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
22nd International Meshing Roundtable
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.
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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