Design of Spatial Information Systems

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DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF
JOENSUU JOENSUU, FINLAND

• Design of Spatial Information Systems
• Lecture 5
• Models of Spatial Data
• Alexander Kolesnikov

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Geographical objects
A geographic object has three components 1)
Identity (to distinguish an object from others)
2) A description, or descriptive attributes
(name, population, other semantic
information) 3) A spatial components, or spatial
object, or spatial extent a) geometry
(location, shape, and so on) b) topology
(spatial relationships, adjacency, and so on )
The entire set (Identity, Description, Spatial
object) constitutes a geographical object, also
called an entity or feature.
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Example of geographical objects

• Vector map of planar subdivision

http//cs.joensuu.fi/koles/svf/
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Entity-based model Types of spatial objects

• Zero-dimensional (0-D) objects or points
• Shape is not considered as useful, or the area
  is small with respect
• to the embedding space size.
• One-dimensional (1-D) objects or polylines
• Commonly used for representing networks
  (roads, hydrography,
• elevation lines, )
• Two-dimensional (2-D) objects or polygons and
  regions
• Entities with large areas (lakes, fields,
  forest stands, ...).
• Scale of interest
• Airport can be viewed as a point (on a map of
  air links)
• or polygons (inner organization of the airport)
• Road can be viewed as polyline (on a
  communication scheme)
• or polygons (detailed plan of the road).

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One-dimensional (1-D) objects Polylines

• A polyline is defined as set of line segments or
  edges, such that each
• segment endpoint (called vertex) is shared by
  exactly two segments,
• except for two endpoints (called extreme points),
  which belongs to
• only one segment.
• A polyline is closed if the two extreme points
  are identical,
• otherwise the polyline is open.

.
vertex
extreme point
open
Open polyline
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One-dimensional (1-D) objects Polylines

• A simple polyline is such that no pairs of
  nonconsecutive edges
• intersect at any place.
• A polyline is monotone with respect to a line L
  if every line L
• orthogonal to L meets the polyline at one point
  at most.

L
L
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Examples of polylines
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Two-dimensional (2-D) objects Polygons
2-D objects or surfacic objects are mostly used
for representing entities with large areas, such
a parcels, forest stands, fields, etc. A polygon
is a region of of the plane bounded by a closed
polyline, called its boundary
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Two-dimensional (2-D) objects Polygons
A polygon is simple if its boundary is a simple
polyline.
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Two-dimensional (2-D) objects Polygons
A convex polygon P is such that for any pair of
points A and B in P the segment AB is fully
included in P.
A
A
B
B
Convex polygon
Non-convex polygon
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Two-dimensional (2-D) objects Polygons
A monotone polygon is a simple polygon such that
its boundary P can be split into exactly two
monotone polylines MC1 and MC2. The monotonicity
is usually expressed with respect to the axes.
MC1

MC2

Non-monotone polygon
Monotone polygon
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Polygons
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Topological properties of polygons
Adjacent Disjoint Intersecting
More about it later ..
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Linear of non-linear description

• The description of linear and surfacic objects
  is based on line segments.
• We use only linear approximation of entities.
• Some entities could be more precisely
  represented with higher-order
• polynomials in x and y, circular and elliptic
  arcs, splines, etc.

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Example of non-linear approximation

• Some entities could be more precisely
  represented with higher-order
• polynomials in x and y, circular and elliptic
  arcs, splines, etc.
• Example Oracle Spatial line segments
  circular arcs

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Linear vs. non-linear approximation

• Linear
• Simple design and querying spatial
  information
• -- More memory space required to store the
  objects
• Non-linear
• More precise representation of spatial
  objects
• -- More time-consuming operations

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Vector mode

• In a vector mode, objects are constructed from
  points and edges as primitives.
• A point is represented by its pair of
  coordinates, whereas linear and surfacic objects
  are represented by structures (lists, sets,
  arrays) on the point representation.

p1100,90
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Vector mode Polyline

• A polyline L is represented by a list of points
  ltp1,,pngt,
• each pi being a point (vertex).
• Each pair (pi, pi1), with iltn, represents
  one of the
• polylines edges.

L1lt p1, p2, p3, p4, p5gt
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Vector mode Polygon

• A polygon P is also represented as a list of
  points,
• ltp1,,pngt,.
• The pair (pi,pi1) is also an edge of the
  polygon.

P1ltp1, p2, p3, p4, p5gt
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Vector mode Region

• A region R is union of polygons, P1,,Pn,.

