

presentation graphics [NPW06]

– Placement of point signatures

in polygons of buildings for real estate maps [NKP08]

3.4 Label and Symbol Placement

(110)

• Displacement and placement of tree row symbols

– Roads as well as tree rows are given as polylines only – Placement of the tree symbols on the points of the

tree rows does not result in an equidistant pattern – The visualization of roads is much

wider than the actual street width

– The tree symbols are often hidden by the line signatures of the streets

– An alternative placement and a displacement is needed

3.4 Label and Symbol Placement

(111)

• One single road from the DLM25 (example, XML/GML encoding)

3.4 Label and Symbol Placement

<gml:name> Badstrasse </gml:name>

<gml:centerLineOf>

<gml:coord><gml:X>4437952.980</gml:X><gml:Y>5331812.550</gml:Y></gml:coord>

<gml:coord><gml:X>4437960.070</gml:X><gml:Y>5331818.450</gml:Y></gml:coord>

<gml:coord><gml:X>4437967.200</gml:X><gml:Y>5331825.410</gml:Y> </gml:coord>

</gml:centerLineOf>

<Zustand> in Betrieb </Zustand>

<Funktion> Strassenverkehr </Funktion>

<VerkehrsbedeutungInneroertlich> Anliegerverkehr </VerkehrsbedeutungInneroertlich>

<Widmung> Gemeindestrasse </Widmung>

</Attribute>

</Strasse>

</AtkisMember>

(112)

• A tree row from the DLM25

3.4 Label and Symbol Placement

<gml:centerLineOf>

<gml:coord><gml:X>3524258.170</gml:X><gml:Y>5800238.690</gml:Y>

</gml:coord>

...

</gml:coord>

</gml:centerLineOf>

<Vegetationsmerkmal> Laubholz </Vegetationsmerkmal>

</Attribute>

</Baumreihe>

</AtkisMember>

(113)

• Direct visualization

3.4 Label and Symbol Placement

(114)

• Simple displacement procedure

3.4 Label and Symbol Placement

for all t : treeRow do begin

if exists s : street (distance(t,s) ≤

minDistance(s.dedication)) then

for all p : t.coord do begin

r := refSegment(s,p);

move(p,r) end do

end if end do;

(115)

• Visualization with displacement

3.4 Label and Symbol Placement

(116)

• Placement procedure

3.4 Label and Symbol Placement

for all t : treeRow do begin

l := length(t.centerLineOf);

n := ⌊l/distanceConst⌋ + 1;

t’ : new treeRow;

for i=1 to n do begin

computePoint

(t’.coord[i],

t.centerLineOf, distanceConst) end do

end do;

(117)

• Visualization with displacement and placement

3.4 Label and Symbol Placement

(118)

• Placement of point signatures in polygons of buildings

– Derivation of the real estate map (1:1.000) from ALKIS inventory data extracts relatively straight forward

– No generalization and no displacement is needed – Representation of buildings, parcels, border points,

etc., with the given signature library and the derivation rules

– E.g. symbolisation of buildings as colored polygons with a boundary line and a typical point signature depending on the attribute building function

3.4 Label and Symbol Placement

(119)

• A building from an ALKIS inventory data extract

3.4 Label and Symbol Placement

<gml:featureMember>

<AX_Gebaeude gml:id="DEHHSERV00001FN1">

...

<gml:exterior><gml:Ring>

...

<gml:pos>3567807.047 5930017.550</gml:pos>

<gml:pos>3567810.850 5930024.755</gml:pos>

...

<gml:pos>3567807.047 5930017.550</gml:pos>

...

</gml:Ring></gml:exterior>

</gml:Polygon></position>

</AX_Gebaeude>

</gml:featureMember>

(120)

• For many point signatures which are related to buildings so-called presentation objects are

supplied in the inventory data, defining the

optimal position of the respective signature (given in "world coordinates")

3.4 Label and Symbol Placement

<gml:featureMember>

<AP_PPO gml:id="DEBWL00100000fAW">

<gml:Point><gml:pos>3540847.175 5805897.864</gml:pos></gml:Point>

</position>

</AP_PPO>

</gml:featureMember>

(121)

• But some buildings lack the presentation objects

• An obvious, easily determined position for the signature:

– Choose the center of the smallest axis parallel

rectangle, which encloses the polygon of the building – min(x

₁

, ..., x

_n

)+((max(x

₁

, ..., x

_n

)−min(x

₁

, ..., x

_n

))/2),

– min(y

₁

, ..., y

_n

)+((max(y

₁

, ..., y

_n

)−min(y

₁

, ..., y

_n

))/2)

3.4 Label and Symbol Placement

(122)

• Unfortunately, the results are not always satisfactory

• Therefore, heuristic procedure, based on

– Convexity

– (approximate) symmetry points – (approximate) symmetry axis – Various quality criteria

– Discrete increments

3.4 Label and Symbol Placement

(123)

3.4 Label and Symbol Placement

if polygon of building convex:

choose centroid

if signature frame fits completely in polygon of building:

place there

otherwise choose appropriate point with the smallest distance to

the centroid

else if symmetry point in polygon of building:

place there

otherwise further procedure with symmetry axes

⇒ generation of a new presentation object

with "optimal" positioning coordinates

centroid best symmetry point

best symmetry axis

finally chosen point

(124)

• The procedure is not suited for the placement of signatures for churches/chapels

– Besides the determination of an appropriate position – Also the signatures alignment to the shape of the

building’s polygon is needed

– An alignment to the north south axis is rarely optimal – Crosses for churches as parallel as possible to the

churches naves

– Crossbrace of cross should be placed in the transept

3.4 Label and Symbol Placement

(125)

• Heuristic procedure

– Determine a preferable large cross that just fits in the building’s polygon

– Proportions of the large cross and the church signature are the same

– If the large cross is found, place the signature just in the intersection point

• For this purpose first simplify the building’s polygon

3.4 Label and Symbol Placement

(126)

• In several rotation angles:

look for a preferable large, well placed cross

– Restriction of the potential

rotation angles and positioning points (e.g. consider minimum distance to boundaries of the

building’s polygon)

– Evaluate all appropriate crosses within a rotation angle

– Evaluate all the best crosses (e.g. lengths of the crosses, alignments)

3.4 Label and Symbol Placement

(127)

• Placement of the signature in the best cross of all rotation angles

⇒ Generation of a new presentation object with

"optimal" positioning coordinates and

"optimal" rotation angle

3.4 Label and Symbol Placement

(128)

• Both methods applied to inventory data extracts

3.4 Label and Symbol Placement

(129)

• Mapping of spatial data

– Topographic map – Thematic map

• Properties of maps

– Graticule – Projections

– Gauß-Krüger coordinate system

– Body of map, map frame, map margin

3.5 Summary

(130)

• Signatures, text, color

– Point signatures – Line signatures – Area signatures – Derivation rules

– TK25, real estate map

• Geometric generalization

– Smoothing of polylines – Simplification of polylines

3.5 Summary

(131)

– Douglas/Peucker algorithm

– Polygon to polyline conversion – Simplification of polygons

– Geometric generalization of building’s ground plans

• Text and symbol placement

– Methods for text placement simulated annealing

– Displacement and placement of symbols for tree rows – Placement of point signatures in building’s polygons

3.5 Summary

2 4 1 5 6

8 7 3

(132)

3.5 Summary

GIS

^graticule

map

text

signatures

color

collect manage

analyse

display

generalization

area labelling simplifying

lines polygon

→ line

design elements

placement

topographic

thematic

building signatures

tree rows as optimization problem