Skip to main content
SpringerLink
Log in

Radial Supershapes for Solid Modeling

  • Surface Modeling and Computational Geometry
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

In the previous work, an efficient method has been proposed to represent solid objects as multiple combinations of globally deformed supershapes. In this paper, this framework is applied with a new supershape implicit function that is based on the notion of radial distance and results are presented on realistic models composed of hundreds of hierarchically globally deformed supershapes. An implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives’ implicit representations using R-function theory. The surface corresponding to the zero-set of the implicit equation is efficiently and directly polygonized using the primitives’ parametric forms. Moreover, hierarchical global deformations are considered to increase the range of shapes that can be modeled. The potential of the approach is illustrated by representing complex models composed of several hundreds of primitives inspired from CAD models of mechanical parts.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hoffmann C M. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers Inc., 1989.

  2. Rossignac J R. Constraints in constructive solid geometry. In Proc. the 1986 Workshop on Interactive 3D Graphics, Chapel Hill, North Carolina, USA, 1986, pp.93–110.

  3. Rossignac J R, Requicha A A G. Constructive non-regularized geometry. Computer-Aided Design, 1991, 23(1): 21–32.

    Google Scholar 

  4. Rossignac J R, Voelcker H B. Active zones in csg for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms. ACM Trans. Graphics, 1989, 8(1): 51–87.

    Google Scholar 

  5. Ohtake Y, Belyaev A, Pasko A. Dynamic mesh optimization for polygonized implicit surfaces with sharp features. The Visual Computer, 2003, 19(2-3): 115–126.

    Google Scholar 

  6. B Wyvill, K Van Overveld. Polygonization of implicit surfaces with constructive solid geometry. J. Shape Modelling, 1996, 2(4): 257–274.

    Google Scholar 

  7. Krishnan S, Manocha D, Gopi M, Culver T, Keyser J. Boole: A boundary evaluation system for Boolean combinations of sculptured solids. International Journal of Computational Geometry & Applications, 2001, (1): 105–144.

  8. Piegl L, Tiller W. The NURBS Book. Second Edition, Springer, 1997.

  9. Biermann H, Kristjansson D, Zorin D. Approximate Boolean operations on free-form solids. In Proc. SIGGRAPH′01, Los Angeles, CA, USA, 2001, pp.185–194.

  10. Adzhiev V, Kazakov M, Pasko A, Savchenko V. Hybrid system architecture for volume modeling. Computers & Graphics, 2000, 24(1): 194–203.

    Article  Google Scholar 

  11. Allègre R, Barbier A, Galin E, Akkouche S. A hybrid shape representation for free-form modeling. In Proc. Shape Modeling International, Genova, Italy, June 7–9, 2004, pp.7–18.

  12. Barr A H. Superquadrics and angle-preserving transformations. IEEE Computer Graphics and Applications, 1981, 1(1): 481–484.

    MathSciNet  Google Scholar 

  13. Barr A H. Global and local deformation of solid primitives. Computer Graphics, 1984, 18(3): 21–30.

    Google Scholar 

  14. Jaklič A, Leonardis A, Solina F et al. Segmentation and Recovery of Superquadrics. Dordrecht: Kluwer Academic Publisher, 2000.

    Google Scholar 

  15. Jaklič A, Solina F. Moments of superellipsoids and their application to range image registration. IEEE Trans. Systems, Man, and Cybernetics, 2003, 33(4): 648–657.

    Google Scholar 

  16. Montiel M E, Aguado A S, Zaluska E. Surface subdivision for generating superquadrics. The Visual Computer, 1998, 14(1): 1–17.

    Article  Google Scholar 

  17. Gielis J, Beirinckx B, Bastiaens E. Superquadrics with rational and irrational symmetry. In Proc. 8th ACM Symp. Solid Modeling and Applications, Seattle, USA, 2003, pp.262–265.

  18. Gielis J. A generic geometric transformation that unifies a wide range of natural and abstract shapes. American Journal of Botany, 2003, 90: 333–338.

    Google Scholar 

  19. Fougerolle Y D, Gribok A, Foufou S, Truchetet F, Abidi M A. Boolean operations with implicit and parametric representation of primitives using R-functions. IEEE Trans. Visualization and Computer Graphics, 2005, 11(5): 529–539.

    Google Scholar 

  20. Ricci A. A constructive geometry for computer graphics. The Computer Journal, 1972, 16(2): 157–160.

    MathSciNet  Google Scholar 

  21. Blinn J F. A generalization of algebraic surface drawing. ACM Trans. Graphics, 1982, 1(3): 235–256.

    Article  Google Scholar 

  22. Pasko A, Adzhiev V, Sourin A et al., Savchenko V. Function representation in geometric modeling: Concepts, implementation and applications. The Visual Computer, 1995, 11(8): 429–446.

