Current performance-driven building design methods are not widely adopted outside the research field for several reasons that make them difficult to integrate into a typical design process. In the early design phase, in particular, the time-intensity and the cognitive load associated with optimization and form parametrization are incompatible with design exploration, which requires quick iteration. This research introduces a novel method for performance-driven geometry generation that can afford interaction directly in the 3d modeling environment, eliminating the need for explicit parametrization, and is multiple orders faster than the equivalent form optimization. The method uses Machine Learning techniques to train a generative model offline. The generative model learns a distribution of optimal performing geometries and their simulation contexts based on a dataset that addresses the performance(s) of interest. By navigating the generative model's latent space, geometries with the desired characteristics can be quickly generated. A case study is presented, demonstrating the generation of a synthetic dataset and the use of a Variational Autoencoder (VAE) as a generative model for geometries with optimal solar gain. The results show that the VAE-generated geometries perform on average at least as well as the optimized ones, suggesting that the introduced method shows a feasible path towards more intuitive and interactive early-phase performance-driven design assistance.
Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered fragments, is fundamental to numerous applications, and yet most of the literature has focused thus far on less realistic puzzles whose pieces are identical squares. Here we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer's sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results to indicate that such puzzles are solvable completely automatically.