Volumetric T-spline Construction Using Boolean Operations

  • Lei Liu
  • Yongjie Zhang
  • Thomas J. R. Hughes
  • Michael A. Scott
  • Thomas W. Sederberg


In this paper, we present a novel algorithm for constructing a volumetric T-spline from B-reps inspired by Constructive Solid Geometry (CSG) Boolean operations. By solving a harmonic field with proper boundary conditions, the input surface is automatically decomposed into regions that are classified into two groups represented, topologically, by either a cube or a torus. We perform two Boolean operations (union and difference) with the primitives and convert them into polycubes through parametric mapping. With these polycubes, octree subdivision is carried out to obtain a volumetric T-mesh, and sharp features detected from the input model are also preserved. An optimization is then performed to improve the quality of the volumetric T-spline. Finally we extract trivariate Bézier elements from the volumetric T-spline, and use them directly in isogeometric analysis.


volumetric T-spline Boolean operations polycubes parametric mapping sharp feature isogeometric analysis 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lei Liu
    • 1
  • Yongjie Zhang
    • 1
  • Thomas J. R. Hughes
    • 2
  • Michael A. Scott
    • 3
  • Thomas W. Sederberg
    • 4
  1. 1.Department of Mechanical EngineeringCarnegie Mellon UniversityPittsburghUSA
  2. 2.Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  3. 3.Department of Civil and Environmental EngineeringBrigham Young UniversityProvoUSA
  4. 4.Department of Computer ScienceBrigham Young UniversityProvoUSA

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