    Article  Google Scholar 

  23. Rvachev V L. Geometric Applications of Logic Algebra. Naukova Dumka, 1967. (In Russian)

  24. Shapiro V. Theory of R-functions and applications: A primer. Technical Report TR91-1219, Computer Science Department, Cornell University, Ithaca, NY, 1991.

    Google Scholar 

  25. Shapiro V, Tsukanov I. Implicit functions with guaranteed differential properties. In Symposium on Solid Modeling and Applications, Ann Arbor, Michigan, USA, 1999, pp.258–269.

  26. Wyvill B, Guy A, Galin E. Extending the CSG tree — Warping, blending and Boolean operations in an implicit surface modeling system. Computer Graphics Forum, 1999, 18(2): 149–158.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Le2i Lab. UMR CNRS 5158, Université de Bourgogne, 12 rue de la fonderie, 71200, Le Creusot, France

    Yohan D. Fougerolle, Sebti Foufou & Frédéric Truchetet

  2. IRIS Lab., The University of Tennessee, Ferris Hall, Knoxville, 37996, TN, U.S.A.

    Andrei Gribok & Mongi A. Abidi

Authors
  1. Yohan D. Fougerolle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrei Gribok
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebti Foufou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Frédéric Truchetet
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mongi A. Abidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yohan D. Fougerolle.

Additional information

A preliminary version of this paper appeared in Proc. Pacific Graphics 2005, Macau.

Yohan D. Fougerolle received his M.S. degree in electrical engineering from the University of Burgundy, Dijon, France, in 2002. He is a Ph.D. candidate in electrical and computer engineering at the University of Burgundy, Le Creusot, France and was a visiting research scholar in the Imaging, Robotics, and Intelligent Systems Laboratory, Knoxville, Tennessee from 2002 to 2005. His research interests include computer vision, solid modeling and surface reconstruction.

Andrei Gribok is a research assistant professor in the Department of Computer and Electrical Engineering at the University of Tennessee, Knoxville and also holds a position of an adjunct professor of statistics in the Department of Statistics at the same university. His area of expertise is inverse and ill-posed problems in engineering, statistical learning and model misspecification in statistics. His publications list includes three book chapters and numerous journal and conference papers. Dr. Gribok has a B.S. degree in system science and an M.S. degree in nuclear engineering from the Moscow Institute of Physics and Engineering. He received his Ph.D. degree from the Moscow Institute of Biological Physics in the area of acoustical pattern recognition, artificial intelligence and nondestructive testing. He has 15 years of experience in industry as well as in academia. Dr. Gribok worked as an invited scientist in the Cadarache Nuclear Research Centre in France where his work focused on nuclear power plants monitoring, diagnostics and ultrasonic imaging.

Sebti Foufou received his Ph.D. degree in computer science in 1997 from the University of Claude Bernard Lyon I, France. He has been working as an associate professor in the Computer Science Department at the University of Burgundy, France. His research interests concern geometric modeling and CAD-CAM topics and surfaces blending, subdivision surfaces, and geometric constraints solving. Currently, he is working as a temporary guest researcher at the National Institute of Standards and Technology, Gaithersburg, Maryland, on smart machining systems, tolerances, assembly modeling, and PLM.

Frédéric Truchetet received his M.S. degree in physics from Dijon University, France, in 1973 and a Ph.D. degree in electronics from the same university in 1977. He was for two years with Thomson-CSF as a research engineer and he is currently full professor in Le2i. His research interests are focused on image processing for artificial vision inspection and particularly on wavelets transform, multiresolution edge detection and image compression. He has authored and co-authored more than 150 international publications, three books, and holds one patent. He is a member of GRETSI, ASTI, IEEE, SPIE, Chairman of SPIE’s conference on wavelet applications in industrial processing and member of numerous technical committees of international conferences in the area of computer vision.

Mongi A. Abidi is a professor and deputy director of the Department of Electrical and Computer Engineering, directs activities in the Imaging, Robotics, and Intelligent Systems Laboratory. He received his Ph.D. degree in electrical engineering at The University of Tennessee in 1987, M.S. degree in electrical engineering from the University of Tennessee in 1985, and principal engineer in electrical engineering at the National Engineering School of Tunis, Tunisia in 1981. Dr. Abidi conducts research in the field of 3D imaging, specifically in the areas of scene building, scene description, and data visualization.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fougerolle, Y.D., Gribok, A., Foufou, S. et al. Radial Supershapes for Solid Modeling. J Comput Sci Technol 21, 238–243 (2006). https://doi.org/10.1007/s11390-006-0238-y

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11390-006-0238-y

Keywords

Search

Navigation