Conformal solid T-spline construction from boundary T-spline representations

Authors:
Yongjie Zhang;Wenyan Wang;Thomas J. Hughes
Affiliations:
Department of Mechanical Engineering, Carnegie Mellon University Pittsburgh, Pittsburgh, USA 15213;Department of Mechanical Engineering, Carnegie Mellon University Pittsburgh, Pittsburgh, USA 15213;Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA 78712
Venue:
Computational Mechanics
Year:
2013

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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.