Using 3D printers for manufacturing objects has become an easy, low cost process in a variety of emerging applications, such as assistive technologies. To this end, it may be necessary to split the object in smaller parts, providing that they precisely connect. This work presents a framework to build objects with connecting parts, which is divided in main three steps: 3D reconstruction; mesh segmentation; and 3D printing. The framework includes a new method for 3D model segmentation, which allows the generation of connecting parts from cutting planes. The segmentation process uses a binary space partitioning tree to represent cut regions of the mesh obtained from the scanned object. To close these cut regions and, at the same time, to consider constraints defined by the added connectors, it is used a Constrained Delaunay Triangulation. Thus, it is guaranteed a set of closed meshes for 3D printing. Experimental results show the application of this framework in two different areas: assistive technologies, by creating anatomically adjustable orthoses; and cultural heritage, where parts of scanned sculptures can be printed for preservation and restoration activities.