Poisson disk distributions have many applications in the field of computer graphics. Besides sampling, Poisson disk distributions are used in object distribution, non-photorealistic rendering and procedural texturing. Over the years, a large number of methods for generating Poisson disk distributions have been proposed, making it difficult to choose the right method for a given application. In this paper, we present a detailed comparison of most techniques for generating Poisson disk distributions. The methods we study include dart throwing, relaxation dart throwing, Lloyd's relaxation, Shade's Poisson disk tiles, tiled blue noise samples, fast hierarchical importance sampling with blue noise properties, edge-based Poisson disk tiles, template Poisson disk tiles, corner-based Poisson disk tiles and recursive Wang tiles for real-time blue noise. Analysing all of these methods within a single framework is one of the major contributions of this work.

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The tesselated spheres in the left image are rendered with two different types of a blue plastic BRDF, yet they are perceived as made from the same material. The objects in the right image are rendered with an identical blue plastic BRDF, yet their appearance is very different.

Figure 1: (Left) We present a procedural noise that offers accurate spectral control. The user can interactively manipulate the power spectrum. (Middle) We apply the noise to a surface without the need for texture coordinates, and provide high-quality anisotropic filtering. Thanks to increased expressiveness of the noise, a simple colormap is enough to produce visually interesting textures. (Right) Since our surface noise does not require a texture parameterization, the surface can evolve dynamically and even sustain topology changes. AbstractNoise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a surface, while high-quality rendering requires anisotropic filtering. A noise function that is procedural and fast to evaluate offers several additional advantages. Unfortunately, no existing noise combines all of these properties. In this paper we introduce a noise based on sparse convolution and the Gabor kernel that enables all of these properties. Our noise offers accurate spectral control with intuitive parameters such as orientation, principal frequency and bandwidth. Our noise supports two-dimensional and solid noise, but we also introduce setup-free surface noise. This is a method for mapping noise onto a surface, complementary to solid noise, that maintains the appearance of the noise pattern along the object and does not require a texture parameterization. Our approach requires only a few bytes of storage, does not use discretely sampled data, and is nonperiodic. It supports anisotropy and anisotropic filtering. We demonstrate our noise using an interactive tool for noise design.

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.