Convex Hull Construction Research Articles

FRT*: fast reactive tree for mobile robot replanning in unknown dynamic environments

Purpose This study aims to introduce the fast reactive tree (FRT*) algorithm for enhancing replanning speed and reducing the overall cost of navigation in unknown dynamic environments. Design/methodology/approach FRT* comprises four key components: inverted tree build, convex hull construction, dead nodes inform activation and lazy-rewiring replanning. First, an initial path is found from the inverted tree where the valid structure is preserved to minimise re-exploration areas during the replanning phase. As the robot encounters environment changes, convex hulls are extracted to sparsely describe impacted areas. Next, the growth direction of the modified tree is biased by the inform activation of dead nodes to avoid unnecessary exploration. In the replanning phase, the tree structure is optimized using the proposed lazy-rewiring replanning to find a high-quality path with low computation burden. Findings A series of comprehensive simulation experiments demonstrate that the proposed FRT* algorithm can efficiently replan short-cost feasible paths in unknown dynamic environments. The differential wheeled mobile robot with varying reference linear velocities is used to validate the effectiveness and adaptability of the proposed strategy in real word scenarios. Furthermore, ablation studies are conducted to analyze the significance of the key components of FRT*. Originality/value The proposed FRT* algorithm introduces a novel approach to addressing the challenges of navigation in unknown dynamic environments. This capability allows mobile robots to safely and efficiently navigate through unknown and dynamic environments, making the method highly applicable to real-world scenarios.

Building Coarse to Fine Convex Hulls With Auxiliary Vertices for Palette-Based Image Recoloring.

Constructing a convex hull for the pixel colors of an image by viewing them as 3D points can extract a set of palette colors for the image, then image recoloring can be achieved by modifying the palette colors. For better recoloring effect, the convex hull should contain more pixels (inclusive) and be more compact. Otherwise, reconstruction error would occur or the extracted palette color would be less representative, yielding wrong recoloring results or less effective edit. We observe that convex hulls constructed by prior methods can contain all the image pixels, but are far from compact. Efforts have been made to optimize the vertices of convex hull to increase the compactness but are still not perfect. In this paper, we propose a novel coarse to fine convex hull construction scheme with auxiliary vertices. We start by constructing a coarse convex hull whose vertices are directly image pixels which is thus the most compact but cannot contain all pixels. We then make a remedy by adding auxiliary vertices into the coarse convex hull to obtain a fine convex hull. More auxiliary vertices are added, more image pixels will be contained into the fine convex hull. The auxiliary vertices are image pixels too so that the compactness can still be maintained. During editing, the auxiliary vertices are not allowed to be edited for edit convenience, but deformed as-rigid-as-possible with the adjusting of other vertices. Our convex hull is both inclusive and compact. Extensive experiments validate the effectiveness of the proposed method.

Method for Delineating the Formula Limit of the Continental Shelf under the Maximum Area Principle Constraint

In current practices of determining continental shelf area, the measured sediment thickness data do not effectively reflect the distribution of sediments across the area due to its dispersed nature. This issue raises potential limitations in unknown optimal survey line layout strategies for maximizing the posterior determination area. This paper adopts the binary search algorithm, relies on existing sediment thickness grid data, and uses geodetic formulas to build an ellipsoidal surface grid distance calculation model. This model quickly screens potential areas for the 1% sediment thickness line candidate points set. By constraining the azimuth parameter values during the construction process of the ellipsoidal point feature buffer zones, efficiently select the candidate points set for the 1% sediment thickness line. Furthermore, by elucidating the essential meanings of points on the formula limit and combining the candidate points set of the foot of the continental slope (FOS)+60 n mile line, the polygon minimal convex hull construction technique and a baseline points optimization algorithm with a length threshold are used to efficiently select points on formula limit. Experimental results demonstrate that this method can effectively assist coastal states in optimizing the determination of continental shelf area to the fullest extent under the length threshold requirements of the United Nations Convention on the Law of the Sea. Experiments have proven that compared to the traditional intersection method, the method presented in this paper can help coastal countries delineate a larger continental shelf area. In typical application scenarios, the gain in area can reach 77,278,427 m2 accounting for 0.51% of the total area.

