We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural functor from the Fukaya category to the category of matrix factorizations of the constructed Landau-Ginzburg model. As applications, it is applied to elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds to construct their mirrors and functors. In particular it recovers and strengthens several interesting results of Etingof-Ginzburg, Bocklandt and Smith, and gives a unified understanding of their results in terms of mirror symmetry and symplectic geometry. As an interesting application, we construct an explicit global deformation quantization of an affine del Pezzo surface as a noncommutative mirror to an elliptic orbifold.

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We propose an approach for automatic generation of building models by assembling a set of boxes using a Manhattan-world assumption. The method first aligns the point cloud with a per-building local coordinate system, and then ts axis-aligned planes to the point cloud through an iterative regularization process. The refined planes partition the space of the data into a series of compact cubic cells (candidate boxes) spanning the entire 3D space of the input data. We then choose to approximate the target building by the assembly of a subset of these candidate boxes using a binary linear programming formulation. The objective function is designed to maximize the point cloud coverage and the compactness of the final model. Finally, all selected boxes are merged into a lightweight polygonal mesh model, which is suitable for interactive visualization of large scale urban scenes. Experimental results and a comparison with state-of-the-art methods demonstrate the effectiveness of the proposed framework.

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