A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

Probabilistic Marching Cubes

In this paper we revisit the computation and visualization of equivalents to isocontours in uncertain scalar fields. We model uncertainty by discrete random fields and, in contrast to previous methods, also take arbitrary spatial correlations into account. Starting with joint distributions of the random variables associated to the sample locations, we compute level crossing probabilities for cells of the sample grid. This corresponds to computing the probabilities that the well‐known symmetry‐reduced marching cubes cases occur in random field realizations. For Gaussian random fields, only marginal density functions that correspond to the vertices of the considered cell need to be integrated. We compute the integrals for each cell in the sample grid using a Monte Carlo method. The probabilistic ansatz does not suffer from degenerate cases that usually require case distinctions and solutions of ill‐conditioned problems. Applications in 2D and 3D, both to synthetic and real data from ensemble simulations in climate research, illustrate the influence of spatial correlations on the spatial distribution of uncertain isocontours.     

Topology‐based Visualization of Transformation Pathways in Complex Chemical Systems

Studying transformation in a chemical system by considering its energy as a function of coordinates of the system's components provides insight and changes our understanding of this process. Currently, a lack of effective visualization techniques for high‐dimensional energy functions limits chemists to plot energy with respect to one or two coordinates at a time. In some complex systems, developing a comprehensive understanding requires new visualization techniques that show relationships between all coordinates at the same time. We propose a new visualization technique that combines concepts from topological analysis, multi‐dimensional scaling, and graph layout to enable the analysis of energy functions for a wide range of molecular structures. We demonstrate our technique by studying the energy function of a dimer of formic and acetic acids and a LTA zeolite structure, in which we consider diffusion of methane.     

A new approach of data clustering using a flock of agents

This paper presents a new bio-inspired algorithm (FClust) that dynamically creates and visualizes groups of data. This algorithm uses the concepts of a flock of agents that move together in a complex manner with simple local rules. Each agent represents one data. The agents move together in a 2D environment with the aim of creating homogeneous groups of data. These groups are visualized in real time, and help the domain expert to understand the underlying structure of the data set, like for example a realistic number of classes, clusters of similar data, isolated data. We also present several extensions of this algorithm, which reduce its computational cost, and make use of a 3D display. This algorithm is then tested on artificial and real-world data, and a heuristic algorithm is used to evaluate the relevance of the obtained partitioning.     

Light scattering from filaments

Photorealistic visualization of a huge number of individual filaments like in the case of hair, fur, or knitwear is a challenging task: Explicit rendering approaches for simulating radiance transfer at a filament get totally impracticable with respect to rendering performance and it is also not obvious how to derive efficient scattering functions for different levels of (geometric) abstraction or how to deal with very complex scattering mechanisms. We present a novel uniform formalism for light scattering from filaments in terms of radiance, which we call the bidirectional fiber scattering distribution function (BFSDF). We show that previous specialized approaches, which have been developed in the context of hair rendering, can be seen as instances of the BFSDF. Similar to the role of the BSSRDF for surface scattering functions, the BFSDF can be seen as a general approach for light scattering from filaments, which is suitable for deriving approximations in a canonic and systematic way. For the frequent cases of distant light sources and observers, we deduce an efficient far field approximation (bidirectional curve scattering distribution function, BCSDF). We show that on the basis of the BFSDF, parameters for common rendering techniques can be estimated in a non-ad-hoc, but physically-based way     

Topology-controlled volume rendering

Topology provides a foundation for the development of mathematically sound tools for processing and exploration of scalar fields. Existing topology-based methods can be used to identify interesting features in volumetric data sets, to find seed sets for accelerated isosurface extraction, or to treat individual connected components as distinct entities for isosurfacing or interval volume rendering. We describe a framework for direct volume rendering based on segmenting a volume into regions of equivalent contour topology and applying separate transfer functions to each region. Each region corresponds to a branch of a hierarchical contour tree decomposition, and a separate transfer function can be defined for it. The novel contributions of our work are: 1) a volume rendering framework and interface where a unique transfer function can be assigned to each subvolume corresponding to a branch of the contour tree, 2) a runtime method for adjusting data values to reflect contour tree simplifications, 3) an efficient way of mapping a spatial location into the contour tree to determine the applicable transfer function, and 4) an algorithm for hardware-accelerated direct volume rendering that visualizes the contour tree-based segmentation at interactive frame rates using graphics processing units (GPUs) that support loops and conditional branches in fragment programs     

Identification of the female-produced sex pheromone of the scarab beetle,Hoplia equina

Hoplia equina LeConte (Coleoptera: Scarabaeidae: Melolonthinae) is a beetle pest of cranberry beds in Massachusetts. Larvae feed on the roots of the cranberry plant, reducing yield as well as vine density. The female sex pheromone was identified as 2-tetradecanone. There were eight compounds found in the airborne volatiles collected from females that elicited antennal responses from males. Of the eight compounds tested (nonanal, decanal, dodecanal, 2-dodecanone, 2-tridecanone, 2-tetradecanone, 2-pentadecanone, and 2-hexadecanone), 2-tetradecanone was the only one that attracted male beetles in the field. Combining any of the other seven antennally active compounds with 2-tetradecanone did not increase male capture.     

Formal aspects of computing: LATEX style guide for authors

This guide is for authors who are preparing papers forFormal Aspects of Computing using the \(LaT_E X\) document preparation system and the FAC style file.