On the route to a spatio-temporal geoscience information system, an appropriate data model for geo-objects in space and time has been developed. In this model, geo-objects are represented as sequences of geometries and properties with continuous evolution in each time interval. Because geomodeling software systems usually model objects at specific time instances, we want to interpolate the geometry and properties from two models of an object with only geometrical constraints (no physical or mechanical constraints). This process is called spatio-temporal data construction or morphological interpolation of intermediate geometries. This paper is strictly related to shape morphing, shape deformation, cross-parameterization and compatible remeshing and is only concerned with geological surfaces. In this study, two main sub-solutions construct compatible meshes and find trajectories in which vertices of the mesh evolve. This research aims to find an algorithm to construct spatio-temporal data with some constraints from the geosciences, such as cutting surfaces by faulting or fracturing phenomena and evolving boundaries attached to other surfaces. Another goal of this research is the implementation of the algorithm in a software product, namely a gOcad plug-in. The four main procedures of the algorithm are cutting the surfaces, setting up constraints, partitioning and calculating the parameterizations and trajectories. The software has been tested to construct data for a salt dome and other surfaces in regard to the geological processes of faulting, deposition and erosion. The result of this research is an algorithm and software for the construction of spatio-temporal data.
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