Adaptive CAD model (re-)construction with THB-splines

Computer Aided Design (CAD) software libraries rely on the tensor-product NURBS model as standard spline technology. However, in applications of industrial complexity, this mathematical model does not provide sufficient flexibility as an effective geometric modeling option. In particular, the multivariate tensor-product construction precludes the design of adaptive spline representations that support local refinements. Consequently, many patches and trimming operations are needed in challenging applications. The investigation of generalizations of tensor-product splines that support adaptive refinement has recently gained significant momentum due to the advent of Isogeometric Analysis (IgA) [2], where adaptivity is needed for performing local refinement in numerical simulations. Moreover, traditional CAD models containing many small (and possibly trimmed) patches are not directly usable for IgA. Truncated hierarchical B-splines (THB-splines) provide the possibility of introducing different levels of resolution in an adaptive framework, while simultaneously preserving the main properties of standard B-splines. We demonstrate that surface fitting schemes based on THB-spline representations may lead to significant improvements for the geometric (re-)construction of critical turbine blade parts. Furthermore, the local THB-spline evaluation in terms of B-spline patches can be properly combined with commercial geometric modeling kernels in order to convert the multilevel spline representation into an equivalent - namely, exact - CAD geometry. This software interface fully integrates the adaptive modeling tool into CAD systems that comply with the current NURBS standard. It also paves the way for the introduction of isogeometric simulations into complex real world applications.

[1]  Jiansong Deng,et al.  Dimensions of spline spaces over T-meshes , 2006 .

[2]  Tom Lyche,et al.  Polynomial splines over locally refined box-partitions , 2013, Comput. Aided Geom. Des..

[3]  Harald Schoenenborn,et al.  Determination of Blade-Alone Frequencies of a Blisk for Mistuning Analysis Based on Optical Measurements , 2009 .

[4]  John A. Evans,et al.  An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces , 2012 .

[5]  David R. Forsey,et al.  Multiresolution Surface Reconstruction for Hierarchical B-splines , 1998, Graphics Interface.

[6]  David R. Forsey,et al.  Hierarchical B-spline refinement , 1988, SIGGRAPH.

[7]  David R. Forsey,et al.  Surface fitting with hierarchical splines , 1995, TOGS.

[8]  Tom Lyche,et al.  T-spline Simplication and Local Renement , 2004 .

[9]  Jun Wang,et al.  Parallel and adaptive surface reconstruction based on implicit PHT-splines , 2011, Comput. Aided Geom. Des..

[10]  Gábor Renner,et al.  Advanced surface fitting techniques , 2002, Comput. Aided Geom. Des..

[11]  Hendrik Speleers,et al.  THB-splines: The truncated basis for hierarchical splines , 2012, Comput. Aided Geom. Des..

[12]  T. Hughes,et al.  Local refinement of analysis-suitable T-splines , 2012 .

[13]  Jiansong Deng,et al.  Polynomial splines over general T-meshes , 2010, The Visual Computer.

[14]  Bert Jüttler,et al.  Algorithms and Data Structures for Truncated Hierarchical B-splines , 2012, MMCS.

[15]  Yimin Wang,et al.  Curvature-guided adaptive TT-spline surface fitting , 2013, Comput. Aided Des..

[16]  B. Simeon,et al.  A hierarchical approach to adaptive local refinement in isogeometric analysis , 2011 .

[17]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..

[18]  Kai Hormann,et al.  Surface Parameterization: a Tutorial and Survey , 2005, Advances in Multiresolution for Geometric Modelling.

[19]  Bert Jüttler,et al.  On the completeness of hierarchical tensor-product B-splines , 2014, J. Comput. Appl. Math..

[20]  Michael A. Scott,et al.  Isogeometric spline forests , 2014 .

[21]  Thomas J. R. Hughes,et al.  Conformal solid T-spline construction from boundary T-spline representations , 2013 .

[22]  Bert Jüttler,et al.  Bases and dimensions of bivariate hierarchical tensor-product splines , 2013, J. Comput. Appl. Math..

[23]  T. Hughes,et al.  Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline , 2012 .

[24]  Andrea Bressan,et al.  Some properties of LR-splines , 2013, Comput. Aided Geom. Des..

[25]  Jiansong Deng,et al.  Polynomial splines over hierarchical T-meshes , 2008, Graph. Model..

[26]  Nicholas S. North,et al.  T-spline simplification and local refinement , 2004, SIGGRAPH 2004.

[27]  Hendrik Speleers,et al.  Effortless quasi-interpolation in hierarchical spaces , 2015, Numerische Mathematik.

[28]  Günther Greiner,et al.  Interpolating and approximating scattered 3D-data with hierarchical tensor product B-splines , 2010 .

[29]  Hendrik Speleers,et al.  Strongly stable bases for adaptively refined multilevel spline spaces , 2014, Adv. Comput. Math..

[30]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..

[31]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[32]  T. Hughes,et al.  Converting an unstructured quadrilateral mesh to a standard T-spline surface , 2011 .