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

Authors:
Wenyan Wang;Yongjie Zhang;Michael A. Scott;Thomas J. Hughes
Affiliations:
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, USA 15213;Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, USA 15213;Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA 78712;Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA 78712
Venue:
Computational Mechanics
Year:
2011

Citing 6
Cited 3

T-splines and T-NURCCs

ACM SIGGRAPH 2003 Papers
T-spline simplification and local refinement

ACM SIGGRAPH 2004 Papers
Polycube splines

Proceedings of the 2007 ACM symposium on Solid and physical modeling
Automatic and interactive mesh to T-spline conversion

SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Watertight trimmed NURBS

ACM SIGGRAPH 2008 papers
Control point removal algorithm for t-spline surfaces

GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing

Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline

Computational Mechanics
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Journal of Computational Physics
An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics

Computational Mechanics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a novel method for converting any unstructured quadrilateral mesh to a standard T-spline surface, which is C 2-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.