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Outline

1	Spatio-temporal database support for long-period scientific data
2	Objective: Database support for long-period scientific data, like used in geological applications Balanced restoration of structural basin evolution
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4	Conceptual model -- Design objectives Enabling change in discretization Separate meshes from vertices Building several meshes from one set of vertices Automatic consistency w.r.t. vertices Spatio-temporal data structures Dynamic: Insert, Delete, Update operations on 4D geometries Extending existing 3D data types with time Reuse of spatial functionality
5	3D conceptual model extended by time -- database type MovingVertex Time isomorphic to the reals Location and shape of geometries is a function of time Vertices move on their trajectories Properties of the model: Trajectory piecewise linear Change in direction => Snapshot Linear interpolation also w.r.t. time => const velocity/no acceleration Change in velocity => Snapshot
6	-- Database type TemporalSimplex Assemble complex geometries from moving vertices Separates meshes from vertices A moving simplex comprises: References to its moving vertices Temporal interval of validity A moving complex comprises: Set of moving simplexes Temporal interval of validity Integrity constraints!
7	Representing time-dependent simplicial complexes applying key-frame interpolation
8	Hierarchy of operations
9	Examples for spatio-temporal operations: Base operations on temporal simplexes Operations on a per-timestep basis not sufficient Geometric base operations Analogues in the pure-spatial setting: e.g. segment/triangle Euclidean distance O(1)-operations Operations involve two consecutive timesteps on the merged timeline of the two objects
10	Base operations in the scope of this work Minimum Euclidean distance operation Operands: Spatial or spatio-temporal objects Types of operations: Scalar function min-dist Temporal function when-min-dist Intersection-operations Operand: Plane or Halfspace or Bounding box Types of operations: Boolean predicate intersects Temporal function when-intersects Object-generating function intersection
11	Base operations on temporal simplexes -- Implementing minimum Euclidean distance Definition: Minimum Euclidean distance Solution by: Parameterization of the simplex movement (shared time parameter) Substitution into Euclidean distance formula Analytical search of minimum partial derivatives, solving system of equations
12	Base operations on temporal Simplexes -- Example intersection Model is not closed under intersection Contrast to purely spatial model: Approximation must be performed by query system
13	System architecture: Extending GeoToolKit
14	Examination with geological and artificial datasets
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16	Summary and future work Conclusions Need for spatio-temporal database types and operations Spatio-temporal operations metric queries (minimum Euclidean distance) intersection-queries Applications Future Work Enhance existing operations through geometric filters and index support Extend conceptual model: more operations on spatio-temporal types New applications (kinematics of landform)
17	Sponsors and contact information