On the influence of spatial sampling on climate networks

Peer reviewedPublisher PD

Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Fourier Analysis of Stochastic Sampling Strategies for Assessing Bias and Variance in Integration

Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these high-dimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image. We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.</jats:p

Texture Resampling While Ray-Tracing: Approximating the Convolution Region Using Caching

We present a cache-based approach to handling the difficult problem of performing visually acceptable texture resampling/filtering while ray-tracing. While many good methods have been proposed to handle the error introduced by the ray-tracing algorithm when sampling in screen space, handling this error in texture space has been less adequately addressed. Our solution is to introduce the Convolution Mask Approximation Module (CMAM). The CMAM locally approximates the convolution region in texture space as a set of overlapping texture triangles by using a texture sample caching system and ray tagging. Since the caching mechanism is hidden within the CMAM, the ray-tracing algorithm itself is unchanged while achieving an adequate level of texture filtering (area sampling as opposed to point sampling/interpolation in texture space). The CMAM is easily adapted to incorporate prefiltering methods such as MIP mapping and summed-area tables as well as direct convolution methods such as elliptical weighted average filtering

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

Simulators, graphic

Includes bibliographical references (pages 1607-1608).There are many situations in which a computer simulation with a graphic display can be very useful in the design of a robotic system. First of all, when a robot is planned for an industrial application, there are many commercially available arms that can be selected. A graphics-based simulation would allow the manufacturing engineer to evaluate alternative choices quickly and easily. The engineer can also use such a simulation tool to design interactively the workcell in which the robot operates and integrate the robot with other systems, such as part feeders and conveyors with which it must closely work. Even before the workcell is assembled or the arm first arrives, the engineer can optimize the placement of the robot with respect to the fixtures it must reach and ensure that the arm is not blocked by supports. By being able to evaluate workcell designs off-line and away from the factory floor, changes can be made without hindering factory production and thus the net productivity of the design effort can be increased