Tunable Salt-Inclusion Chalcogenides for Ion Exchange, Photoluminescence, and Scintillation

Salt-inclusion chalcogenides (SICs) consisting of covalent and ionic building blocks have emerged as functional materials exhibiting novel topologies that result from the combination of the chalcogenide-based frameworks and the salt inclusions contained within them. Nine compositions of a novel family of SICs [Cs6X]AGa6Q12 (A = Na, K, and Rb; X = F, Cl, and Br; Q = S and Se) were synthesized via halide/polychalcogenide flux crystal growth and structurally characterized. Ex situ powder X-ray diffraction analysis was used to determine the optimal synthesis temperatures at which the titled SIC materials crystallized in the flux. Density functional theory calculations coupled with convex hull construction were performed to predict the stability of [Cs6X]AGa6Q12 compositions as a function of X, A, and Q and to identify their decomposition pathways. A combination of single-crystal X-ray diffraction and energy-dispersive spectroscopy was used to study single-crystal-to-single-crystal (SC-SC) ion-exchange-reaction, a process that also allowed for the synthesis of two additional members of this family, [Cs6F]NaGa6S12 and [Cs6–xRbxBr]RbGa6S12, which did not form during the direct flux crystal growth. Furthermore, single crystals of [Cs6X]AGa6Q12:Mn2+ were obtained through direct flux crystal growth and SC-SC ion-exchange reactions and studied for their photoluminescent behavior using individual single crystals. The emission profile changed as a function of Mn2+-content, the A cation identity, and the synthesis method used. Finally, radioluminescence measurements were carried out on [Cs6Cl]NaGa6S12:Mn2+ bulk samples, resulting in bright orange scintillation.

Canonical tessellations of decorated hyperbolic surfaces

A decoration of a hyperbolic surface of finite type is a choice of circle, horocycle or hypercycle about each cone-point, cusp or flare of the surface, respectively. In this article we show that a decoration induces a unique canonical tessellation and dual decomposition of the underlying surface. They are analogues of the weighted Delaunay tessellation and Voronoi decomposition in the Euclidean plane. We develop a characterisation in terms of the hyperbolic geometric equivalents of Delaunay’s empty-discs and Laguerre’s tangent-distance, also known as power-distance. Furthermore, the relation between the tessellations and convex hulls in Minkowski space is presented, generalising the Epstein–Penner convex hull construction. This relation allows us to extend Weeks’ flip algorithm to the case of decorated finite type hyperbolic surfaces. Finally, we give a simple description of the configuration space of decorations and show that any fixed hyperbolic surface only admits a finite number of combinatorially different canonical tessellations.

A General-Purpose Multi-Dimensional Convex Landscape Generator

Heuristic and evolutionary algorithms are proposed to solve challenging real-world optimization problems. In the evolutionary community, many benchmark problems for empirical evaluations of algorithms have been proposed. One of the most important classes of test problems is the class of convex functions, particularly the d-dimensional sphere function. However, the convex function type is somewhat limited. In principle, one can select a set of convex basis functions and use operations that preserve convexity to generate a family of convex functions. This method will inevitably introduce bias in favor of the basis functions. In this paper, the problem is solved by employing insights from computational geometry, which gives the first-ever general-purpose multi-dimensional convex landscape generator. The new proposed generator has the advantage of being generic, which means that it has no bias toward a specific analytical function. A set of N random d-dimensional points is generated for the construction of a d-dimensional convex hull. The upper part of the convex hull is removed by considering the normal of the polygons. The remaining part defines a convex function. It is shown that the complexity of constructing the function is O(Md3), where M is the number of polygons of the convex function. For the method to work as a benchmark function, queries of an arbitrary (d−1) dimensional input are generated, and the generator has to return the value of the convex function. The complexity of answering the query is O(Md). The convexity of the function from the generator is verified with a nonconvex ratio test. The performance of the generator is also evaluated using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) gradient descent algorithm. The source code of the generator is available.

The cosmic-ray staircase: the outcome of the cosmic-ray acoustic instability

ABSTRACT Recently, cosmic rays (CRs) have emerged as a leading candidate for driving galactic winds. Small-scale processes can dramatically affect global wind properties. We run two-moment simulations of CR streaming to study how sound waves are driven unstable by phase-shifted CR forces and CR heating. We verify linear theory growth rates. As the sound waves grow non-linear, they steepen into a quasi-periodic series of propagating shocks; the density jumps at shocks create CR bottlenecks. The depth of a propagating bottleneck depends on both the density jump and its velocity; ΔPc is smaller for rapidly moving bottlenecks. A series of bottlenecks creates a CR staircase structure, which can be understood from a convex hull construction. The system reaches a steady state between growth of new perturbations, and stair mergers. CRs are decoupled at plateaus, but exert intense forces and heating at stair jumps. The absence of CR heating at plateaus leads to cooling, strong gas pressure gradients and further shocks. If bottlenecks are stationary, they can drastically modify global flows; if their propagation times are comparable to dynamical times, their effects on global momentum and energy transfer are modest. The CR acoustic instability is likely relevant in thermal interfaces between cold and hot gas, as well as galactic winds. Similar to increased opacity in radiative flows, the build-up of CR pressure due to bottlenecks can significantly increase mass outflow rates, by up to an order of magnitude. It seeds unusual forms of thermal instability, and the shocks could have distinct observational signatures, on ∼kpc scales.

