In this article we revisit the problem of blue noise sampling with a strong focus on the spectral properties of the sampling patterns. Starting from the observation that oscillations in the power spectrum of a sampling pattern can cause aliasing artifacts in the resulting images, we synthesize two new types of blue noise patterns: step blue noise with a power spectrum in the form of a step function and single-peak blue noise with a wide zero-region and no oscillations except for a single peak. We study the mathematical relationship of the radial power spectrum to a spatial statistic known as the radial distribution function to determine which power spectra can actually be realized and to construct the corresponding point sets. Finally, we show that both proposed sampling patterns effectively prevent structured aliasing at low sampling rates and perform well at high sampling rates.

Molecular dynamics is a widely used simulation technique to investigate material properties and structural changes under external forces. The availability of more powerful clusters and algorithms continues to increase the spatial and temporal extents of the simulation domain. This poses a particular challenge for the visualization of the underlying processes which might consist of millions of particles and thousands of time steps. Some application domains have developed special visual metaphors to only represent the relevant information of such data sets but these approaches typically require detailed domain knowledge that might not always be available or applicable. We propose a general technique that replaces the huge amount of simulated particles by a smaller set of representatives that are used for the visualization instead. The representatives capture the characteristics of the underlying particle density and exhibit coherency over time. We introduce loose capacity-constrained Voronoi diagrams for the generation of these representatives by means of a GPU-friendly, parallel algorithm. This way we achieve visualizations that reflect the particle distribution and geometric structure of the original data very faithfully. We evaluate our approach using real-world data sets from the application domains of material science, thermodynamics and dynamical systems theory.

Abstract We investigate semi‐stochastic tilings based on Wang or corner tiles for the real‐time synthesis of example‐based textures. In particular, we propose two new tiling approaches: (1) to replace stochastic tilings with pseudo‐random tilings based on the Halton low‐discrepancy sequence, and (2) to allow the controllable generation of tilings based on a user‐provided probability distribution. Our first method prevents local repetition of texture content as common with stochastic approaches and yields better results with smaller sets of utilized tiles. Our second method allows to directly influence the synthesis result which—in combination with an enhanced tile construction method that merges multiple source textures—extends synthesis tasks to globally‐varying textures. We show that both methods can be implemented very efficiently in connection with tile‐based texture mapping and also present a general rule that allows to significantly reduce resulting tile sets.

We present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd's method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd's method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

In many applications today user interaction is moving away from mouse and pens and is becoming pervasive and much more physical and tangible. New emerging interaction technologies allow developing and experimenting with new interaction methods on the long way to providing intuitive human computer interaction. In this paper, we aim at recognizing gestures to interact with an application and present the design and evaluation of our sensor-based gesture recognition. As input device we employ the Wii-controller (Wiimote) which recently gained much attention world wide. We use the Wiimote's acceleration sensor independent of the gaming console for gesture recognition. The system allows the training of arbitrary gestures by users which can then be recalled for interacting with systems like photo browsing on a home TV. The developed library exploits Wii-sensor data and employs a hidden Markov model for training and recognizing user-chosen gestures. Our evaluation shows that we can already recognize gestures with a small number of training samples. In addition to the gesture recognition we also present our experiences with the Wii-controller and the implementation of the gesture recognition. The system forms the basis for our ongoing work on multimodal intuitive media browsing and are available to other researchers in the field.