Constrained Matching of Point Clouds and Surfaces

In this thesis we are concerned with the geometric matching of shapes. We consider the local and rigid alignment of point clouds and the reconstruction of ruled surfaces from point clouds within an active shape framework. The emerging nonlinear and occasionally non-smooth optimization problems center around minimizations of the squared and unsigned distance function, respectively. Several application specific requirements impose side conditions on this optimization. The alignment of point clouds without mutual penetration reconstructs broken objects in a physical meaningful way. For an effective alignment of input data acquired at high frame rates, we constrain the registration of input shapes locally to a kinematic surface in a space-time model. We consider ruled surface approximations to compute optimal tool paths for production technologies. In particular, for cylindrical flank milling, we minimize undercut errors and stress along the cutting tool by introducing constraints. For architecture, we join multiple ruled surface patches and discuss ways to achieve smooth and visually pleasing designs.