R1P1, P2, P3
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Structure notation

• 1) Point xreal, yreal (array of
  coordinates)
• 2) Polyline ltpointgt (list of points)
• 3) Polygon ltpointgt (list of points)
• 4) Region polygon (union of
  polygons)
• Starting point n ways to start the boundary
  description
• Order of scanning the vertices clockwise and
  counterclockwise
• We will use counterclockwise order for objects
• and clockwise for holes

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2-dimensional objects
How to distinguish a simple polygon from a
non-simple one, a convex polygon from non-convex
one, or a set of adjacent polygons from a set of
disjoint or intersecting polygons. Examples of
adjacent, disjoint and intersecting polygons.
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Models for collection of objects
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Models for collection of objects

• Spaghetti model
• A network model
• Topological model

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Spaghetti model (1)

• The geometry of any spatial object of the
  collection
• is described independently of other objects.

• The objects of interest are
• Point xreal,yreal
• Polyline ltPointgt
• Polygon ltPointgt
• Region Polygon

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Spaghetti model (2)
points p10,6 p20,0, p36,0, p46,6
p56,4, p66,0, p711,0,
p811,4 Polygon P1 ltp1,p2,p3,p4gt Polygon P2
ltp5,p6,p7,p8gt
.
.
6 5 4 3 2 1 0
p1
.
.
p4
p5
p8
P1
P2
.
.
.
.
p2
p6
p3
p7
0 1 2 3 4 5 6 7 8 9 10 11 12
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Spaghetti model (3)

• No topology stored in such a model, and all
  topological relationships must be computed on
  demand.
• This structure also implies representation
  redundancy
• the boundary between two adjacent regions is
  represented twice.
• The model enables the heterogeneous
  representation that would mix points, polylines
  and regions with no restrictions.
• Polylines might intersect in the plane without
  the intersection points of these lines being
  stored explicitly in the database.

?
Pk
?
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Spaghetti model (2)
The main advantage of the model is its
simplicity. In addition, because all objects
are stored independently, it provides the end
user with easy input of new objects into the
collection. The drawbacks of the model are
mainly due to the lack of explicit information
about the topological relationships among spatial
objects, such as adjacency or inclusion. a)
there is no straightforward way to find out
whether the boundaries of two polygons share a
point. b) data stored with some redundancy,
the common boundary of two polygons is
represented twice. c) risk of inconsistency is
incurred boundary of two adjacent countries
might have slightly different coordinates due to
different sources of information simplification.
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Examples of Spaghetti Models
1. ESRI Shapefile (shp) 2. MapInfo MIF/MID
(.mif, mid) 3. SVF, Simple Vector Graphics
(.svf) 4. ...
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Network model (1)

• The network spatial model was first designed for
  representing networks in network (graph)-based
  applications such as transportation services or
  utility management (electricity telephone
  lines, roads, etc.)
• In this model, topological relationships among
  points and polylines are stored.

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Network model (1)

• Node is a distinguish point that connects a list
  of Arcs.
• An Arc is a polyline that starts at a Node and
  ends at a
• Node.

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Network model (2)

• There are two types of points namely, regular
  points and nodes.
• A node is either an arc end point (extreme) or
  an isolated point in the plane.
• Other line and polygon vertices are regular
  points.
• Depending on the implementation, the network is
  either planar or nonplanar.

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Network model (3)

• Depending on the implementation, the network is
  either planar or nonplanar.
• In a planar network, each edge intersection is
  recorded as a node, even though the node does not
  correspond to a geographic object.
• In a nonplanar network, edges may cross without
  producing an intersection. (Example ground
  transportation with tunnels and passes)

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Network model (3)

• The objects of interest are
• point xreal,yreal
• node point,ltarcgt
• arc nodestart, nodeend, ltpointgt
• polygon ltpointgt
• region polygon
• One advantage of this approach is its intrinsic
  description of a networked topology, with the
  notion of connectivity useful for optimal path
  search.
• No information on the relationships between 2D
  objects is stored in this model.

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Example Spaghetti model
L1 lt1,20, 5,17, 8,23gt L2 lt8,23,
10,16, 9,5gt L3 lt8,23,12,23, 18,17,
20,26, 35,16, 25,0, 9,5gt L4 lt0,0,
4,5, 6,0, 9,5gt
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Example Network model (1)
Points p15,17 p212,13 p310,16
p420,26 p535,16 p625,0 p76,0
p84,5 p91,20 p100,0
p119,5 p128,23 p1310,16
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Example Network model (2)
Nodes N1 p9, ltA1gt N2 p12, ltA1, A2, A3gt
N3 p10, ltA4gt N4 p11, ltA2, A3, A4gt
Arcs A1 N1, N2, ltp1gt A2 N2, N4, ltp13gt
A3 N4, N2, ltp6, p5, p4, p3, p2gt A4 N3,
N4, ltp8,p7gt
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Topological model (1)

• The topological model is similar to the network
  model, except that the network is planar.
• This network induces a planar subdivision into
  adjacent polygons, some of which may not
  correspond to actual geographic objects.
• The objects of interest are
• point xreal,yreal
• node point,ltarcgt
• arc nodeSTART, nodeEND,
• polyLEFT, polyRIGHT, ltpointgt
• polygon ltarcgt
• region polygon

