Discrete element textures

A variety of phenomena can be characterized by repetitive small scale elements within a large scale domain. Examples include a stack of fresh produce, a plate of spaghetti, or a mosaic pattern. Although certain results can be produced via manual placement or procedural/physical simulation, these methods can be labor intensive, difficult to control, or limited to specific phenomena.

We present discrete element textures, a data-driven method for synthesizing repetitive elements according to a small input exemplar and a large output domain. Our method preserves both individual element properties and their aggregate distributions. It is also general and applicable to a variety of phenomena, including different dimensionalities, different element properties and distributions, and different effects including both artistic and physically realistic ones. We represent each element by one or multiple samples whose positions encode relevant element attributes including position, size, shape, and orientation. We propose a sample-based neighborhood similarity metric and an energy optimization solver to synthesize desired outputs that observe not only input exemplars and output domains but also optional constraints such as physics, orientation fields, and boundary conditions. As a further benefit, our method can also be applied for editing existing element distributions.