Related papers: Procedural Wang Tile Algorithm for Stochastic Wall…

The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand,…

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…

This paper presents a stochastic Wang tiling based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite…

The paper presents a concept/technique to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a…

We present a novel and flexible learning-based method for generating tileable image sets. Our method goes beyond simple self-tiling, supporting sets of mutually tileable images that exhibit a high degree of diversity. To promote diversity…

Microstructural geometry plays a critical role in the response of heterogeneous materials. Consequently, methods for generating microstructural samples are increasingly crucial to advanced numerical analyses. We extend Sonon et al.'s…

Stochastic porous structures are ubiquitous in natural phenomena and have gained considerable traction across diverse domains owing to their exceptional physical properties. The recent surge in interest in microstructures can be attributed…

In this paper, we introduce a novel design paradigm for modular architectured materials that allows for spatially nonuniform designs from a handful of building blocks, which can be robotically assembled for efficient and scalable…

We tackle the problem of texture synthesis in the setting where many input images are given and a large-scale output is required. We build on recent generative adversarial networks and propose two extensions in this paper. First, we propose…

Wang tile based representation of a heterogeneous material facilitates fast synthesis of non-periodic microstructure realizations. In this paper, we apply the tiling approach in numerical homogenization to determine the Representative…

Image tiling -- the seamless connection of disparate images to create a coherent visual field -- is crucial for applications such as texture creation, video game asset development, and digital art. Traditionally, tiles have been constructed…

In the past decade, exemplar-based texture synthesis algorithms have seen strong gains in performance by matching statistics of deep convolutional neural networks. However, these algorithms require regularization terms or user-added spatial…

Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic…

We seek to cover a parametric domain with a set of evenly spaced bands which number and widthvaries according to a density field. We propose an implicit procedural algorithm, that generates theband pattern from a pixel shader and adapts to…

Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the…

Texturing is a fundamental process in computer graphics. Texture is leveraged to enhance the visualization outcome for a 3D scene. In many cases a texture image cannot cover a large 3D model surface because of its small resolution.…

2D texture maps and 3D voxel arrays are widely used to add rich detail to the surfaces and volumes of rendered scenes, and filtered texture lookups are integral to producing high-quality imagery. We show that filtering textures after…

The emergence of 3D Gaussian Splatting has fundamentally redefined the capabilities of photorealistic neural rendering by enabling high-throughput synthesis of complex environments. While procedural methods like Wang Tiles have recently…

We give a constructive method that can decrease the number of prototiles needed to tile a space. We achieve this by exchanging edge to edge matching rules for a small atlas of permitted patches. This method is illustrated with Wang tiles,…

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…