This article combines pathfinding and influence fields (or influence maps) in a way that the influence costs replace the traditional distance costs. By placing repulsors and attractors in the game world, we are mixing their influence fields into an overall game influence field, which determines the influence costs in finding a path between a start and a goal node. For that purpose, we introduce an automated method to place such attractors and repulsors, which builds upon the concept of thinning graph (and its dual). This thinning graph is a sort of medial axis of the set of passable tiles of the game map. As a result, we obtain bounded-search pathfinders that avoid obstacles (repulsors) and follows checkpoints (attractors) in an intuitive manner. Moreover, the well-known problem underlying the influence fields, called local extremum trap (i.e., an agent may enter into a place from where there is no escape away), is solved in an elegant way. Also, our influence-driven bounded-search pathfinders are comparable to other influence-based pathfinders in terms of memory expenditure and time performance.

Abstract This paper surveys mesh segmentation techniques and algorithms, with a focus on part‐based segmentation, that is, segmentation that divides a mesh (featuring a 3D object) into meaningful parts. Part‐based segmentation applies to a single object and also to a family of objects (i.e. co‐segmentation). However, we shall not address here chart‐based segmentation, though some mesh co‐segmentation methods employ such chart‐based segmentation in the initial step of their pipeline. Finally, the taxonomy proposed in this paper is new in the sense that one classifies each segmentation algorithm regarding the dimension (i.e. 1D, 2D and 3D) of the representation of object parts. The leading idea behind this survey is to identify the properties and limitations of the state‐of‐the‐art algorithms to shed light on the challenges for future work.

BACKGROUND: Protein cavities play a key role in biomolecular recognition and function, particularly in protein-ligand interactions, as usual in drug discovery and design. Grid-based cavity detection methods aim at finding cavities as aggregates of grid nodes outside the molecule, under the condition that such cavities are bracketed by nodes on the molecule surface along a set of directions (not necessarily aligned with coordinate axes). Therefore, these methods are sensitive to scanning directions, a problem that we call cavity ground-and-walls ambiguity, i.e., they depend on the position and orientation of the protein in the discretized domain. Also, it is hard to distinguish grid nodes belonging to protein cavities amongst all those outside the protein, a problem that we call cavity ceiling ambiguity. RESULTS: We solve those two ambiguity problems using two implicit isosurfaces of the protein, the protein surface itself (called inner isosurface) that excludes all its interior nodes from any cavity, and the outer isosurface that excludes most of its exterior nodes from any cavity. Summing up, the cavities are formed from nodes located between these two isosurfaces. It is worth noting that these two surfaces do not need to be evaluated (i.e., sampled), triangulated, and rendered on the screen to find the cavities in between; their defining analytic functions are enough to determine which grid nodes are in the empty space between them. CONCLUSION: This article introduces a novel geometric algorithm to detect cavities on the protein surface that takes advantage of the real analytic functions describing two Gaussian surfaces of a given protein.

Detecting and analyzing protein cavities provides significant information about active sites for biological processes (e.g., protein-protein or protein-ligand binding) in molecular graphics and modeling. Using the three-dimensional structure of a given protein (i.e., atom types and their locations in 3D) as retrieved from a PDB (Protein Data Bank) file, it is now computationally viable to determine a description of these cavities. Such cavities correspond to pockets, clefts, invaginations, voids, tunnels, channels, and grooves on the surface of a given protein. In this work, we survey the literature on protein cavity computation and classify algorithmic approaches into three categories: evolution-based, energy-based, and geometry-based. Our survey focuses on geometric algorithms, whose taxonomy is extended to include not only sphere-, grid-, and tessellation-based methods, but also surface-based, hybrid geometric, consensus, and time-varying methods. Finally, we detail those techniques that have been customized for GPU (Graphics Processing Unit) computing.

In virtual worlds (including computer games), users develop trust relationships from their in-world interactions with others. However, these trust relationships end up not being represented in the data structures (or databases) of such virtual worlds, though they sometimes appear associated with reputation and recommendation systems. In addition, as far as we know, the user is not provided with a personal trust tool to sustain his/her decision-making while he/she interacts with other users in the virtual or game world. In order to come up with a computational formal representation of these personal trust relationships, we need to succeed in converting in-world interactions into reliable sources of trust-related data. In this paper, we develop the required formalisms to gather and represent in-world interactions-which are based on the activity theory-as well as a method to convert in-world interactions into trust networks. In the companion paper, we use these trust networks to produce a computational trust decision based on subjective logic. This solution aims at supporting in-world user (or avatar) decisions about others in the game world.

