Skip to main content
SpringerLink
Log in

A Differential Method for Parametric Surface Intersection

  • Conference paper
Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3044))

Included in the following conference series:

Abstract

In this paper, a new method for computing the intersection of parametric surfaces is proposed. In our approach, this issue is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs), which are to be numerically integrated. In order to determine the initial value for this system, a simple procedure based on the vector field associated with the gradient of the distance function between points lying on each of the parametric surfaces is described. Such a procedure yields a starting point on the nearest branch of the intersection curve. The performance of the presented method is analyzed by means of some illustrative examples that contain many of the most common features found in parametric surface intersection problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdel-Malek, K., Yeh, H.J.: On the determination of starting points for parametric surface intersections. Computer Aided Design 28(1), 21–35 (1997)

    Article  Google Scholar 

  2. Anand, V.: Computer Graphics and Geometric Modeling for Engineers. John Wiley and Sons, New York (1993)

    Google Scholar 

  3. Bajaj, C., Hoffmann, C.M., Hopcroft, J.E.H., Lynch, R.E.: Tracing surface intersections. Computer Aided Geometric Design 5, 285–307 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Barnhill, R.E., Kersey, S.N.: A marching method for parametric surface/surface intersection. Computer Aided Geometric Design 7, 257–280 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barnhill, R.E. (ed.): Geometry Procesing for Design and Manufacturing. SIAM, Philadelphia (1992)

    Google Scholar 

  6. Chandru, V., Dutta, D., Hoffmann, C.M.: On the geometry of Dupin cyclides. The Visual Computer 5, 277–290 (1989)

    Article  Google Scholar 

  7. Choi, B.K., Jerard, R.B.: Sculptured Surface Machining. Theory and Applications. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  8. Farin, G.: An SSI bibliography. In: Barnhill, R. (ed.) Geometry Processing for Design and Manufacturing, pp. 205–207. SIAM, Philadelphia (1992)

    Google Scholar 

  9. Farin, G., Hoschek, J., Kim, M.S. (eds.): The Handbook of Computer-Aided Geometric Design. North-Holland, Amsterdam (2002)

    Google Scholar 

  10. Grandine, T.A., Klein, F.W.: A new approach to the surface intersection problem. Computer Aided Geometric Design 14, 111–134 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Grandine, T.A.: Applications of contouring. SIAM Review 42, 297–316 (2000)

    Article  MathSciNet  Google Scholar 

  12. Hoschek, J., Lasser, D.: Computer-Aided Geometric Design. A.K. Peters, Wellesley (1993)

    MATH  Google Scholar 

  13. Iglesias, A.: Computational methods for geometric processing of surfaces: blending, offsetting, intersection, implicitization. In: Sarfraz, M. (ed.) Advances in Geometric Modeling, ch. 5, John Wiley and Sons, Chichester (2003)

    Google Scholar 

  14. The Mathworks Inc: Using Matlab. Natick, MA (1999)

    Google Scholar 

  15. Kriezis, G.A., Patrikalakis, N.M., Wolters, F.E.: Topological and differentialequation methods for surface reconstructions. Computer Aided Design 24(1), 41–55 (1992)

    Article  MATH  Google Scholar 

  16. Patrikalakis, N.M., Maekawa, T.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  17. Piegl, L., Tiller, W.: The NURBS Book. Springer, Heidelberg (1997)

    Google Scholar 

  18. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes, 2nd edn. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  19. Pratt, M.J., Geisow, A.D.: Surface-surface intersection problems. In: Gregory, J.A. (ed.) The Mathematics of Surfaces, pp. 117–142. Clarendon Press, Oxford (1986)

    Google Scholar 

  20. Puig-Pey, J., Gálvez, A., Iglesias, A.: A new differential approach for parametricimplicit surface intersection. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 897–906. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  21. Sederberg, T.W., Meyers, R.J.: Loop detection in surface patch intersections. Computer Aided Geometric Design 5, 161–171 (1988)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, E-39005, Santander, Spain

    A. Gálvez, J. Puig-Pey & A. Iglesias

Authors
  1. A. Gálvez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Puig-Pey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Iglesias
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gálvez, A., Puig-Pey, J., Iglesias, A. (2004). A Differential Method for Parametric Surface Intersection. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24709-8_69

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24709-8_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22056-5

  • Online ISBN: 978-3-540-24709-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation