On Problems and Benefits of 3D Topology on Under-Specified Geometries in Geomorphology
Marc-O. Löwner
Institute for Geodesy and Photogrammetry, Technische Universität Braunschweig, Pockelsstraße 3, 30106 Braunschweig, Germany e-mail: m-o.loewner@tu-bs.de
J. Pouliot et al. (eds), Progress and New Trends in 3D Geoinformation Sciences,
Lecture Notes in Geoinformation and Cartography, DOI: 10.1007/978-3-642-29793-9_9,
Springer-Verlag Berlin Heidelberg 2013 ,P P 155 - 170 :
Abstract
The science of geomorphology is working on natural 3D landforms. This includes the change of landforms as well as the processes causing these changes. The main concepts of geomorphology, i.e. the sediment budget and the sediment cascade approach can definitely be enhanced by introducing 3D geometrical and topological specifications of the Open Geospatial Consortium. The ISO 19107, Spatial Schema, implements OGC’s Abstract Specification. It enables the modelling of real world 3D phenomena to represent them as formal information models. Unfortunately, OGC’s concepts are not widely applied in the science of geomorphology. In this article we are going to show the explicit benefit of 3D topology for the science of geomorphology. Analysing topological relationships of landforms can be directly related to geomorphic insights. This includes firstly, the process-related accessibility of landforms and therefore material properties, and secondly, the chronological order of landform creation. Further, a simple approach is proposed to use the benefits of the abstract specification 3D topologic model, when only under-specified geometries are available. Often, no sufficient data is available on natural landforms to model valid 3D solids. Following clearly defined geometric conditions the introduced class _UG_Solid mediates between primitives of lower dimension and a GM_Solid . The latter is the realisation of a _UG_Solid that definitely holds the 3D geometry we need to associate with the 3D topological concepts.
1 Introduction and Problem Statement
The Open Geospatial Consortium’s Abstract Specifications (OGC 2012) enable the modelling of real world phenomenon to represent them as formal information models (Kottman and Reed 2009). These information models may include geometry, attributes and topological relationships of real world objects. The main advantage of international accepted standards like OGC’ Abstract Specification is interoperability. This means the seamless exchange of data and a simplified application of analysis concepts. The main document presenting the Abstract Specification is the ISO 19107 ‘Spatial Schema’ (Herring 2001) defining geometric primitives and complexes from 0D to 3D according to the boundary representation (Foley et al. 1995). Next to other concepts, Spatial Schema is implemented in the Geography Markup Language (GML) (Lake et al. 2004). The release of GML led to a number of application schemas e.g. City Geography Markup Language (CityGML) (Gröger et al. 2012). However, CityGML mainly represents models on manmade environments.
Spatial Schema also provides a topology package mainly to convert computational geometry algorithms into combinatorial ones (Herring 2001, p. 104). Topological primitives (i.e. node, edges, faces and solids) need realizations in the form of geometric primitives with the same dimension. Thus, if no valid 3D geometry is provided for features that are known to be 3 dimensional, no 3D topology can be applied
In the science of the land’s surface, geomorphology, objects under examination are definitely volumetric. Built of sediment that is allocated by mainly externally driven processes geometry concepts of the Spatial Schema would be helpful to resent such sediment storages. Topological concepts may support the analysis of geomorphic systems in two aspects. Firstly, identifying neighbouring features and features connected via material transporting processes and, secondly, supporting analysis of landform’s chronological order within a geomorphic system
However, OGC’s 3D concepts are not widely accepted in geomorphology. This is different with the simple feature concept implemented by main GIS companies. The main reason is that 3D data is difficult to collect due to complex phenomena and limited prospecting methods. Thus, especially 3D topology is not applicable to the science of geomorphology, since the topology package of Spatial Schema needs to refer to a valid geometry representation.
In this article a new class for 3D objects with under-specified geometry is proposed. _UG_Solid mediates between Spatial Schema’s geometric primitives with a dimension less than 3 on the one side and a GM_Solid on the other. Constraints to aggregate a _UG_Solid are defined. The introduction of _UG_Solid enables the application of 3D topological concepts to geometric objects that are known to be volumetric but have to be constructed from sparse data.
In the next section the nature and main concepts of geomorphology will be outlined. A special focus is put on the topological aspects of landforms. Special cases of topological relationships between 3D solids will directly be related to geomorphic insights (Sect. 2.2). In Sect. 3 an application model on geomorphic objects and processes will be reviewed. Data acquisition and modelling problems have been identified as the main problems for the acceptance of 3D concepts (Sect. 3.3). Section 4 focuses on utilization the 3D topological concepts. Constraints for building an under-specified 3D geometry will be defined and proven for geomorphology. Section 5 follows up with a discussion.
5 Discussion
It was demonstrated that geomorphology is a science investigating natural 3D objects. These objects change their 3D shape in time due to material transporting processes. On the one hand landforms influence these processes and on the other hand they are their product. As a result, the 3D georelief aggregated by landforms is a complex system of neighbouring objects of different age and material. It is argued that OGC’s spatial schema concepts are useful to represent and to analyse such geomorphic systems in principle.
Here, for the first time the explicit benefit of 3D topology for the science of geomorphology was brought out by a collection of clear examples. Analysing topological relationships of landforms directly gains our understanding in processrelated accessibility of landforms and therefore material properties. Even the chronological order of landform creation can be analysed using topology. Unfortunately, 3D concepts representing geometry and thus 3D topology are not very common in the community of geoscientists.
Data acquisition and modelling problems have been identified as the main reason for the rejection of 3D spatial concepts in geomorphology. Apparently, there is no need to apply the overhead of a 3D concept, when data is sparely available. Moreover, 2D and 2.5D concepts seem to be sufficient to geomorphologist. This, as can be shown with the example of topological analysis is definitely not the case. However, overhead and a very strict formulism hinder geomorphologists to model their perception of do a real (Satzbau: of do) 3D world with 3D concepts.
Here, a simple approach is proposed to use the benefits of the abstract specification 3D topologic model, when only under-specified geometries are available. If no sufficient data is available for a clear 3D object, this approach helps to apply 3D topology on it. It was proven on examples that the formulated constraints ensure the realisation of a _UG_Solid by a GM_Solid. Nevertheless, the approach presented is incomplete. First, this must be said in terms of dimensions, since 0D–2D underspecified Geometries are not covered. Second, no relationship between the GM_Primitives has been modelled. This is surely a focus worthwhile for future research.
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