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Rational splines and multidimensional geologic modeling

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Computer Graphics in Geology

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 41))

Abstract

Traditional 2D and 2.5D methods of geologic interpretation are no longer adequate to visualize and interpret the wealth of multidimensional data available to the geologist. This has created a need for computer-based methods of 3D analysis (3D GIS) with capabilities which allow the geologist to integrate the data, interpret geologic features, and visualize attributes in their true 3D spatial relationships.

These requirements are met by solid volume modeling techniques. Most use a semi-transparent depiction of both surface and internal features, and have no manual equivalents. One system which has been used to create stratigraphic and structural geologic models is based on nonuniform rational B-splines (NURBS). This technology is an alternative to more well known solids modeling approaches (e.g., polygon meshes, 3D grid and isosurfaces, voxels), and holds promise of providing a unified basis for geologic modeling.

NURBS are piecewise, parametric polynomials that can describe all large complex surfaces and solids, and they provide a single, uniform and precise mathematical form capable of representing the free-form curves, surfaces, and solids necessary for geologic modeling. Splines are n-dimensional, making them extensible to representation of distributed attributes within a defined solid. Functional integration between graphic elements (e.g., points, lines, wireframes, surfaces, solids) is also possible because the elements share a common mathematical basis.

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Author information

Authors and Affiliations

  1. Intergraph Corporation, Mail Stop IW-17a5, 35894, Huntsville, Alabama, U.S.A.

    T. R. Fisher & R. Q. Wales

  2. Intergraph Corporation, Suite 200, 675 Bering Drive, 77057, Houston, Texas, U.S.A.

    T. R. Fisher & R. Q. Wales

Authors
  1. T. R. Fisher
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  2. R. Q. Wales
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Reinhard Pflug John W. Harbaugh

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© 1992 Springer-Verlag

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Fisher, T.R., Wales, R.Q. (1992). Rational splines and multidimensional geologic modeling. In: Pflug, R., Harbaugh, J.W. (eds) Computer Graphics in Geology. Lecture Notes in Earth Sciences, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0117782

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  • DOI: https://doi.org/10.1007/BFb0117782

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55190-4

  • Online ISBN: 978-3-540-46768-7

  • eBook Packages: Springer Book Archive

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