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Abstract
With the emergence of novel NURBS-based iso-geometric modeling methodologies, particularly the compositional approach of the Hierarchical Partition of Unity Field Composition (HPFC), there is a need to compose trivariate NURBS solids and quickly perform classifications of subdomains of the resulting composition. An algorithm and accompanying data structure utilizing a hierarchical subdivision of the solids using bounding constructs at different levels of refinements is presented. An overlap-box-sweep algorithm is introduced for computing the actual intersection points. The result of the composition is a hybrid representation containing the original trivariate NURBS solids, a list of oriented intersection segments, a hierarchy of decomposed patches, the partial triangulations and associated hierarchy of bounding constructs. For the purposes of this discussion, we assume the bounding regions of the trivariate NURBS solids can be trivially extracted and consider the boundaries of the solids as a collection of non-trimmed outer NURBS patches. Several examples illustrating the developed hybrid scheme are included.