, Volume 7, Issue 1, pp 55–71 | Cite as

Interpretive Tools for 3-D Structural Geological Modeling Part I: Bézier-Based Curves, Ribbons and Grip Frames

  • E.A. de Kemp
  • K.B. Sprague


Interpreting the geometry of geological objects is a standard activity of field-based geologists. We present new graphics tools that will aid in extending this activity from 2-D geological mapping into a 3-D environment. Much of the existing 3-D geological modeling software supports the construction of objects with the input of dense control data. However, for regional mapping and near mine exploration work, sparse data is the norm. Tools are required therefore, which give the expert interpreter full control of the graphics objects, while at the same time constraining interpretations to specific control data from field observations. We present the initial results of a software design and programming project for the visualization of complex regional scale geologic objects using Bézier-based graphics tools that are optimized for sparse data interpretation. We also introduce the concept of a structural ribbon, which is a 3-D extended map trace, along with methods for the optimization of surface construction using graphical grip frames.

3-D Bézier interpolation ribbons grip frames surface modeling structural geology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.M. Stesky. Spheristat 2: User Manual, Pangaea Scientific: Brockville, Ontario, Canada, 1998.Google Scholar
  2. 2.
    F.C. Phillips. The Use of Stereographic Projection in Structural Geology, 3rd edition. Edward Arnold: London, U.K., 1971.Google Scholar
  3. 3.
    C.M. Knox-Robinson and S. Gardoll. “GIS-stereoplot: An interactive steronet plotting module for Arcview 3.0 geographic information system,” Computers and Geosciencs, Vol. 24(3):243–250, 1998.Google Scholar
  4. 4.
    A.B. Smith and S.J. Gardoll. “Structural analysis in mineral exploration using a geographic information systems-adapted stereographic-projection plotting program,” Australian Journal of Earth Sciences, Vol. 44:445–452, 1997.Google Scholar
  5. 5.
    A.K. Lobeck. Block Diagrams. Emerson-Trussell: Amherst, USA, 1958.Google Scholar
  6. 6.
    D. Ragan. Structural Geology—An Introduction to Geometrical Techniques, 3rd edition. John Wiley and Sons: New York, USA, 1985.Google Scholar
  7. 7.
    K.S. Dueholm, A.A. Gardeand, and A.K. Pedersen. “Preparation of accurate geological and structural maps, cross-sections or block diagrams from colour slides, using multi-model photogrammetry,” Journal of Structural Geology, Vol.15(7):933–937, 1993.Google Scholar
  8. 8.
    K.S. Hatch. “Creating an isometric block diagram from a topographic map using Aldus Freehand,” Bulletin, Society of University Cartographers, Vol. 28(1):37–39, 1994.Google Scholar
  9. 9.
    E.M. Schetselaar. “Computerized field-data capture and GIS analysis for generation of cross sections in 3–D perspective views,” Computers & Geosciences, Vol. 21(5):687–701, 1995.Google Scholar
  10. 10.
    S. Marshak and G. Mitra. Basic Methods of Structural Geology. Prentice Hall: Englewood Cliffs, New Jersey, USA, 1988.Google Scholar
  11. 11.
    C. Nash, P. Leeming, H. Kotasek, and R. Carey. “Integrated interpretation of imaged airborne geophysical survey and remote sensing data with the aid of vectorized CAD/GIS coverages: Halls Creek Mobile Belt, Australia,” Proceedings Volume I, Eleventh Thematic Conference on Applied Geologic Remote Sensing, Las Vegas, Nevada, 343–352, 1996.Google Scholar
  12. 12.
    E.M. Schetselaar. “Shear zone mapping using ERS-1 SAR images of the Paleoproterozoic Taltson magmatic zone, Canadian Shield, northeastern Alberta,” International Institute for Aerospace Survey and Earth Sciences Survey (ITC) Journal, Vol. 2:166–175, 1996.Google Scholar
  13. 13.
    J.R. Harris, C. Bowie, A.N. Rencz, D. Viljoen, P. Huppé, G. Labelle, J. Broome, and A.B. Baker. “Production of image maps for earth science applications,” Proceedings, Tenth Thematic Conference on Geologic Remote Sensing, San Antonio, Texas, Vol. 2:247–257, May 9–12, 1994.Google Scholar
  14. 14.
    W.J. McGaughey and M.A. Vallée. “3–D ore delineation in three dimensions”, in Proceedings of Exploration 97: Fourth Decennial Conference on Mineral Exploration, Toronto, Canada, 639–650, 1997.Google Scholar
  15. 15.
    E. Argand. “La tectonique de l'Asie. Congrès géologique international, Belgique,” Comptes Rendus, 171–372, 1922.Google Scholar
  16. 17.
    G.E. Farin. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, Second edition, Academic Press, Inc.: San Diego, CA, USA, 1990.Google Scholar
  17. 18.
    D.G. De Paor. “Bézier curves and geological design,” in Structural Geology and Personal Computers, Pergamon Press, 389–417, 1996.Google Scholar
  18. 19.
    E.A. de Kemp. 3–D Integration and Visualization of Structural Field Data: Tools For Regional Subsurface Mapping. Ph.D. Thesis, Université du Québec à Chicoutimi, Canada, 2000.Google Scholar
  19. 20.
    E.A. de Kemp. “3–D visualization of structural field data: Examples from the Archean Caopatina Formation, Abitibi greenstone belt, Québec, Canada,” Computers and Geosciences, Vol. 26:509–530, 2000.Google Scholar
  20. 21.
    A. Rockwood and P. Chambers. Interactive Curves and Surfaces: A MultiMedia Tutorial on CAGD, Morgan Kaufmann Publishers, Inc.: San Franciso, C.A., USA, 1996.Google Scholar
  21. 22.
    J.-L. Mallet. “Discrete smooth interpolation,” ACM Transactions on Graphics, Vol. 8(2):121–144, 1989.Google Scholar
  22. 23.
    M.R. St-Onge, D.J. Scott, N. Wodicka, and S.B. Lucas. “Geology of the McKellar Bay-Wight Inlet-Frobisher Bay area, southern Baffin Island, Northwest Territories. Canadian Shield/Bouclier canadien,” Geological Survey of Canada, Current Research, C:43–53, 1998.Google Scholar
  23. 24.
    E.A. de Kemp. “Variable 3–D geometrical projection of curvilinear geological features through direction cosine interpolation of structural field observations,” Computers and Geosciences, Vol. 24(3):269–284, 1998.Google Scholar
  24. 25.
    E.A. de Kemp. “Visualization of complex geological structures using 3–D Bézier construction tools,” Computers and Geosciences, Vol. 25(4):581–597, 1999.Google Scholar
  25. 26.
    E.A. de Kemp, D. Corrigan, and M.R. St-Onge. “Evaluating the potential for 3D structural modelling of the Archean and Paleoproterozoic rocks of Central Baffin Island, Nunavut, Canada,” Geological Survey of Canada, Current Research, C24:9, 2001.Google Scholar
  26. 27.
    T. Ackland. “On osculatory interpolation, where the given values of the function are at unequal intervals,” Journal of the Institute of Actuaries, Vol. 49:369–375, 1915.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • E.A. de Kemp
    • 1
  • K.B. Sprague
    • 2
  1. 1.ESS-GSC Continental Geoscience Division—Geological Survey of CanadaOttawa
  2. 2.ESS-PPISB-ESS_INFO Databases and Geospatial Applications—Ottawa

Personalised recommendations