Efficient and accurate reconstruction of imaging-derived geometries and subsequent quality mesh generation are enabling technologies for both clinical and research simulations. A challenging part of this process is the introduction of computable, orthogonal boundary patches, namely, the outlets, into treed structures, such as vasculature, arterial or airway trees. We present efficient and robust algorithms for automatically identifying and truncating the outlets for complex geometries. Our approach is based on a conceptual decomposition of objects into tips, segments, and branches, where the tips determine the outlets. We define the tips by introducing a novel concept called the average interior center of curvature and identify the tips that are stable and noise resistant. We compute well-defined orthogonal planes, which truncate the tips into outlets. The rims of the outlets are connected into curves, and the outlets are then closed using Delaunay triangulation. We illustrate the effectiveness and robustness of our approach with a variety of complex lung and coronary artery geometries.