Geomodeling

@book{mallet:hal-04055829,
 abstract = {During the eighties, it became clear that, in spite of their success in modeling simple surfaces, classic automatic mapping systems would never be able to model complex surfaces and, more generally, complex geological volumes affected by severe tectonic events with overturned folds, salt domes and reverse faults. At the same time, experience using traditional Computer Aided Design software developed for the car industry brought out its inability to accommodate the complex data encountered in the geosciences. For this reason, within the framework of the gOcad research project, I proposed in 1989 a completely different strategy involving the discrete modeling of natural objects. In this discrete approach, the geometry of any object is defined by a finite set of nodes (points) in the 3D space, while its topology is modeled by links bridging these nodes. For example, if the object to be modeled is composed of surfaces, then the links can be arranged in such a way that the mesh so defined generates triangular facets. These facets can be interpolated locally by flat triangles or, if need be, by curvilinear triangles. It is not difficult to imagine how this strategy can be extended to the modeling of curves and volumes. In practice, such a discrete approach is of no interest without a powerful mathematical tool able to interpolate the location (x, y, z) of the nodes defining the geometry of the objects in the 3D space. For this reason, I proposed a new method, called “Discrete Smooth Interpolation” (DSI) which today is at the heart of the gOcad research project. This new interpolation method was specially designed for modeling natural objects, while taking into account a wide range of complex and more, or less, precise data. In fact, adopting a new mathematical core for a Computer Aided Design system has huge consequences which render inadequate most of the existing tools developed for traditional systems. The new research fields thus opened up resulted in the launching of the gOcad research project in the fall of 1989. After a decade of research, the tools developed within the framework of the gOcad project are now well-honed and widely used in the oil and gas industry for modeling complex geological structures in the sub-surface. At the same time, some exciting applications have come to light in very different fields such as, for example, medecine, anthropology or the environmental sciences. This book presents some of the more important methods to have constituted the backbone of the gOcad project from its early days to the present.},
 author = {Mallet, Jean Laurent},
 hal_id = {hal-04055829},
 hal_version = {v1},
 publisher = {{Oxford University Press Inc, USA}},
 title = {{Geomodeling}},
 url = {https://hal.univ-lorraine.fr/hal-04055829},
 year = {2002}
}