Automatic decomposition of 3D solids into contractible pieces using Reeb graphs

This work is motivated by the need to generate volumetric spline models for isogeometric analysis. There exist numerous constructions of volumetric spline models that represent contractible solids. We present a novel decomposition algorithm that splits general solids into pieces that can be dealt with by these existing methods. More precisely, we present a method to automatically decompose solid objects in boundary representation into pieces with fewer or no tunnels by cutting them with auxiliary surfaces. The segmentation is guided by a reduced form of the object's boundary and volume Reeb graphs with respect to several Morse functions, the level sets of which define the cutting surfaces. Special attention is paid to the selection of suitable cutting surfaces, where we employ a quality criterion to avoid the creation of badly shaped pieces.