Approche de la modélisation d'objets géologiques déformés : conception, structure logique et algorithmique, résultats

The present study is concemed with sorne aspects of 3D geometrical modeling of a " geological scenary": 1) We con si der the geometries of the most commonplace geological bodies as well as that of the whole "scenary". Such geometries most often depend from the geological processes that generated the objects (surface alteration, erosion, sedimentation, magma intrusion or extrusion ... ) or that transformed them (folding, faulting, metamorphism ... ). Besides, deducing a geometry from local data (field mapping, drilling data ... ) is generally not a straightforward process: it relies on a geological interpretation which takes place before any other mode ling. Thus computer aided mode ling most frequent! y provides a "model of model". 2) The review of sorne of the modelings that have been undertaken prior to the present study put sorne light on the various possible approaches. We show that it may be profitable in many cases to take into account the geological specificities of the modeled objects and thus to approximate by mean of a "dynamic" or "generative" approach the geometrical consequences of the processes that affected these objects. We also consider the relationships that a computer aided model may bear with the original data: it may be desirable either to geta "truly exact model" or on the contrary an "analogue" that may be used as a mere interpolation tool. We insist on the interset of a "forward-backward" method in order to obtain faithfull generative models. 3) We then focus on a particular problem: the modeling of irregularly shaped objects which may be either deformed or combined with each others by mean of boolean operations, as it is the case for granitic intrusions and for the surrounding terrains that are intruded and partly digested. We show that such a modeling depends on the choice of an adequate data structure: this must allow an easy definition of the objetct and, above ail, must not be too sensitive to manipulations through boolean operators and through similar type transformations (STT) which allow to simulate folding and faulting. 4) We review sorne classical data structures. Boundary representations (B.rep) are of very common use in solid modeling and have several advantages, but their pratical implementation for representing geological bodies may be rather complicated. CSG and space partitionings that are independent from the represented objects ( horizontal slices, classical or mixt octtrees) appear inadequate, since they are destroyed, when the objects are deformed. In contrast, binary space partitionings (BSP) are very appealing, since they are only dependent from the objects themselves and are thus unaffected by displacements and more generally by affine transformations. We consequently define an hybrid structure, the BSP mixt tree, which allows in addition manipulations of the object by STI operators. Objects that are deformed or composed by boolean operators can thus be represented by trees that are easily deduced from those representing the original objects. 5) The GRANITE software which bas been built, allows to represent as a BSP tree any polyedric object, even if it is composed of disconnected volumes or if it comprises holes, to add or to substract if from similar objects and to deform it using STI operators. We present results which allow to produce objects showing very irregular shapes and comprising thousands of faces, in rather limited computation times.