Spatial Models in Thinking and Communication

Spatial models joint external and internal aspects of human activity,mental schemas of thinking,and spatial structures of things.These models represent objects of knowledge,valuation,and transformation due to similarity with them in various relations,and they participate in inter-subject communication using schemata common for many people.The spatial models can reproduce a modelled object or be productive regarding it.These models are created in cognitive modus of comprehension as images of objects known at various mental levels;in projective modus,they appear as projects of object’s transformation and planes of subject’s actions;in communicative modus,they are interpreted as spatial texts expressing certain senses.All of them interact in spatial thinking,which deals with the relationship of parts and the whole,unlike logical thinking operating with genus-species relations.Both practical and theoretical thinking use common spatial schemas as means of internal modelling,which are elaborated in collective and individual experience.Due to their simplicity and unification,these schemas can serve also as units of spatial codes mediating the objects representation and inter-subject communication through spatial texts created in the semiotized space.

3D topological relationships of landforms and their spatial schema-based representation

The science of geomorphology works on natural 3D landforms.Research includes the change of landforms as well as the processes causing these changes.Material transport processes lead to a composition of a geomorphic system that follows a certain spatial hierarchy.The analysis of 3D topological relations of landforms can help to investigate geomorphic systems in two ways.First,chronological order of geomorphic genesis can be derived and,second,indications of material source can be found.However,at least some 3D geometric information is needed if topology is supposed to be derived and examined.Landforms cannot simply be reconstructed by surface measurements.Data capture is a major problem when buried features are under investigation.Subsurface information is gathered by drillings or geophysical methods that reveal point or line information.Unfortunately,the ISO 19107 Spatial Schema does not offer a valid representation of 3D geometry from sparse data,either by aggregating a surface and one or few points or by aggregating a surface and a line.Here,we discuss the possibilities for the analysis of chronological order of landform genesis and material dependencies that arise from applying 3D topological relationships to geomorphic system analysis.We show five relationships that are able to be observed in nature.Further,we introduce a new class for the representation of 3D objects with under-specified geometry.A_UG_Solid mediates between the Spatial Schema’s geometric primitives with a dimension less than three on the one side and a GM_Solid on the other side.Constraints to aggregate such a_UG_Solid are defined.The introduction of a_UG_Solid facilitates the application of 3D topological concepts to geometric objects that are known to be volumetric but have to be modeled from sparse data.