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13. Spatiotemporal Databases13. Spatiotemporal Databases

• Extreme Point Data Models

• Parametric Extreme Point Data Models

• Geometric Transformation Data Models

• Queries

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Spatiotemporal objects - have spatial and temporal

extents

Spatial extent- the set of points in space that belong to an object

Temporal extent- the set of time instances when an object exists

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13.1 Extreme Point Data Models

Extreme points – the endpoints of intervals and

the corner vertices of polygonal or polyhedral objects

Examples: extreme points data models include:

Rectangle data model and

Worboys’ data model

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Extreme Point Data ModelsExtreme Point Data Models

Rectangles data model --- for each objectSpatial extent : a set of rectangles.

Temporal extent: a set of time intervals.

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Rectangles Data ModelRectangles Data Model

Archaeological Site (Figure 13.1)

Id X Y T

1 [3,6] [3,6] [100,200]

2 [8,11] [3,7] [150,350]

3 [2,4] [5,10] [250,400]

3 [2,10] [8,10] [250,400]

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Worboys’ Data Model --- for each object

Spatial extent: a set of triangles,

represented by corner vertices

Temporal extent: a set of time intervals,

represented by From and To endpoints

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Worboys’ Data ModelWorboys’ Data Model

Park (Figure 13.2)

Id Ax Ay Bx By Cx Cy From To

Fountain 10 4 10 4 10 4 1980 1986

Road 5 10 9 6 9 6 1995 1996

Road 9 6 9 3 9 3 1995 1996

Tulip 2 3 2 7 6 3 1975 1990

Park 1 2 1 11 12 11 1974 1996

… … … … … … … … …

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13.2 13.2 ParametricParametric Extreme Point Data Models Extreme Point Data Models

Extend the extreme point data models by specifying the extreme points as linear, polynomial, or periodic functions of time

Examples: parametric rectangles and parametric 2-spaghetti data

models

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Parametric Rectangles Data Model ---

for each object

Spatial extent: a set of intervals, whose endpoints are represented by functions of

time

(time t is the only parameter)

Temporal extent: a time interval, whose endpoints are represented by From and To constants

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Example: Plankton

X Y T

[5+t, 10+2t] [5+t, 15+3t] [0, 20]

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The Parametric 2-Spaghetti Data Model---

for each objectSpatial Extent: set of triangles, whose corner vertices

represented as functions of timeTemporal Extent: A constant time interval

Example: Net

Ax Ay Bx By Cx Cy From To

3 3-t 4+0.5t 4-0.5t 5+t 3 0 10

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13.2.1 Periodic Parametric Data Models13.2.1 Periodic Parametric Data Models

Periodic Parametric Rectangles Data Model ---

Spatial Extent: a set of triangles, whose corner vertices are represented as periodic functions of time

Temporal Extent: Periodic intervals

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1 2 3

1-

2-

3-

4-

12:00 am3:00 am

5:00 am

Parking Lot

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Example: Tide (Figure 13.6)

Ax Ay Bx By Cx Cy From To P End

1 4 1 4-t’ t’+1 4 0 2 11.5 +∞

1 4 1 2 3 4 2 9.5 11.5 +∞

1 2 3 4 3 6-t’ 2 3 11.5 +∞

1 2 1 4-t’ 3 6-t’ 2 3 11.5 +∞

1 2 3 4 3 3 3 8.5 11.5 +∞

1 2 1 1 3 3 3 8.5 11.5 +∞

1 1 3 3 3 6-t’ 3 5 11.5 +∞

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13.3 13.3 Geometric Transformation Data ModelsGeometric Transformation Data Models

• Generalize geometric transformations by using a time parameter.

• Types of geometric transformations: scaling, translation, linear, affine.

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13.3 Geometric Transformation Data Models13.3 Geometric Transformation Data Models

Geometric Transformation -- bijection of d-dimensional space into itself.

Example:Affine Motion: x’ = Ax + BLinear Motion: x’ = AxScaling: x’ = Ax where A is diagonalTranslation: x’ = x + BIdentity: x’ = x

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Geometric Transformation Data Model ---defines each spatiotemporal object as some spatial object together with a continuous transformation that produces an image of the spatial object for every time instant

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13.4 Queries13.4 QueriesQuerying Parametric Extreme Point Databases ---

allow only the constraints of the type x=c, x<=c, or x>= c.

Example: Find where and when will it snow given Clouds(X, Y, T, humidity) Region(X, Y, T, temperature)

(SELECT x, y, t FROM Clouds

WHERE humidity >= 80) INTERSECT

(SELECT x, y, t FROM Region WHERE temperature <= 32)

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Example:

Window(id, x, y, t) -- open windows on a computer screen, where id is the identifier, x, y spatial points

of the window, and t is the time when it is active.

Which windows are completely hidden by other

windows?

Seen(i) :- Window(i, x, y, t),

not Window(i2, x, y, t2),

t2 > t.

Hidden(i) :- Window(i, x, y, t),

not Seen(i).