Various case studies in different application domains have shown the great potential of visual parameter space analysis to support validating and using simulation models. In order to guide and systematize research endeavors in this area, we provide a conceptual framework for visual parameter space analysis problems. The framework is based on our own experience and a structured analysis of the visualization literature. It contains three major components: (1) a data flow model that helps to abstractly describe visual parameter space analysis problems independent of their application domain; (2) a set of four navigation strategies of how parameter space analysis can be supported by visualization tools; and (3) a characterization of six analysis tasks. Based on our framework, we analyze and classify the current body of literature, and identify three open research gaps in visual parameter space analysis. The framework and its discussion are meant to support visualization designers and researchers in characterizing parameter space analysis problems and to guide their design and evaluation processes.

We investigate the relative efficiency of thermodynamic integration, three variants of the exponential formula, also referred to as thermodynamic perturbation, and Bennett's acceptance ratio method to compute relative and absolute solvation free energy differences. Our primary goal is the development of efficient protocols that are robust in practice. We focus on minimizing the number of unphysical intermediate states (λ-states) required for the computation of accurate and precise free energy differences. Several indicators are presented which help decide when additional λ-states are necessary. In all tests Bennett's acceptance ratio method required the least number of λ-states, closely followed by the "double-wide" variant of the exponential formula. Use of the exponential formula in only strict "forward" or "backward" mode was not found to be competitive. Similarly, the performance of thermodynamic integration in terms of efficiency was rather poor. We show that this is caused by the use of the trapezoidal rule as method of numerical quadrature. A systematic study focusing on the optimization of thermodynamic integration is presented in a companion paper.

We attempt to optimize the efficiency of thermodynamic integration, as defined by the minimal number of unphysical intermediate states required for the computation of accurate and precise free energy differences. The suitability of various numerical quadrature methods is tested. In particular, we compare the trapezoidal rule, Simpson's rule, Gauss-Legendre, Gauss-Kronrod-Patterson, and Clenshaw-Curtis integration, as well as integration based on a cubic spline approximation of the integrand. We find that Simpson's rule and spline integration are already significantly more efficient that the trapezoidal rule, i.e., correct free energy differences can be obtained using fewer λ-states. We demonstrate that Simpson's rule can be used advantageously with nonequidistant values of the abscissa, which increases the flexibility of the method. Efficiency is enhanced even further if higher order methods, such as Gauss-Legendre, Gauss-Kronrod-Patterson, or Clenshaw-Curtis integration, are used; no more than seven λ-states, which in the case of Clenshaw-Curtis integration include the physical end states, were required for accurate results in all test problems studied. Thus, the performance of thermodynamic integration can equal that of Bennett's acceptance ratio method. We also show, however, that the high efficiency found here relies on the particular functional form of the soft-core potential used; overall, thermodynamic integration is more susceptible to the details of the hybrid Hamiltonian used than Bennett's acceptance ratio method. Therefore, we recommend Bennett's acceptance ratio method as the most robust method to compute alchemical free energy differences; nevertheless, scenarios when thermodynamic integration may be preferable are discussed.

Abstract-Graphics artists commonly employ physically-based simulation for the generation of effects such as smoke, explosions, and similar phenomena. The task of finding the correct parameters for a desired result, however, is difficult and time-consuming as current tools provide little to no guidance. In this paper, we present a new approach for the visual exploration of such parameter spaces. Given a three-dimensional scene description, we utilize sampling and spatio-temporal clustering techniques to generate a concise overview of the achievable variations and their temporal evolution. Our visualization system then allows the user to explore the simulation space in a goal-oriented manner. Animation sequences with a set of desired characteristics can be composed using a novel search-by-example approach and interactive direct volume rendering is employed to provide instant visual feedback. A user study was performed to evaluate the applicability of our system in production use.

Illustrations play a major role in the education process. Whether used to teach a surgical or radiologic procedure, to illustrate normal or aberrant anatomy, or to explain the functioning of a technical device, illustration significantly impacts learning. Although many specimens are readily available as volumetric data sets, particularly in medicine, illustrations are commonly produced manually as static images in a time-consuming process. Our goal is to create a fully dynamic three-dimensional illustration environment which directly operates on volume data. Single images have the aesthetic appeal of traditional illustrations, but can be interactively altered and explored. In this paper we present methods to realize such a system which combines artistic visual styles and expressive visualization techniques. We introduce a novel concept for direct multi-object volume visualization which allows control of the appearance of inter-penetrating objects via two-dimensional transfer functions. Furthermore, a unifying approach to efficiently integrate many non-photorealistic rendering models is presented. We discuss several illustrative concepts which can be realized by combining cutaways, ghosting, and selective deformation. Finally, we also propose a simple interface to specify objects of interest through three-dimensional volumetric painting. All presented methods are integrated into VolumeShop, an interactive hardware-accelerated application for direct volume illustration.