Converting an unstructured quadrilateral mesh to a standard T-spline surface

Wang, Wenyan; Zhang, Yongjie; Scott, Michael; Hughes, Thomas
October 2011
Computational Mechanics;Oct2011, Vol. 48 Issue 4, p477
Academic Journal
This paper presents a novel method for converting any unstructured quadrilateral mesh to a standard T-spline surface, which is C-continuous except for the local region around each extraordinary node. There are two stages in the algorithm: the topology stage and the geometry stage. In the topology stage, we take the input quadrilateral mesh as the initial T-mesh, design templates for each quadrilateral element type, and then standardize the T-mesh by inserting nodes. One of two sufficient conditions is derived to guarantee the generated T-mesh is gap-free around extraordinary nodes. To obtain a standard T-mesh, a second sufficient condition is provided to decide what T-mesh configuration yields a standard T-spline. These two sufficient conditions serve as a theoretical basis for our template development and T-mesh standardization. In the geometry stage, an efficient surface fitting technique is developed to improve the geometric accuracy. In addition, the surface continuity around extraordinary nodes can be improved by adjusting surrounding control nodes. The algorithm can also preserve sharp features in the input mesh, which are common in CAD (Computer Aided Design) models. Finally, a Bézier extraction technique is used to facilitate T-spline based isogeometric analysis. Several examples are tested to show the robustness of the algorithm.


Related Articles

  • Spline-wavelets in the case of a single local coarsening of a grid. Dem'yanovich, Yu. // Journal of Mathematical Sciences;May2013, Vol. 191 Issue 1, p52 

    The structure of the spline-wavelet decomposition in the case of a single local coarsening of an irregular grid is discussed. Algorithms of decomposition and reconstruction are presented. The wavelet flow generated by the values of continuous differentiable function at grid points is evaluated....

  • Parallel Mesh Adaptive Techniques for Complex Flow Simulation: Geometry Conservation. Casagrande, Angelo; Leyland, Pénélope; Formaggia, Luca // Modelling & Simulation in Engineering;2012, p1 

    Dynamic mesh adaptation on unstructured grids, by localised refinement and derefinement, is a very efficient tool for enhancing solution accuracy and optimising computational time. One of the major drawbacks, however, resides in the projection of the new nodes created, during the refinement...

  • SOFTWARE.  // Microwave Journal;Jan2006, Vol. 49 Issue 1, p186 

    The article presents information on the software Q3D Extractorâ„¢ v7 from Ansoft Corp. This tool is the most recent release of the 3D quasi-static electromagnetic parasitic extraction tool. The Q3D Extractor computes 3D RLC/2D RLCG parameters from interconnect structures and automatically...

  • An improved contraction-based method for mesh skeleton extraction. Yu, Liyang; Han, Qi; Niu, Xiamu // Multimedia Tools & Applications;Dec2014, Vol. 73 Issue 3, p1709 

    Contraction-based skeleton extraction methods have the feature that during skeleton extraction process, the correspondence between skeleton and mesh regions can be obtained, which makes this class of algorithm attractive. Besides, among all mesh skeleton extraction methods, contraction-based...

  • Efficient List Ranking on the Reconfigurable Mesh, with Applications. Hayashi, T.; Nakano, K.; Olariu, S. // Theory of Computing Systems;1998, Vol. 31 Issue 5, p593 

    Finding a vast array of applications, the list-ranking problem has emerged as one of the fundamental techniques in parallel algorithm design. Surprisingly, the best previously known algorithm to rank a list of n items on a reconfigurable mesh of size n � n was running in O(log n) time. It...

  • An adaptive solution of the 3-D Euler equations on an unstructured grid. Zhu, Z.Q.; Wang, P.; Tuo, S.F. // Acta Mechanica;2002, Vol. 155 Issue 3/4, p215 

    Presents an adaptive algorithm of the three-dimensional surface unstructured grid. Spatial discretization of the cell-centered finite volume formulation on the unstructured grid; Application of a novel cell reconstruction procedure; Euler solution for an adaptive tetrahedral grid.

  • AUTOMATIC RECOGNITION OF FEATURES FROM CAD MODELS FOR MESH GENERATION. XIANGWEI ZHANG; LILI HUANG // Journal of Theoretical & Applied Information Technology;12/15/2012, Vol. 46 Issue 1, p322 

    Automatic recognition of features from CAD models is one of the key technologies for mesh generation. This paper studies the algorithm for automatic recognition of features from CAD models in STL data format. Firstly, a new STL data file with topological connection is constructed for the...

  • Multiscale mesh generation on the sphere. Lambrechts, Jonathan; Comblen, Richard; Legat, Vincent; Geuzaine, Christophe; Remacle, Jean-Fran�ois // Ocean Dynamics;Dec2008, Vol. 58 Issue 5/6, p461 

    A method for generating computational meshes for applications in ocean modeling is presented. The method uses a standard engineering approach for describing the geometry of the domain that requires meshing. The underlying sphere is parametrized using stereographic coordinates. Then, coastlines...

  • A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions. Kalyani, Parcha; Rama Chandra Rao, Patibanda S.; Madhusudhan Rao, Ammiraju Sowbhagya // Applied Mathematics;Apr2013, Vol. 4 Issue 4, p583 

    In this communication we have used Bickley's method for the construction of a sixth order spline function and apply it to solve the linear fifth order differential equations of the form yv (x) + g (x) y (x) = r (x) where g (x) and r (x) are given functions with the two different problems of...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics