Boots – shoes – and leggings
Patent
1991-05-20
1995-11-07
Zimmerman, Mark K.
Boots, shoes, and leggings
395120, 364421, G06T 1700
Patent
active
054653231
DESCRIPTION:
BRIEF SUMMARY
SUMMARY OF THE INVENTION
The present invention is generally concerned with investigations within a three-dimensional body and is particularly concerned with a new process of obtaining a representation of a surface within a body on the basis of a limited set of known geometrical data relating to said surface.
Investigations within three-dimensional bodies are of major concern in geology, geophysics and biology.
In geophysics, for example, it is necessary to obtain as accurate as possible representations of surfaces situated, for example, at the interface between two areas of different kinds or with different properties, on the basis of data obtained from prospecting, or during exploitation of an underground resource.
How effectively the three-dimensional body is investigated, especially in prospecting for oil or other underground resources, depends on the accuracy with which this type of surface can be reconstituted and represented.
In medicine and biology there are various known processes for obtaining representations of cross-sections through a living body or the like and the aim is also to reconstitute and represent in three dimensions a surface situated at the interface between two media, for example the contours of a bodily organ.
There already exist a number of modeling techniques for obtaining a representation of a surface within a three-dimensional body that is to be exploited or treated. Particularly worthy of mention are the Bezier interpolation method and the spline functions method (for more details reference should be had to Geometric Modeling, M. E. Mortenson, Ed. John Wiley, 1985).
However, all these known techniques are ill suited to handling heterogeneous data, by which is meant data relating to the coordinates of points on the surface, to fixed orientations of the surface, to geometrical links between two separate points, etc. Also, these techniques are ill-suited to a wide spread of surfaces or to surface anomalies such as folds and breaks, and to discontinuous surfaces. To be more precise, in some cases the functions used in these techniques are not convergent or have no solution or have no single solution.
Finally, the known techniques are not able to take into account the concept of the degree of certainty with which some surface data is known.
The present invention is directed to alleviating the drawbacks of the prior art processes and to proposing a process that can allow for non-homogeneous and/or highly diverse geometrical data and for the anomalies mentioned above and other anomalies, providing in each case a single and unambiguous model of the surface.
Another object of the invention is to propose a process that can use geometrical data and at the same time data as to the degree of certainty or accuracy of said data.
To this end, the present invention firstly consists in a process for modeling a surface representing for example the interface between two areas of different kinds or with different properties in a three-dimensional body such as a geological formation or a living body, characterized in that it comprises the steps of: relating to the surface and associated with respective points on said surface; the mesh; following data: consequently to the data relating thereto, weighted sum of the actual coordinates of the node and of its satellites, roughness indices associated with each node and a global index of violation of said geometrical data, not known by an iterative method in which for each step of the iteration there are added a weighted combination of the actual coordinates of the satellite and of the satellites of the satellites of said node and a combination of the geometrical data associated with said node, in such a way as to minimize said sum, and each node.
The invention also concerns a device for modeling a surface representing for example the interface between two areas of different kinds or with different properties in a three-dimensional body such as a geological formation or a living body, characterized in that it comprises: data relating to the surface and a
REFERENCES:
patent: 4930092 (1990-05-01), Reilly
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"Machine Contouring Using Minimum Curvature" I. Briggs; Geophysics 17.1, 1984.
"Triangular Bernstein-Bezier Patches", G. Farin; Computer-aided Geometric Design, Aug. 1986.
"Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams" L. Guibas et al; ACM transactions on Graphics, Apr. 1985.
"Three-dimensional Graphic Display of Disconnected Bodies"; J. Mallet; Mathematical Geology, 1988.
"Geometric Modeling and Geostatistics" J. Mallet; Geostatistics, 1989.
"Discrete Smooth Interpolation", J. Mallet' ACM Transactions on Graphics, Apr. 1989.
"Geometric Modeling", M. Mortenson; 1985.
"FEM Shape Optimization: A Case for Interactive Graphics", S. Singh, et al; Computers and Graphics, 1982.
Association Scientifique pour la Geologie et de ses Applications
Compagnie Generale de Geophysique
Societe National Elf Aquitaine (Production)
Total Compagnie Francaise des Petroles
Zimmerman Mark K.
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