Representing, manipulating, and inferring trust from the user point of view certainly is a grand challenge in virtual worlds, including online games. When someone meets an unknown individual, the question is “Can I trust him/her or not?” This requires the user to have access to a representation of trust about others, as well as a set of operators to undertake inference about the trustability of other users/players. In this paper, we employ a trust representation generated from in-world data in order to feed individual trust decisions. To achieve that purpose, we assume that such a representation of trust already exists; in fact, it was proposed in another paper of ours. Thus, the focus here is on the trust mechanisms required to infer trustability of other users/players. More specifically, we use an individual trust representation deployed as a trust network as base to the inference mechanism that employs two subjective logic operators (consensus and discount) to automatically derive trust decisions. The proposed trust inference system has been validated through OpenSimulator scenarios, which has led to a 5% increase on trustability of avatars in relation to the reference scenario (without trust).

DNA encodes the genetic information of most living beings, except viruses that use RNA. Unlike other types of molecules, DNA is not usually described by its atomic structure being instead usually described by its base-pair sequence, i.e., the textual sequence of its subsidiary molecules known as nucleotides ( adenine (A), cytosine (C), guanine (G), and thymine (T)). The three-dimensional assembling of DNA molecules based on its base-pair sequence has been, for decades, a topic of interest for many research groups all over the world. In this paper, we survey the major methods found in the literature to assemble and visualize DNA molecules from their base-pair sequences. We divided these methods into three categories: predictive methods, adaptive methods, and thermodynamic methods . Predictive methods aim to predict a conformation of the DNA from its base pair sequence, while the goal of adaptive methods is to assemble DNA base-pairs sequences along previously known conformations, as needed in scenarios such as DNA Monte Carlo simulations. Unlike these two geometric methods, thermodynamic methods are energy-based and aim to predict secondary structural motifs of DNA in cases where hydrogen bonds between base pairs might be broken because of temperature changes. We also present the major software tools that implements predictive, adaptive, and thermodynamic methods.

BACKGROUND: Plasmid DNA molecules are closed circular molecules that are widely used in life sciences, particularly in gene therapy research. Monte Carlo methods have been used for several years to simulate the conformational behavior of DNA molecules. In each iteration these simulation methods randomly generate a new trial conformation, which is either accepted or rejected according to a criterion based on energy calculations and stochastic rules. These simulation trials are generated using a method based on crankshaft motion that, apart from some slight improvements, has remained the same for many years. RESULTS: In this paper, we present a new algorithm for the deformation of plasmid DNA molecules for Monte Carlo simulations. The move underlying our algorithm preserves the size and connectivity of straight-line segments of the plasmid DNA skeleton. We also present the results of three experiments comparing our deformation move with the standard and biased crankshaft moves in terms of acceptance ratio of the trials, energy and temperature evolution, and average displacement of the molecule. Our algorithm can also be used as a generic geometric algorithm for the deformation of regular polygons or polylines that preserves the connections and lengths of their segments. CONCLUSION: Compared with both crankshaft moves, our move generates simulation trials with higher acceptance ratios and smoother deformations, making it suitable for real-time visualization of plasmid DNA coiling. For that purpose, we have adopted a DNA assembly algorithm that uses nucleotides as building blocks.

The color is a valuable communication resource, not just as part of the message itself, but also as a way of discriminating between the diverse contents of a given message. However, not all people have the ability to distinguish the color in a normal way. About 5% of the world population (8% of men) has a visual impairment, called color vision deficiency (CVD) or, simply, colorblindness. This vision deficiency also has a negative impact in both virtual and real worlds, because it compromises the correct interpretation of the contents across different media and environments. This issue is critical because of the increasing availability of multimedia contents in many places, particularly over the web. This article proposes a novel algorithm to adjust the colors for dichromate people (deuteranopes and protanopes), in particular for still images found over the web via browsers that take advantage of HTML5 markup language for graphics.

Current GPU-based workstations are inadequate to triangulate and rendering large molecular datasets with thousands and hundreds of thousands, not to say millions, of atoms. The problem is not so the lack of processing power, but the memory limitations of current GPU graphics cards. For example, the NVidia GeForce GTX 590 graphics card comes with two 1.5GB GPUs. We tackle here this problem using a OpenMP-CUDA solution that runs on a loosely-coupled GPU cluster. Basically, we propose a fast, scalable, parallel triangulation algorithm for molecular surfaces that takes advantage of multicore processors of CPUs and GPUs of modern hardware architectures, where each CPU core works as the master of a single GPU, being the processing burden distributed over the CPU cores available in a single computer or a cluster. As much as we know, this is the first marching cubes algorithm that triangulates molecular surfaces on multiple GPUs using CUDA and OpenMP.

