Volumetric Boolean sum

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.