1. L12-S1 Spatiotmporal DB 2003 SJSU -- CmpE Database Design Dr. M.E. Fayad, Professor Computer Engineering Department, Room #283I College of Engineering San José State University One Washington Square San José, CA 95192-0180 http://www.engr.sjsu.edu/~fayad

2. L12-S2 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 2 Lesson 12: Spatiotemporal Databases

3. L12-S3 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Lesson Objectives 3 Understand Extreme Point Data Models Explore Parametric Extreme Point Data Models Explore Geometric Transformation Data Models Write Queries

4. L12-S4 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Spatial applications deals with objects whose position shape and size change over time. So called spatiotemporal object Real World Examples: –Vehicle or human trajectories archival data –Fire front monitoring –Flight simulators –Weather forecast 4 Spatiotemporal Objects

5. L12-S5 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Identified by oid is time evolving spatial object. Its evolution (or history) is represented by a set of instances (oid, si, ti) where si is space stamp and ti is timestamp. These applications require efficient indexing because of high volume and complexity of data. 4 Spatiotemporal Objects

6. L12-S6 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Has a spatial extent and a temporal extent. Spatial extent = a set of points in space. Temporal extent is set of time instances when an object exists. Each spatiotemporal data model captures both extents of the object. 4 Spatiotemporal Objects

7. L12-S7 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 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 5 Extreme Point Data Models (1)

8. L12-S8 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Rectangles data model --- for each object Spatial extent : a rectangle of a union of a set of rectangles. Temporal extent: a time interval or a union of a set of time intervals. 6 Extreme Point Data Models (2)

9. L12-S9 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 7 Extreme Point Data Models (3)

10. L12-S10 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad  Rectangles data model represents the spatial extent of d- dimensional rectangle as the cross product of d intervals, one for each dimension.  Each spatial and temporal interval is represented by its endpoints which called extreme points of the intervals.  Each tuple of the rectangle model represents just a combination of one rectangle and one time interval.  Several tuples need to be used to describe objects whose spatial or temporal extents are composed of a set of intervals. 6 Extreme Point Data Models (4)

11. L12-S11 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 8 Rectangles Data Model Archaeological Site (Figure 13.1) IdXYT 1[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]

12. L12-S12 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 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 9 Worboys’ Data Model (1)

13. L12-S13 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 10 Worboys’ Data Model (2)

14. L12-S14 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 11 Worboys’ Data Model (3) Park (Figure 13.2) IdAxAyBxByCxCyFromTo Fountain104 4 419801986 Road510969619951996 Road96939319951996 Tulip23276319751990 Park12111121119741996 ………………………

15. L12-S15 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad In rectangle data model – spatial and temporal extents are independent of each other. In Worboy ’ s data model – spatial extents are related to each other but the spatial and temporal extents are still independent of each other. 12 Rectangle vs. Worboys

16. L12-S16 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Conclusions: only represent objects that appear and disappear suddenly Hence, they cannot represent continuously moving objects 12 Extreme point spatiotemporal data models

17. L12-S17 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Use a time parameter t and can represent continuously moving objects. 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 12 Parametric Extreme Point Data Models

18. L12-S18 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 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 13 Parametric Rectangles Data Model (1)

19. L12-S19 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 14 Parametric Rectangles Data Model (2) Example: Plankton X Y T [5+t, 10+2t] [5+t, 15+3t] [0, 20]

20. L12-S20 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad  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 The Parametric 2-Spaghetti Data Model Ax Ay Bx By Cx Cy From To 3 3-t4+0.5t 4-0.5t 5+t 3 0 10

21. L12-S21 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Periodic movements can be classified as either cyclic (where object repeats its movement from the same position and with the same velocity every period.) or acyclic periodic movement (is the composition of cyclic periodic movement and nonperiodic movement, such as movement of light. 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 16 Periodic Parametric Data Models

22. L12-S22 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 17 Periodic Parametric Rectangles Data Model 123 1- 2- 3- 4- 12:00 am 3:00 am 5:00 am Parking Lot

23. L12-S23 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Periodic Parametric Rectangles Data Model 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 +∞

24. L12-S24 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Generalize geometric transformations by using a time parameter. Types of geometric transformations: scaling, translation, linear, affine. 19 Geometric Transformation Data Models (1)

25. L12-S25 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad  Geometric Transformation -- a 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 20 Geometric Transformation Data Models (2)

26. L12-S26 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad 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 21 Geometric Transformation Data Models (3)

27. L12-S27 Spatiotmporal DB 2003 SJSU – CmpE --- M.E. Fayad Querying Parametric Extreme Point Databases --- allow only the constraints of the type x=c, 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) 22 Queries