A new approach for grasp quality calculation using continuous boundary formulation of grasp wrench space

In this paper, we aim to use a continuous formulation to efficiently calculate the well-known wrench-based grasp metric proposed by Ferrari and Canny which is the minimum distance from the wrench space origin to the boundary of the grasp wrench space. Considering the L∞ metric and the nonlinear friction cone model, the challenge of calculating this metric is to determine the boundary of the grasp wrench space. Instead of relying on convex hull construction, we propose to formulate the boundary of the grasp wrench space as continuous functions. By doing so, the problem of grasp quality calculation can be efficiently solved as typical least-square problems and it can be easily implemented by employing off-the-shelf optimization algorithms. Numerical tests will demonstrate the advantages of the proposed formulation compared to the conventional convex hull-based methods.

First principles study of d0-d half-Heusler alloys containing group-IV, -V, and -VI sp atoms as prospective half-metals for real spintronic applications

Employing the full-potential linearized augmented plane-wave method in framework of the density functional theory, the electronic structure, magnetism, structural stability, and half-metallicity of 420 XYZ d0-d half-Heusler alloys composed of d0 alkali metals X = K, Rb, Cs; 3d transition-metals Y = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn; and group-IV, -V, and -VI elements Z = C, Si, Ge, Sn, Pb, N, P, As, Sb, Bi, O, S, Se, Te are systematically investigated with a goal of identifying compounds of interest for spintronic devices. The calculations led to the introduction of eighty nine new robust half-metallic ferromagnetic compounds with half-metallic gaps in the range 0.04–1.12 eV (within GGA) at the corresponding optimized lattice constants and atomic arrangements. The robustness of these half-metallic gaps against uniform and uniaxial strains are tested. The calculated total spin magnetic moments of all half-metallic structures were integer quantities in units of Bohr magneton, in agreement with either Slater-Pauling rule Mt = (Zt − 8) or Mt = (Zt − 18). It is estimated using Monte Carlo simulations that the Curie temperatures of the half metals, in most cases, are notably higher than the room-temperature. To study the thermodynamic and mechanical (dynamic) phase stability of these half-metallic structures at ambient conditions, the convex hull construction and elastic constants analysis have been employed, respectively. These considerations reveal that many of the d0-d half-metallic structures introduced here may be grown epitaxially under appropriate conditions for real spintronic applications.

Optimal base point selection method based on convex hull construction technology

The primary purpose of maritime delimitation is to ensure the maximum internal waters area obtained. In order to grantee the maximum internal waters area obtained with the selected base point, the idea and method of optimal selection of the territorial sea base points with the convex hull (minimum convex hull) construction technology is proposed. The ideal base points are selected by constructing convex hull for all alternative base points, which makes it possible to realize the automatic selection of base points under the principle of the maximum internal waters area.

The construction of local convex hull on the task of pattern recognition

In this research paper analyzes and explores the problems of pattern recognition methods and biological object identification algorithms. We encountered two different problems in the process. The first is the modernization of the pattern recognition algorithm; the second is associated with the identification of a biological object. The algorithm problem was solved by constructing local convex hull during modernization. In the second, the Orthoptera insect group was selected as a biological object on the recommendation of experts. Orthoptera is a taxonomic insect division that includes locusts and other winged insects. Approaches to determining the characteristics of orthoptera types and preparing their samples, as well as the formation of identification models, are recommended. The algorithm for calculating estimates (ACE) was chosen when identifying the choice of orthoptera. The ACE based on the principle of partial precedence. Approaches to the formation of a training-test selection for the choice of orthopters are proposed. As mentioned above, in this work is proposed to develop an information recognition system designed to solve the problems associated with the identification of Orthoptera Insecta, as well as for the experimental study of the specie of the locust family.

Multi-Node Localization and Identity Estimation Based Multi-Beacon Searching Algorithm

The accuracy of multi-nodes localization and identity estimation algorithms directly affected the performance of multi-agent systems like WSN, multi-robot, cellular phone and so on. In this paper, a novel algorithm is introduced in order to achieve high accuracy for multi-nodes localization and identity estimation, this algorithm is named multi-beacon searching algorithm. In this algorithm, the concept of the grid is employed for estimating the location and identity of nodes, in which the environment represented by a grid of reference beacons, for each beacon, light-emitting diode (LED) is used. Whereas, each node in the environment is equipped with four LDR sensors which are used to sense the lighting of LEDs according to a proposed searching algorithm. The localization process achieved based on three proposed algorithms: Firstly, a modified binary search algorithm is utilized to estimate the approximate location of the node by a group of neighbor LEDs. Secondly, the accurate localization algorithm is used to find the accurate location of each node by reducing the number of neighbor LEDs. Finaly, two algorithms are introduced to evaluate the location and identification of each node: the centroid algorithm and the minimum bounded circle algorithm. In the minimum bounded circle algorithm, a new faster algorithm called the maxima boundaries convex hull algorithm for polygon convex hull construction is introduced instead of the Chan's algorithm. Several simulation processes have been implemented for testing the proposed algorithms. The obtained results show that the proposed algorithms have very good performance in estimating the accurate localizations of the nodes.