SUMMARY Computing the surface of a molecule (e.g., a protein) plays an important role in the analysis of its geometric structure as needed in the study of interactions between proteins, protein folding, protein docking, and so forth. There are a number of algorithms for the computation of molecular surfaces and their triangulations, but only a few take advantage of graphics processing unit computing. This paper describes a graphics processing unit‐based marching cubes algorithm to triangulate molecular surfaces. In the end of the paper, a performance analysis of three implementations (i.e., serial CPU, CUDA, and OpenCL) of the marching cubes‐based triangulation algorithm takes place as a way to realize beforehand how molecular surfaces can be rendered in real‐time in the future. Copyright © 2011 John Wiley & Sons, Ltd.

The problem addressed in this paper consists in triangulating the van der Waals surface without computing the geometric intersections of its atoms. Recall that the van der Waals surface is useful in computational molecular biology and biochemistry to, for example, determine the volume occupied by a molecule, as well as other important geometric properties. Assuming that every atom is represented by a ball, this amounts to compute the surface of the union of a number of balls. The novelty of our method lies in avoiding the computation of surface-surface intersections (SSI) of two or more balls.

Previous work on implicit surfaces has almost exclusively focused on homogeneously 2-dimensional surfaces, regardless of whether they are manifold or not. Consequently, current geometric and graphical systems, and even commercial mathematical software packages, cannot generate non-homogeneous implicit surfaces such as, for example, the Steiner surface or the Whitney surface correctly. This paper overcomes these difficulties by introducing a new uniform space partitioning-based algorithm that generates a polygonization for implicit surfaces possibly with self-intersections and isolated 0-and 1-dimensional singularities.

Computing molecular surfaces is important to measure areas and volumes of molecules, as well as to infer useful information about interactions with other molecules. Over the years many algorithms have been developed to triangulate and to render molecular surfaces. However, triangulation algorithms usually are very expensive in terms of memory storage and time performance, and thus far from real-time performance. Fortunately, the massive computational power of the new generation of low-cost GPUs opens up an opportunity window to solve these problems: real-time performance and cheap computing commodities. This paper just presents a GPU-based algorithm to speed up the triangulation and rendering of molecular surfaces using CUDA. Our triangulation algorithm for molecular surfaces is based on a multi-threaded, parallel version of the Marching Cubes (MC) algorithm. However, the input of our algorithm is not the volume dataset of a given molecule as usual for Marching Cubes, but the atom centers provided by the PDB file of such a molecule. We also carry out a study that compares a serial version (CPU) and a parallel version (GPU) of the MC algorithm in triangulating molecular surfaces as a way to understand how real-time rendering of molecular surfaces can be achieved in the future.

Mathematical systems (e.g., Mathematica, Maple, Matlab, and DPGraph) easily plot planar algebraic curves implicitly defined by polynomial functions. However, these systems, and most algorithms found in the literature, cannot draw many implicit curves correctly; in particular, those with singularities (self-intersections, cusps, and isolated points). They do not detect sign-invariant components either, because they use numerical methods based on the Bolzano corollary, that is, they assume that the curve-describing function f flips sign somewhere in a line segment AB that crosses the curve, or f ( A )· f ( B ) < 0. To solve these problems, we have generalized the False Position (FP) method to determine two types of zeros: (i) crossing zeros and (ii) extremal zeros (local minima and maxima without function sign variation). We have called this method the Generalized False Position (GFP) method. It allows us to sample an implicit curve against the Binary Space Partitioning (BSP), say bisection lines, of a rectangular region of R 2 . Interestingly, the GFP method can also be used to determine isolated points of the curve. The result is a general algorithm for sampling and rendering planar implicit curves with topological guarantees.

We present a novel approach to interactively edit and deform polygonal meshes. The idea is to confine editing operations to mesh regions of interest, called submeshes, leaving others untouched as much as possible. Classical editing operations such as scaling, shearing, and rotation can be then applied to each submesh instead of the whole mesh. Analogously, intuitive deformation operations (e.g. tapering and twisting) as required for animation systems can be applied to submeshes, allowing the user to have control on the local deformations of mesh objects.

This paper is concerned with "open kernel" geometric modelling systems. It uses industrial needs to identify requirements for the geometric objects of a proposed interface. The necessary mixed-dimension cellular objects are formally defined as the fundamental data abstractions for that interface. Such definitions are imperative for the construction of robust functions and the integrity of data transfer. As an example, formal specifications are provided for "set-like" object combination functions.