3D topography

A simplicial complex-based solution in a spatial DBMS

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Current topographic products are usually limited to a real world representation in only two dimensions, extended with some additional point heights and contour lines. Many environmental issues require more precision than analysis on 2D models can offer. At the same time, vast amounts of 3D data are becoming available due to emerging new data acquisition techniques, such as (terrestrial) laser scanning. To extend current models into the third dimension, a data structure is needed to load, update, query, analyse and especially validate the new 3D topographic data in a spatial DBMS. This dissertation presents a new topological approach to 3D data modelling, based on simplicial complexes. Operators and definitions from the field of simplicial homology are used to define and handle the is tetrahedral network (TEN). Simplicial homology provides a solid mathematical foundation for the data structure. The new database approach enables one to derive substantial parts of the data structure efficiently, thus tackling common drawbacks as TEN extensiveness and laboriousness of maintaining topology.