The arrangement of objects into a layout can be challenging for non-experts, as is affirmed by the existence of interior design professionals. Recent research into the automation of this task has yielded methods that can synthesize layouts of objects respecting aesthetic and functional constraints that are non-linear and competing. These methods usually adopt a stochastic optimization scheme, which samples from different layout configurations, a process that is slow and inefficient. We introduce an physics-motivated, continuous layout synthesis technique, which results in a significant gain in speed and is readily scalable. We demonstrate our method on a variety of examples and show that it achieves results similar to conventional layout synthesis based on Markov chain Monte Carlo (McMC) state-search, but is faster by at least an order of magnitude and can handle layouts of unprecedented size as well as tightly-packed layouts that can overwhelm McMC.

A geometric dissection is a set of pieces which can be assembled in different ways to form distinct shapes. Dissections are used as recreational puzzles because it is striking when a single set of pieces can construct highly different forms. Existing techniques for creating dissections find pieces that reconstruct two input shapes exactly. Unfortunately, these methods only support simple, abstract shapes because an excessive number of pieces may be needed to reconstruct more complex, naturalistic shapes. We introduce a dissection design technique that supports such shapes by requiring that the pieces reconstruct the shapes only approximately. We find that, in most cases, a small number of pieces suffices to tightly approximate the input shapes. We frame the search for a viable dissection as a combinatorial optimization problem, where the goal is to search for the best approximation to the input shapes using a given number of pieces. We find a lower bound on the tightness of the approximation for a partial dissection solution, which allows us to prune the search space and makes the problem tractable. We demonstrate our approach on several challenging examples, showing that it can create dissections between shapes of significantly greater complexity than those supported by previous techniques.

Interchangeable components allow an object to be easily reconfigured, but usually reveal that the object is composed of parts. In this work, we present a computational approach for the design of components which are interchangeable, but also form objects with a coherent appearance which conceals their composition from parts. These components allow a physical realization of Assembly Based Modelling, a popular virtual modelling paradigm in which new models are constructed from the parts of existing ones. Given a collection of 3D models and a segmentation that specifies the component connectivity, our approach generates the components by jointly deforming and partitioning the models. We determine the component boundaries by evolving a set of closed contours on the input models to maximize the contours' geometric similarity. Next, we efficiently deform the input models to enforce both C0 and C1 continuity between components while minimizing deviation from their original appearance. The user can guide our deformation scheme to preserve desired features. We demonstrate our approach on several challenging examples, showing that our components can be physically reconfigured to assemble a large variety of coherent shapes.

The visual perception of object affordances has emerged as a useful ingredient for building powerful computer vision and robotic applications. In this paper we introduce a novel approach to reason about liquid containability - the affordance of containing liquid. Our approach analyzes container objects based on two simple physical processes: the Fill and Transfer of liquid. First, it reasons about whether a given 3D object is a liquid container and its best filling direction. Second, it proposes directions to transfer its contained liquid to the outside while avoiding spillage. We compare our simplified model with a common fluid dynamics simulation and demonstrate that our algorithm makes human-like choices about the best directions to fill containers and transfer liquid from them. We apply our approach to reason about the containability of several real-world objects acquired using a consumer-grade depth camera.

Zoomorphic shapes are man-made shapes that possess the form or appearance of an animal. They have desirable aesthetic properties, but are difficult to create using conventional modeling tools. We present a method for creating zoomorphic shapes by merging a man-made shape and an animal shape. To identify a pair of shapes that are suitable for merging, we use an efficient graph kernel based technique. We formulate the merging process as a continuous optimization problem where the two shapes are deformed jointly to minimize an energy function combining several design factors. The modeler can adjust the weighting between these factors to attain high-level control over the final shape produced. A novel technique ensures that the zoomorphic shape does not violate the design restrictions of the man-made shape. We demonstrate the versatility and effectiveness of our approach by generating a wide variety of zoomorphic shapes.