“Watertight trimmed NURBS” by Sederberg, Finnigan, Li, Lin and Ipson

  • ©Thomas (Tom) W. Sederberg, G Thomas Finnigan, Xin Li, Hongwei Lin, and Heather Ipson

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Title:

    Watertight trimmed NURBS

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Abstract:


    This paper addresses the long-standing problem of the unavoidable gaps that arise when expressing the intersection of two NURBS surfaces using conventional trimmed-NURBS representation. The solution converts each trimmed NURBS into an untrimmed T-Spline, and then merges the untrimmed T-Splines into a single, watertight model. The solution enables watertight fillets of NURBS models, as well as arbitrary feature curves that do not have to follow iso-parameter curves. The resulting T-Spline representation can be exported without error as a collection of NURBS surfaces.

References:


    1. Bjorck, A. 1996. Numerical Methods for Least squares Problems. SIAM.Google Scholar
    2. DeRose, T. D., Kass, M., and Truong, T. 1998. Subdivision surfaces in character animation. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 85–94. Google ScholarDigital Library
    3. Farouki, R. T., Han, C. Y., Hass, J., and Sederberg, T. W. 2004. Topologically consistent trimmed surface approximations based on triangular patches. Computer Aided Geometric Design 21, 5, 459–478. Google ScholarDigital Library
    4. Farouki, R. T. 1999. Closing the gap between CAD model and downstream application (report on the SIAM Workshop on Integration of CAD and CFD, UC Davis, April 12–13, 1999). SIAM News 32, 5, 1–3.Google Scholar
    5. Hunter, G. M., and Steiglitz, K. 1979. Operations on images using quad trees. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 2 (April), 145–153.Google Scholar
    6. Kasik, D. J., Buxton, W., and Ferguson, D. R. 2005. Ten CAD model challenges. IEEE Computer Graphics and Applications 25, 2, 81–92. Google ScholarDigital Library
    7. Katz, S., and Sederberg, T. W. 1988. Genus of the intersection curve of two rational surface patches. Computer Aided Geometric Design 5, 253–258. Google ScholarDigital Library
    8. Krishnan, S., and Manocha, D. 1996. Efficient representations and techniques for computing b-rep’s of csg models with nurbs primitives. In Proc. of CSG’96, 101–122.Google Scholar
    9. Krishnan, S., and Manocha, D. 1997. An efficient surface intersection algorithm based on lower-dimensional formulation. ACM Transactions on Graphics 16, 1 (Jan.), 74–106. Google ScholarDigital Library
    10. Krishnan, S., Manocha, D., Gopi, M., and Keyser, J. 2001. Boole: A boundary evaluation system for Boolean combinations of sculptured solids. International Journal on Computational Geometry and Applications 11, 1, 105–144.Google ScholarCross Ref
    11. Kristjansson, D., Biermann, H., and Zorin, D. 2001. Approximate Boolean operations on free-form solids. In Proceedings of ACM SIGGRAPH 2001, E. Fiume, Ed., Computer Graphics Proceedings, Annual Conference Series, 185–194. Google ScholarDigital Library
    12. Kumar, S. 1996. Interactive rendering of parametric spline surfaces. PhD thesis, The University of North Carolina at Chapel Hill. Google ScholarDigital Library
    13. Litke, N., Levin, A., and Schröder, P. 2001. Trimming for subdivision surfaces. Computer Aided Geometric Design 18, 5 (June), 463–481. Google ScholarDigital Library
    14. Loop, C. 2004. Second order smoothness over extraordinary vertices. In Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 165–174. Google ScholarDigital Library
    15. Moreton, H. 2001. Watertight tessellation using forward differencing. In HWWS ’01: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, ACM, New York, NY, USA, 25–32. Google ScholarDigital Library
    16. Müller, K., Reusche, L., and Fellner, D. 2006. Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces. ACM Transactions on Graphics 25, 2 (Apr.), 268–292. Google ScholarDigital Library
    17. Müller, K., Reusche, L., and Fellner, D. 1999. Planning Report: Interoperability Cost Analysis of the US Automotive Supply Chain. National Institute of Standards and Technology.Google Scholar
    18. Patrikalakis, N. M., and Maekawa, T. 2002. Intersection problems. In Handbook of Computer Aided Geometric Design, North-Holland, G. Farin, J. Hoschek, and M.-S. Kim, Eds., 623–649.Google Scholar
    19. Peters, J. 2000. Patching Catmull-Clark meshes. In Proceedings of ACM SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference Series, 255–258. Google ScholarDigital Library
    20. Samet, H. 1984. The quadtree and related hierarchical data structures. ACM Computing Surveys 16, 2, 187–260. Google ScholarDigital Library
    21. Sederberg, T. W., Li, X., Lin, H., and Finnigan, G. T. Nonuniform NURBS. In Preparation.Google Scholar
    22. Sederberg, T., Anderson, D., and Goldman, R. 1984. Implicit representation of parametric curves and surfaces. Computer Vision, Graphics and Image Processing 28, 72–84.Google ScholarCross Ref
    23. Sederberg, T. W., Zheng, J., Sewell, D., and Sabin, M. A. 1998. Non-uniform recursive subdivision surfaces. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 387–394. Google ScholarDigital Library
    24. Sederberg, T. W., Zheng, J., Bakenov, A., and Nasri, A. 2003. T-Splines and T-NURCCs. ACM Transactions on Graphics 22, 3 (July), 477–484. Google ScholarDigital Library
    25. Sederberg, T. W., Cardon, D. L., Finnigan, G. T., North, N. S., Zheng, J., and Lyche, T. 2004. T-spline simplification and local refinement. ACM Transactions on Graphics 23, 3 (August). Google ScholarDigital Library
    26. Singh, K., and Fiume, E. L. 1998. Wires: A geometric deformation technique. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 405–414. Google ScholarDigital Library
    27. Song, Q., and Wang, J. 2007. Generating g
    n parametric blending surfaces based on partial reparameterization of base surfaces. Comput. Aided Des. 39, 11, 953–963. Google ScholarDigital Library
    28. Song, X., Sederberg, T. W., Zheng, J., Farouki, R. T., and Hass, J. 2004. Linear perturbation methods for topologically consistent representations of free-form surface intersections. Computer Aided Geometric Design 21, 3, 303–319. Google ScholarDigital Library
    29. Stam, J. 1998. Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 395–404. Google ScholarDigital Library
    30. Wang, W., Pottmann, H., and Liu, Y. 2006. Fitting B-spline curves to point clouds by curvature-based squared distance minimization. ACM Transactions on Graphics 25, 2 (Apr.), 214–238. Google ScholarDigital Library


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