Volumetric Boolean sum

Authors:
Gershon Elber;Yong-Joon Kim;Myung-Soo Kim
Affiliations:
Department of Computer Science, Technion - IIT, Haifa 32000, Israel;School of Comp. Science & Eng., Seoul National University, Seoul, Republic of Korea;School of Comp. Science & Eng., Seoul National University, Seoul, Republic of Korea
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

Boolean sum is a well-known surface construction operation (Cohen et al., 2001). In the light of the growing interest in trivariate B-spline and NURBs, for example in Isogeometry analysis, in this work we extend this operator for trivariate volumetric elements. Consider six arbitrary tensor product B-spline and/or NURBs surfaces that share boundaries along a cube-like topology. The volume that is enclosed by these six surfaces is parameterized using a volumetric extension of the Boolean sum for surfaces, while the boundaries of the proposed volumetric extension interpolate the six input surfaces. Finally, a generalization of the Boolean sum idea is presented for the general multivariate case.