Algebraic specification and development in geometric modeling

Bertrand, Yves; Dufourd, Jean-François; Francon, J; Lienhardt, Pascal

doi:10.1007/3-540-56610-4_57

Cited by 16 publications

(11 citation statements)

References 15 publications

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“…Compared with other existing 3D solid modelling approaches (e.g. Boissonnat, 1988;Bertrand et al, 1992), a major original feature of this modeller is that the 3D description of the geological space is achieved through a potential field formulation in which geological boundaries are iso-potential surfaces, and their dips are represented by gradients of the potential. The model is built in a georeferenced system and uses (i) a digital elevation model (DEM), (ii) a simplified geological map (lithological contact information) and (iii) foliation dips measured within the different units (local gradient information).…”

Section: D Geological Modellingmentioning

confidence: 99%

3D geological modelling of a polyphase deformed pre‐Variscan IOCG mineralization located at the southeastern border of the Ossa Morena Zone, Iberian Massif (Spain)

Gumiel¹,

Arias

Martin-Izard

2010

Geological Journal

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A previously unrecorded group of stratiform and stratabound-type magnetite beds (IOCG) has been found at the southeastern border of the Ossa Morena Zone (Variscan Massif of Spain). These mineralizations, hosted in Upper Precambrian-Lower Cambrian rocks, are located in a transpressive belt, and were strongly deformed by the Variscan Orogeny, thus showing polyphase noncoaxial folding. This folding has been recognized by the interference patterns observed in magnetite beds outcropping in old mine workings. A detailed mapping of several adits shows a Ramsay type 1 'egg box' or dome-and-basin interference pattern which arises when both D 1 (NW-SE trending) and D 2 (NE-SW trending) fold axes and axial planes are orthogonal or at a high angle to each other. An analysis of the magnetitic layers using orthogonal thickness and conic functions has been carried out to characterize fold profiles geometry.Deformation is also accommodated by oblique WNW-ESE trending thrust faults which produce centimetric to metric displacements of the magnetite beds. A 22% shortening in the NE-SW direction and 24% in the NW-SE direction has been estimated. Finally, as polyphase folding and thrust structures in three dimensions have a complex geometry, a 3D geological modelling has been carried out to obtain a better insight into the geometry of mineralized magnetite bodies.

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Section: D Geological Modellingmentioning

confidence: 99%

3D geological modelling of a polyphase deformed pre‐Variscan IOCG mineralization located at the southeastern border of the Ossa Morena Zone, Iberian Massif (Spain)

Gumiel¹,

Arias

Martin-Izard

2010

Geological Journal

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“…Thus, the use of algebraic specifications in computer graphics were first distinguished in [30] and has also interested specialists of specifications [21]. Subsequently, the combinatorial maps and their extensions were algebraicly specified to develop topology-based modelers [5,6,11,12].…”

Section: Related Workmentioning

confidence: 99%

“…For the consistency of the geometric objects, the above definitions introduces some constraints which cannot always be satisfied during construction and manipulation. Inspired by the algebraic specifications of [5,6], basic operators, which release some of these constraints, can be defined in a formal way on a gmap type. They will be progressively specified by introducing higherorder features of the typed -calculus.…”

Section: Embedded Gmapsmentioning

confidence: 99%

“…We will limit ourselves to the description of planar objects for which the mathematical model of generalized maps of dimension 2 [28], or ¾-gmaps, is particularly well adapted to our formal descriptions and manipulations in -calculus. It should be noted that generalized maps of dimensions 2, 3 or 4 are today extensively used in modelers and applications [5][6][7][8]20]. …”

Section: Embedded Gmapsmentioning

confidence: 99%

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Parametrizing geometric objects using λ-calculus

Dufourd¹,

Luther²

2002

Proceedings of the 18th Spring Conference on Computer Graphics

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This paper focuses on the general parameterization in geometric modeling. We have adapted the -calculus formalism to an existing geometrical model which has an applicative representation: the generalized maps embedded in the plane. We investigated how this allows us to parameterize geometric objects by other objects, which can themselves be functional, rather than just by values such as size, shape or position. Thus, conditional, iterative, recursive and shared objects can be built and managed in an homogenous way. We have based the study on an interactive prototype implemented in Objective Caml. Its interface offers two consistent working views. The first interacts with geometric objects while the second interacts with the corresponding programs. We have examined in detail various higher-order operations where -calculus abstraction and application are used extensively to demonstrate how such objects can be built and manipulated. We will illustrate the force of our proposals using more complex constructions.

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“…Examples are the half-face of Lopes & Tavares (1997) (extension of the half-edge) and the Generalized Maps (G-Maps) (Bertrand et al, 1993;Lienhardt, 1994). The latter structure, which is actually valid to represent a broader class of objects called cellular quasi-manifolds, can be seen as a generalization to d-manifolds of boundary models as each k-cell (where 0 < k ≤ d) is recursively decomposed into cells of lower dimensionality, and the topological relationships between adjacent k-cells are kept.…”

Section: Irregular Decompositionmentioning

confidence: 99%