Abstract
The world of the geologist is, of course, multi-dimensional, but it is an unfortunate fact that traditional interpretation methods (e.g., contoured maps, cross sections, fence diagrams, isometric surfaces) limit the view of this world to two dimensions, or at best quasi-three dimensions (Fisher and Wales, 1990). This is to say spatially and temporally distributed data (especially data such as fluids or rock properties distributions) cannot always be efficiently visualized or analyzed in this setting (Raper, 1989b). Frequently the geologist finds he must envision the third- and sometimes fourth- (temporal) dimensions “in the mind’s eye”; mentally filling in the blanks or gaps between seetions, contoured maps or perhaps a series of vertically registered isometric surfaces. However well this has worked or not worked, the mental image or model is ephemeral, imprecise and unavailable to the next investigator for comparison (Kelk, 1991).
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References
Barlow, Andrew, 1989. Enhanced rendering productivity with NURBS: Computer Graphics Review, v. IV, no. 10, (Oct.), pp. 22–26.
Barteis, R.H., J.C. Beatty, and B.A. Barsky, 1978. An introduction to splines for use in computer graphics and Geometric modeling: Morgan Kaufmann, Los Altos, CA, 476p.
de Boor, Carl, 1978. A practical guide to splines: Springer-Verlag, New York.
Farin, Gerald, 1988. Curves and surfaces for computer aided Geometric design-a practical guide: Academic Press, Boston, 334p.
Faux, I.D., and M.J. Pratt, 1979. Computational geometry for design and manufacture: John Wiley, New York, 331p.
Fisher, T.R., and R.Q. Wales, 1990. 3-D solid modeling of sandstone reservoirs using NURBS-a case study of Noonen Ranch field, Denver basin, Colorado: Geobyte, v. 5, no.1, (Feb.), pp. 39–41.
Giloi, W.K., 1978. Interactive computer graphics-data structures, algorithms, languages: Prentice-Hall, Englewood Cliffs, NJ, 354p.
Harms, J.C., 1966. Stratigraphic traps in valley-fill, western Nebraska: AAPG Bulletin, v. 50, no. 10, pp. 2119–2149.
Herring, J.R, 1990. The mathematical modeling of spatial and non-spatial information in a geographie information system in Mark, D., and others, [eds.], Cognitive and linguistic aspects of geographic space: NATO ASI, Las Naras del Marques, Spain, July 8–12, 1990
Kavouras, Marinos, 1987. A spatial information system for the geosciences: Ph. D. Dissertation., The University of New Brunswick, 229p.
Kelk, Brian, 1990, Personal Communication
Kelk, Brian, 1992. 3-D Modeling in geosciences information systems: the problem in Turner, A.K., [ed.], Three-dimensional modeling with geoscientific information systems: NATO ARW, Santa Barbara, Ca., December 10–15,1989, pp. 29–38 (this volume).
Mallet, J.L., 1988. Three-dimensional graphie display of disconnected bodies: Mathematical Geology, v. 20, no. 8, pp. 977–990.
Mallet, J.L., 1992. GOCAD: a computer aided design program for geological applications in Turner, A.K., [ed.], Three-dimensional modeling with geoscientificinformation systems: NATO ARW, Santa Barbara, Ca., December 10–15, 1989, pp. 123–142 (this volume).
National Bureau of Standards, 1986. IGES “Initial Graphics Exchange Specifications, Version 3.0”: Doc. No. NB-SIR 86–3359, National Bureau of Standards, Gaithersburg, MD.
Paradis, A.R., and R.C. Beleher, 1990. Interactive volume modeling-a new product for 3-D modeling: Geobyte, v. 5, no. 1, pp. 42–44.
Penna, M.A., and R.R. Patterson, 1986. Projective geometry and its applications to computer Graphics: Prentice-Hall, Englewood Cliffs, NJ.
Piegi, Les, 1990. NURBS-a survey: IEEE Computer Graphics and Applications, (in press).
Potter, P.E., 1967. Sand bodies and sedimentary environments-a review: AAPG Bulletin, v. 51, no. 3, pp.337–365.
Raper, J.F., [ed.], 1989a. Three dimensional applications in geographieal information systems: Taylor and Francis, London, 189p.
Raper, J.F., 1989b. The 3-dimensional geoscientific mapping and modelling system: a conceptual design in Raper, J.F., [ed.], Three dimensional applications in geographical information systems: Taylor and Francis, London, pp. 11–19.
Raper, J.F., 1990. Appropriate design criteria for a 3-D geoscientific mapping and modeling system: CASY Colloquium Paper, Denver, May 10, 1990.
Rogers, D.F., and J.A. Adams, 1990. Mathematical elements for computer graphics (2nd ed.): McGraw-Hill, New York, 611p.
Samet, Ranan, 1989. Applications of spatial data structures-computer graphics, image processing, and GIS: Addison-Wesley, Reading, MA, 507p.
Schumaker, L.L., 1981. Spline functions-basic theory: John Wiley, New York, 553p.
Sonnenberg, S.A., 1987. Tectonic, sedimentary, and seismic models for D Sandstone, Zenith field area, Denver basin, Colorado: AAPG Bulletin, v. 71, no. 11, pp. 1366–1377.
Sonnenberg, S.A, and R.J. Weimer, 1981. Tectonics, sedimentation, and petroleum potential, northern Denver basin, Colorado, Wyoming, and Nebraska: Colorado School of Mines Quarterly, v. 76, 45p.
Smith, D.R., and A.R. Paradis, 1989. Three-dimensional GIS for the earth sciences in Raper, J.F., [ed.], Three dimensional applications in geographic information systems: Taylor and Francis, London, pp. 149–154.
Tiller, Wayne, 1983. Rational B-splines for curve and surface representation: IEEE Computer Graphics and Applications, v. 3, no. 6, (Sept.), pp. 61–69.
Turner, A.K., 1989. The role of three-dimensional geographic information systems in subsurface characterization for hydrogeological applications in Raper, J.F., [ed.], Three dimensional applications in geographical information systems: Taylor and Francis, London, pp. 115–129.
Turner, A.K., and J.S. Downey, 1990. Potential applications of three-dimensional geoscientific mapping and modeling systems to the Yucca Mountain project in USGS Bulletin “U. S. Geological Survey Earth-Science Studies for the Yucca Mountain Project — Selected Papers”, (in press).
Turner, A.K., Downey, J.S., and K.E. Kolm, 1990. Potential applications of threedimensional geoscientific mapping and modeling systems to hydrogeological assessments at Yucca Mountain, Nevada in NCGA GIS’ 90 Conference Proceedings, Houston, August 27–29, 1990, (to be published).
Van Driel, J.N., 1989. Three dimensional display of geologic data in Raper, J.F., [ed.], Three dimensional applications in geographical information systems: Taylor and Francis, London, pp. 1–9.
Versprille, K.J., 1975. Computer-aided design applications of the rational B-spline approximation form: Ph. D. Dissertation., Syracuse University.
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Fisher, T.R., Wales, R.Q. (1992). Three Dimensional Solid Modeling of Geo-Objects Using Non-Uniform Rational B-Splines (NURBS). In: Turner, A.K. (eds) Three-Dimensional Modeling with Geoscientific Information Systems. NATO ASI Series, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2556-7_9
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DOI: https://doi.org/10.1007/978-94-011-2556-7_9
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