Jean-Jacques Royer
Centre de Recherches Pétrographiques et Géochimiques
Ecole Nationale Supérieure de Géologie
Computer Department and Modelization
15, rue ND des Pauvres, B.P. 20
54500 Vandoeuvre-Lès-Nancy, France
royer@crpg.cnrs-nancy.fr
Introduction
Extensive work has been done in the area of 3D Visualization and modeling using CAD approach [1]. These methods can be selected it into two categories: namely, CAD objects and natural objects. CAD technology requires the topology of objects at the conception and collaboration stages. It mainly concerns manufactured or industrial objects. Triangles or tetrahedral elements are used to fit the surface or the volume of the final object using spline or Bezier interpolation methods. Several industrial CAD systems are based on such a concept and are widely used in the industry among the most popular ones Auto-CAD, Strim 100. As natural objects are usually investigated from irregular sampling points (bore hole, sections, points), the topology of the underlying real object is not known. This uncertainty as to real shape implies that the classical CAD approach might be irrelevant, as shown by several pioneer works [2].
In fields such as geology or environmental sciences, it frequently need to reconstruct the underlying structure from indirect information or from scarce, irregular, or partial data points. The situation can be further complicated by the presence of discontinuities such faults, fractures or folded layers, holes or non manifold surfaces where the B-spline approach is irrelevant. This is why the natural object approach has been developed specifically to handle complex natural 3D objects. It involves specific data structures and objects oriented program in which will be shortly presented.
Methods
Two steps are required for building a model: (i) construction of the geometric model from the available observations. It is done using elementary elements such as points or atoms, lines (PLINE) and services represented by a set of triangles (TSURF).
The volumes of refined using meshed tetrahedral, voxet or stratigraphic grids (SGRID). Specific interpolation algorithms have been developed to estimate location of on informed location (Discreet Smoothed Interpolation [2,3]). Each of these elementary objects are designed in C++. (ii) construction of the property model: once the geometric or model is built, the physical properties are estimated at all locations in the 3D space. Properties are attached to location (atoms). Refinements based on G-map structures including topological relationships between basic elements have been proposed recently [4]. It generalize the notion of property which can be attached to all kinds of objects (surfaces, tetrahedra, lines, ...). This method also increases the rapidity of algorithms involved in geometric operations such as cut, unison, intersection ...
Visualization and validation of the model: The visualization is done interactively using the GOCAD software [3,5], a powerful tool designed for the interactive 3D modeling of the subsurface involving geophysical applications such as 3D ray tracing, 3D tomography and migration, reservoir simulation of complex geological structures (reverse faults, salt domes, ...). It compromises a Geometrical Data Base specially designed to efficiently carry out operations such as (i) intersection, union of two or more surfaces, (ii) intersection of a surface by a line (ray tracing), surfaces or volumes; (iii) storage of physical properties attached on a layer (velocity, density, porosity, permeability, ...) or a volume (VOXET). The visualization of the information contained in the data base is done interactively in the X-Windows/motif interface using the Unix operating system. The code is written in C++ in an object oriented style. An independent 3D graphics library has been developed in order to simplify the portability of the software including the following interface X graphic interface,GL, Phigs+, Starbase, Xgl, Pexlib. The code run currently on Convex, Digital, HP, IBM, Silicon Graphics, SUN, ... Additional information abou this system can be found in "GOCAD progect" [3] managed by the Association Scientifique pour la Géolotie et ses Application, Pr. J.L. Mallet, Chairman of the Computer Sciences Department of the Nancy School of Geology, Nancy, France.
Results
Some of the results obtained by GOCAD on different situations are illustrated one figures 1 to 3. It concerns both the construction of a geometric and property model for exploitation of mineral resources.
The core of GOCAD is built around a set of C++ object structures. A handler based on menus manages the interface between the user and GOCAD. It includes the notion of multi windowing (called 3D camera) in which the user can visualize virtual 3D objects. Language script can be used to perform arithmetic transformation on properties. A communication process library using TCL assumes interface between external applications. It provides the user of powerful tool for modeling complex objects.
Future development are actually understudy especially link with network technology. A 3D browser including elementary methods for visualizing, transforming objects including intersection, evolution through times, do affirmation, ... is under development using Java. It's mail out user to visualize a go cattle object you created on a specific platform on other computers. Specific compress techniques are required in order to decrease volume of data transfer.
Conclusions
Modeling complex natural objects appears clearly an important challenge. Significant results have been of already obtained [5,6], nevertheless, some problems remain difficult to solve, concerning the data (management of a huge amount of data, different scales, different dates). Several directions are offered with the development of the information highway including parallelization of the computing through the web, data spreading on several computers accessible through the WEB, WEB database, multi visualizations sites using Java technology. It promises exciting research area and the issue is for the future of the visualization of information and data.
References
[1] Farin, G., Triangular Benstein-Bezier patches, Comp. Aided Geom. Design, 3, 1986, 83-130.
[2] Mallet, J.L., Discrete smooth interpolation in geometric modelling, Comp. Aided Design, 24 (4), 1992, 178-191.
[3] Mallet, J.L., Discrete modeling for natural objects, Math. Geology, 29 (2), 1997, 199-220.
[4] Lienhardy, P., N-dimensional generalized combinatorial maps and cellular quasi manifolds. Int J. Comp. Geom. Appl., 4 (3), 1994, 275-324.
[5] Royer, J.J., and Shtuka, A., Stochastic imaging of environmental data, in Geosciences and Water Resources: Environmental Data Modeling, Bardinet C. & Royer J.J. (Eds.), ICSU-CODATA, Springer, Berlin, 1997, 101-114.
[6] Shtuka, A., Samson, P., and Mallet, J.L., Petrological simulation within an object-based reservoir model, European 3-D Reservoir Modeling Conference, Stavanger, 1996.