13. Spatiotemporal Databases

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13. 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 Models

• Rectangles data model --- for each object
• Spatial extent a set of rectangles.
• Temporal extent a set of time intervals.

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Rectangles 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 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 Parametric 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
5t, 102t 5t, 153t 0, 20
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• The Parametric 2-Spaghetti Data Model---
• for each object
• Spatial Extent set of triangles, whose corner
  vertices
• represented as functions of time
• Temporal Extent A constant time interval
• Example Net

Ax Ay Bx By Cx Cy From To
3 3-t 40.5t 4-0.5t 5t 3 0 10
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13.2.1 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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1200 am
300 am
4-
Parking Lot
3-
500 am
2-
1-
1
2
3
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• Example Tide (Figure 13.6)

Ax Ay Bx By Cx Cy From To P End
1 4 1 4-t t1 4 0 2 11.5 8
1 4 1 2 3 4 2 9.5 11.5 8
1 2 3 4 3 6-t 2 3 11.5 8
1 2 1 4-t 3 6-t 2 3 11.5 8
1 2 3 4 3 3 3 8.5 11.5 8
1 2 1 1 3 3 3 8.5 11.5 8
1 1 3 3 3 6-t 3 5 11.5 8
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13.3 Geometric 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 Models

• Geometric Transformation -- bijection of
  d-dimensional space into itself.
• Example
• Affine Motion x Ax B
• Linear Motion x Ax
• Scaling x Ax where A is
  diagonal
• Translation x x B
• Identity 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 Queries

• Querying Parametric Extreme Point Databases ---
• allow only the constraints of the type xc,
  xltc, or xgt 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 gt 80)
• INTERSECT
• (SELECT x, y, t
• FROM Region
• WHERE temperature lt 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 gt t.
• Hidden(i) - Window(i, x, y, t),
  
• not Seen(i).