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Volumetric T-spline Construction Using Boolean Operations

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

22nd International Meshing Roundtable, Springer-Verlag, pp.405-424, October 13-16 2013

INTERNATIONAL
MESHING
ROUNTABLE

22nd International Meshing Roundtable
Orlando, FL
October 13-16,2013

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, U.S.A.
Department of Civil and Environmental Engineering, Brigham Young University, Provo, UT 84602, U.S.A.
Department of Computer Science, Brigham Young University, Provo, UT 84602, U.S.A.
Email: jessicaz@andrew.cmu.edu

Summary
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 B´ezier elements from the volumetric T-spline, and use them directly in isogeometric analysis.

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