Abstract
To achieve a tight integration of design and analysis, conformal solid T-spline construction with the input boundary spline representation preserved is desirable. However, to the best of our knowledge, this is still an open problem. In this paper, we provide its first solution. The input boundary T-spline surface has genus-zero topology and only contains eight extraordinary nodes, with an isoparametric line connecting each pair. One cube is adopted as the parametric domain for the solid T-spline. Starting from the cube with all the nodes on the input surface as T-junctions, we adaptively subdivide the domain based on the octree structure until each face or edge contains at most one face T-junction or one edge T-junction. Next, we insert two boundary layers between the input T-spline surface and the boundary of the subdivision result. Finally, knot intervals are calculated from the T-mesh and the solid T-spline is constructed. The obtained T-spline is conformal to the input T-spline surface with exactly the same boundary representation and continuity. For the interior region, the continuity is C 2 everywhere except for the local region surrounding irregular nodes. Several examples are presented to demonstrate the performance of the algorithm.
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Aigner M, Heinrich C, Jüttler B, Pilgerstorfer E, Simeon B, Vuong AV (2009) Swept volume parameterization for isogeometric analysis. In: IMA international conference on mathematics of surfaces XIII, pp 19–44
Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199(5–8): 229–263
Borden MJ, Scott MA, Evans JA, Hughes TJR (2011) Isogeometric finite element data structures based on B ézier extraction of NURBS. Int J Numer Methods Eng 87: 15–47
Dokken T, Lyche T, Pettersen KF (2012) Polynomial splines over locally refined box-partitions. Comput Aided Geom Des (submitted)
Escobar JM, Cascón JM, Rodríguez E, Montenegro R (2011) A new approach to solid modeling with trivariate T-splines based on mesh optimization. Comput Methods Appl Mech Eng 200(45–46): 3210–3222
Hua J, He Y, Qin H (2004) Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines. In: ACM symposium on solid modeling and applications, pp 47–58
Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: 4135–4195
Martin T, Cohen E, Kirby RM (2009) Volumetric parameterization and trivariate B-spline fitting using harmonic functions. Comput Aided Geom Des 26(6): 648–664
Scott MA, Borden MJ, Verhoosel CV, Sederberg TW, Hughes TJR (2011) Isogeometric finite element data structures based on B ézier extraction of T-splines. Int J Numer Methods Eng 88(2): 126–156
Sederberg TW, Zheng J, Bakenov A, Nasri A (2003) T-splines and T-NURCCs. ACM Trans Graph 22(3): 477–484
Sederberg TW, Cardon DL, Finnigan GT, North NS, Zheng J, Lyche T (2004) T-spline simplification and local refinement. In: ACM SIGGRAPH, pp 276–283
Wang W, Zhang Y, Liu L, Hughes TJR (2012a) Solid T-spline construction from boundary triangulations with arbitrary genus topology. In: In ACM symposium on solid and physical modeling (accepted)
Wang W, Zhang Y, Xu G, Hughes TJR (2012b) Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline. Comput Mech 50(1): 65–84
Zhang Y, Bazilevs Y, Goswami S, Bajaj CL, Hughes TJR (2007) Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comput Methods Appl Mech Eng 196(29–30): 2943–2959
Zhang Y, Wang W, Hughes TJR (2012) Solid T-spline construction from boundary representations for genus-zero geometry. Comput Methods Appl Mech Eng. doi:10.1016/j.cma.2012.01.014
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Zhang, Y., Wang, W. & Hughes, T.J.R. Conformal solid T-spline construction from boundary T-spline representations. Comput Mech 51, 1051–1059 (2013). https://doi.org/10.1007/s00466-012-0787-6
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DOI: https://doi.org/10.1007/s00466-012-0787-6