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Topological model (2)

• As in the network model, a node is represented
  by a point and the list of arcs starting (or
  ending) at this node. If the list is empty, this
  corresponds to a point isolated from the network.
  Examples.
• In addition to its ending points and the list
  vertices, an arc also features the two polygons
  having the arc as a common boundary.
• A polygon is represented by a list of arcs, each
  arc being shared with a neighbor polygon.
• Some redundancy exists for efficiency reasons
  wile accessing objects. For instance, polygons
  can be accessed through either polygons or arcs..
• However, ther is no redundancy in the stored
  geometry, as each point/line is stored only once.

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Example 1 Spaghetti Model
9,25
15,20
12,12
1,10
15,9
3,1
10,0
Polygons P1 lt1,10, 3,1, 10,0, 12,12,
9,25gt P2 lt12,12, 10,0, 15,9, 15,20,
9,25gt
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Example 1 Topological model (1)
Points p11,10 p23,1 p315,20
p415,9 p512,12 p610,0 p79,25

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Example 1 Topological model (2)
Nodes N1 p7, ltA1, A2, A3gt N2 p6, ltA1, A2,
A3gt
Polygons P1 ltA1, A2gt P2 ltA1, A3gt
Arcs A1 N1, N2, P2, P1, ltp5gt A2 N1,
N2, P1, ?, ltp1, p2gt A3 N1, N2, P2, ?, ltp3,
p4gt
Regions R1 P1 R2 P2
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Example 2 Topological model (1)
Points p11,10 p23,1 p315,20
p415,9 p512,12 p610,0
p79,25 p84,12 p92,9 p103,5
p115,10
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Example 2 Topological model (2)
Nodes N1 p7, ltA1, A2, A3gt N2 p6, ltA1, A2,
A3gt N3 p8, ltA4gt
Polygons P1 ltA1, A2, A4gt P2 ltA2, A3gt P3 ltA4gt
Arcs A1 N1, N2, P2, P1, ltp5gt A2 N1,
N2, P1, ?, ltp1, p2gt A3 N1, N2, P2, ?, ltp3,
p4gt A4 N3, N3, P3, P1, ltp9, p10,p11gt
Regions R1 P1 R2 P2 R3 P3
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Example 2 Topological model (3)
Nodes N1 p7, ltA1, A2, A3gt N2 p6, ltA1, A2,
A3gt N3 p8, ltA4gt
Draw the map!
Polygons P1 ltA1, A2, A4gt P2 ltA2, A3gt P3 ltA4gt
Arcs A1 N1, N2, P2, P1, ltp5gt A2 N1,
N2, P1, ?, ltp1, p2gt A3 N1, N2, P2, ?, ltp3,
p4gt A4 N8, N8, P3, P1, ltp9, p10,p11gt
Regions R1 P1 R2 P2 R3 P3
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Topological model Pro Contra
One advantage of the topological model is the
efficient computation of topological queries.
For example, looking polygon adjacent to a given
polygon P is straightforward. P is scanned.
Accessing each of its arcs provides a polygon
adjacent to P. Another advantage is related to
update consistency. Because of object sharing,
consistency maintenance and updates are easier
with the topological model than with the
spaghetti model. Complexity of the resulting
structure may slow down some operations. For
example, displaying a subset of a map requires
scanning a set of lines.
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Current spatial data formats
DXF Drawing Interchange Format (CAD/CAM
applicaions) DIGEST Digital Geographic
Information Exchange Standard
(military application in NATO) TIGER
Topologically Integrated Geographic Encoding and
Referencing (US Census Bureau) STDS
Spatial Data Transfer Standard (US
Geological Survey, USGS) France EDIGeO, a
civilian application of DIGEST format Germany
ALK/ATKIS UK National Transfer Format
(NTF) Canada Spatial Archive and Interchange
Format (SAIF)
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Spatial Data Models

• To be continued?

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TIGER/Line Data Format Spatial objects

• Node A 0-D object that is a topological
  junction of two or more links or chains, or an
  endpoint of a link or chain.
• Entity point A point used for identifying the
  location of point features (or real features
  collapsed to a point), such as towers, buildings,
  etc.
• Chain a simple polyline described by a start
  node, an end node, and a list of intermediate
  points called shape nodes. Chain intersect each
  other only at nodes. (chain?arc).
• a) a complete chain explicitly references left
  and right polygons and start and end nodes. They
  form polygon boundaries.
• b) a network chain does not reference left and
  right polygons
• GT-polygon an area described by the list of
  complete chains that from its boundary.
  GT-polygons are mutually exclusive, and their
  union forms partition of the space.