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Original Articles

A Hybrid Hierarchical Procedure for Composing Trivariate NURBS Solids

Pages 215-226 | Published online: 09 Aug 2013

References

  • Rayasam, M.; Srinivasan, V.; Subbarayan, G.: CAD inspired hierarchical partition of unity constructions for NURBS-based, meshless design, analysis and optimization, International Journal for Numerical Methods in Engineering, 72, 2007, 1452–1489, doi: 10.1002/nme.2046
  • Hughes, T.; Cottrell, J.; Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer methods in applied mechanics and engineering, 194, 2005, 4135–4195, doi: 10.1016/j.cma.2004.10.008
  • Morgan, O. T.; Subbarayan, G.; Anderson, D. C.: Symbolic trivariate solid construction using MathML, under preparation.
  • Martin, T.; Cohen, E.; Kirby, R.: Volumetric parameterization and trivariate B-spline fitting using harmonic functions, Computer Aided Geometric Design, 26, 2009, 648–664, doi: 10.1016/j.cagd.2008.09.008
  • Zhang, Y.; Bazilevs, Y.; Goswami, S.; Bajaj, C. L.; Hughes, T. J. R.: Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Computer methods in applied mechanics and engineering, 196, 2007, 2943–2959, doi: 10.1016/j.cma.2007.02.009
  • Sederberg, T. W.: Implicit and Parametric Curves for Computer Aided Geometric Design, PhD thesis, Purdue University, 1983.
  • Katz S.; Sederberg, T. W.: Genus of the intersection curve of two rational surface patches, Computer Aided Geometric Design, 5(3), 1988, 253–258, doi: 10.1016/0167-8396(88)90006-4
  • Patrikalakis, N.: Surface-to-surface intersections, IEEE Computer Graphics and Applications, 13, 1993, 89–95. doi: 10.1109/38.180122
  • Krishnan S.; Manocha, D.: An efficient surface intersection algorithm based on lower-dimensional formulation, ACM Transactions on Graphics, 16, 1997, 74–106, doi: 10.1145/237748.237751
  • Dokken, T.; Juettler, B.; Skytt, V.: Challenges in surface-surface intersections, in Computational Methods for Algebraic Spline Surfaces, 11–26, 2005, Springer Berlin Heidelberg.
  • Mukundan, H.; Ko, K. H.; Maekawa, T.; Sakkalis, T.; Patrikalakis, N. M.: Tracing surface intersections with validated ode system solver, in Proceedings of the ninth ACM symposium on Solid modeling and applications, SM '04, (Aire-la-Ville, Switzerland, Switzerland), 2004, 249–254.
  • Turner, J.: Accurate solid modeling using polyhedral approximations, IEEE Computer Graphics and Applications, 8, May, 1988, 14–28. doi: 10.1109/38.510
  • Farouki, R. T.; Han, C. Y.; Hass, J.; Sederberg, T. W.: Topologically consistent trimmed surface approximations based on triangular patches, Computer Aided Geometric Design, 21, May 2004, 459–478.
  • Wang, X.; Zhang, W.; Zhang, L.: Intersection of a ruled surface with a free-form surface, Numerical Algorithms, 46, 2007, 85–100, doi: 10.1007/s11075-007-9118-y
  • Puig-Pey, J.; Gálvez, A.; Iglesias, A.: A new differential approach for parametric-implicit surface intersection, Computational Science—ICCS 2003, 2003, 659–659.
  • Casciola G.; Morigi, S.: The trimmed NURBS age, Advances in Computation: Theory and Practice; Recent Trends in Numerical Analysis, Ed. D. Trigiante, Nova Science, 1999.
  • Casale, M.: Free-form Solid Modeling with trimmed surface patches, IEEE Computer Graphics and Applications, 1987, 33–43, doi: 10.1109/MCG.1987.277025
  • Weiler, K.: Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments, IEEE Computer Graphics and Applications, 5, 1985, 21–40, doi: 10.1109/MCG.1985.276271
  • Peterson, J. W.: Tessellation of NURB Surfaces, Graphics Gems 4, Heckbert, P. S. ed., Academic Press, Boston, 1994, 286–320.
  • Hertel, J. N. S.; Mantyla, M.; Mehlhorn, K.: Space sweep solves intersection of convex polyhedra, Acta Informatica, 21, December 1984, 501–519, doi: 10.1007/BF00271644

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