“DINUS: Double Insertion, Non-Uniform, Stationary Subdivision Surfaces” by Müller, Fuenfzig, Reusche, Hansford, Farin, et al. …

  • ©Kerstin Müller, Christoph Fuenfzig, Lars Reusche, Dianne Hansford, Gerald Farin, and Hans J. Hagen




    DINUS: Double Insertion, Non-Uniform, Stationary Subdivision Surfaces



    The Double Insertion, Nonuniform, Stationary subdivision surface (DINUS) generalizes both the nonuniform, bicubic spline surface and the Catmull-Clark subdivision surface. DINUS allows arbitrary knot intervals on the edges, allows incorporation of special features, and provides limit point as well as limit normal rules. It is the first subdivision scheme that gives the user all this flexibility and at the same time all essential limit information, which is important for applications in modeling and adaptive rendering. DINUS is also amenable to analysis techniques for stationary schemes. We implemented DINUS as an Autodesk Maya plugin to show several modeling and rendering examples.


    1. Biermann, H., Martin, I. M., Zorin, D., and Bernardini, F. 2001. Sharp features on multiresolution subdivision surfaces. In Proceedings of the Pacific Graphics Conference. 61–77.
    2. Cashman, T. J., Dodgson, N. A., and Sabin, M. A. 2007. Non-uniform B-spline subdivision using refine and smooth. In IMA Conference on the Mathematics of Surfaces, R. R. Martin, M. A. Sabin, and J. R. Winkler, Eds. Lecture Notes in Computer Science, vol. 4647. Springer, 121–137.
    3. Cashman, T. J., Dodgson, N. A., and Sabin, M. A. 2009. A symmetric, non-uniform, refine and smooth subdivision algorithm for general degree B-splines. Comput.-Aided Geom. Des. 26 1, 94–104.
    4. Catmull, E. and Clark, J. 1978. Recursively generated B-spline surfaces on arbitrary topological meshes. Comput.-Aided Des. 10, 350–355.
    5. Farin, G. 2002. Curves and Surfaces for CAGD, 5th ed. Morgan Kaufmann Publishers.
    6. Hoppe, H., DeRose, T., Duchamp, T., Halstead, H., Jin, H., McDonald, J., Schweitzer, J., and Stuetzle, W. 1994. Piecewise smooth surface reconstruction. In Proceedings of SIGGRAPH Conference. 295–302.
    7. Karciauskas, K., Peters, J., and Reif, U. 2004. Shape characterization of subdivision surfaces: Case studies. Comput.-Aided Geom. Des. 21, 6, 601–614.
    8. Lane, J. and Riesenfeld, R. 1980. A theoretical development for the computer generation and display of piecewise polynomial surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 2, 1, 35–46.
    9. Loop, C. 2002. Smooth ternary subdivision of triangle meshes. In Proceedings of the Conference on Curves and Surfaces Fitting: Saint-Malo. 295–302.
    10. Müller, K., Reusche, L., and Fellner, D. 2006. Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces. ACM Trans. Graph. 25, 2, 268–292.
    11. Ni, T., Nasri, A. H., and Peters, J. 2007. Ternary subdivision for quadrilateral meshes. Comput.-Aided Geom. Des. 24, 6, 361–370.
    12. Schaefer, S. and Goldman, R. 2009. Non-uniform subdivision for B-splines of arbitrary degree. Comput.-Aided Geom. Des. 26, 1, 75–81.
    13. Sederberg, T. W., Cardon, D. L., Zheng, J., and Lyche, T. 2004. T-Spline simplification and local refinement. In Proceedings of SIGGRAPH Conference. 276–283.
    14. Sederberg, T. W., Sewell, D., and Sabin, M. 1998. Non-uniform recursive subdivision surfaces. In Proceedings of SIGGRAPH Conference. 387–394.
    15. Sederberg, T. W., Zheng, J., Bakenov, A., and Nasri, A. 2003. T-Splines and T-NURCCs. In Proceedings of SIGGRAPH Conference. 477–484.
    16. Zorin, D. and Schröder, P. 1999. Subdivision for modeling and animation. In ACM SIGGRAPH 1999 Course Notes.

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