In this thesis, we address the problem of k-set clustering of joints in a mesh. This research is motivated by the problem of rationalizing of joints in structural meshes that are commonly found in architecture, especially as supporting frames to carry the skin of complex shaped buildings. In such meshes, if the overlying surface is complex, then all joints have a unique geometry – namely, all edges (or bars) connected to the joints form a unique geometry. Fabricating such a building with several thousands of joints can be expensive. We show that the problem can be abstracted into a k-set clustering problem with a special geometric structure. We propose a new algorithm to solve this clustering problem. Although the original problem cannot be solved optimally for practical meshes,...[ Read more ]

In this thesis, we address the problem of k-set clustering of joints in a mesh. This research is motivated by the problem of rationalizing of joints in structural meshes that are commonly found in architecture, especially as supporting frames to carry the skin of complex shaped buildings. In such meshes, if the overlying surface is complex, then all joints have a unique geometry – namely, all edges (or bars) connected to the joints form a unique geometry. Fabricating such a building with several thousands of joints can be expensive. We show that the problem can be abstracted into a k-set clustering problem with a special geometric structure. We propose a new algorithm to solve this clustering problem. Although the original problem cannot be solved optimally for practical meshes, we provide an efficient heuristic that can solve the problem effectively, with very good quality results in all practical test cases that we tried. We provide a lower bound for the optimal solution, and in all cases, our heuristic provided results that are fairly close to this lower bound.