Randomized Incremental Construction of Delaunay Triangulations of Nice Point Sets

Randomized incremental construction (RIC) is one of the most important paradigms for building geometric data structures. Clarkson and Shor developed a general theory that led to numerous algorithms which are both simple and efficient in theory and in practice. Randomized incremental constructions are usually space-optimal and time-optimal in the worst case, as exemplified by the construction of convex hulls, Delaunay triangulations, and arrangements of line segments. However, the worst-case scenario occurs rarely in practice and we would like to understand how RIC behaves when the input is nice in the sense that the associated output is significantly smaller than in the worst case. For example, it is known that the Delaunay triangulation of nicely distributed points in {mathbb {E}}^d or on polyhedral surfaces in {mathbb {E}}^3 has linear complexity, as opposed to a worst-case complexity of Theta (n^{lfloor d/2rfloor }) in the first case and quadratic in the second. The standard analysis does not provide accurate bounds on the complexity of such cases and we aim at establishing such bounds in this paper. More precisely, we will show that, in the two cases above and variants of them, the complexity of the usual RIC is O(nlog n), which is optimal. In other words, without any modification, RIC nicely adapts to good cases of practical value. At the heart of our proof is a bound on the complexity of the Delaunay triangulation of random subsets of {varepsilon }-nets. Along the way, we prove a probabilistic lemma for sampling without replacement, which may be of independent interest.

Evolutionary construction of a formation-energy convex hull: Practical scheme and application to a carbon-hydrogen binary system

We present an evolutionary construction technique of formation-energy convex hull to search for thermodynamically stable compounds. In this technique, candidates with a wide variety of chemical compositions and crystal structures are created by systematically applying evolutionary operators, ``mating,'' ``mutation,'' and ``adaptive mutation,'' to two target compounds, and the convex hull is directly updated through the evolution. We applied the technique to carbon-hydrogen binary system at 10 GPa and obtained 15 hydrocarbons within the convex hull distance less than 0.5 mRy/atom: graphane, polybutadiene, polyethylene, butane, ethane, methane, three molecular compounds of ethane and methane, and six molecular compounds of methane and hydrogen. These results suggest that our evolutionary construction technique is useful for the exploration of stable phases under extreme conditions and the synthesis of new compounds.

Salient object detection via two-stage absorbing Markov chain based on background and foreground

This paper proposes a saliency detection method via two-stage absorbing Markov chain based on background and foreground for detecting salient objects in images. Firstly, image preprocessing is performed, followed by convex hull construction and superpixel segmentation, to prepare for subsequent processing. Secondly, according to the boundary connectivity, the superpixels with lower background probability value in the candidate boundary background set B0 are deleted, and the boundary background set B1 is obtained. With the saliency values of the nodes in the boundary-prior saliency map Sbg1, the background seeds are added appropriately in the region outside the candidate boundary background set B0 and the convex hull H, and the background seed set B is obtained after update. Then, the background-absorbing Markov chain is constructed to generate background-absorbing saliency map Sbg2. By fusing the saliency maps Sbg1 and Sbg2, the first-stage background-based saliency map Sbg is obtained. Thirdly, in the range of the convex hull H, the foreground seed set F is determined according to the saliency map Sbg. Then, the foreground-absorbing Markov chain is constructed, to obtain the second-stage foreground-absorbing saliency map Sfg. Finally, the saliency maps Sbg and Sfg of the two stages are combined to obtain a fused saliency map S, and the final saliency map S∗ is obtained after optimization through smoothing mechanism. Compared with the traditional methods, the performance of the proposed method is significantly improved. The proposed method is tested on three public image datasets, and it shows great accuracy in detecting salient objects.

A Combinatorial Approach for Constructing Lattice Structures

Abstract Lattice structures exhibit unique properties including a large surface area and a highly distributed load-path. This makes them very effective in engineering applications where weight reduction, thermal dissipation, and energy absorption are critical. Furthermore, with the advent of additive manufacturing (AM), lattice structures are now easier to fabricate. However, due to inherent surface complexity, their geometric construction can pose significant challenges. A classic strategy for constructing lattice structures exploits analytic surface–surface intersection; this, however, lacks robustness and scalability. An alternate strategy is voxel mesh-based isosurface extraction. While this is robust and scalable, the surface quality is mesh-dependent, and the triangulation will require significant postdecimation. A third strategy relies on explicit geometric stitching where tessellated open cylinders are stitched together through a series of geometric operations. This was demonstrated to be efficient and scalable, requiring no postprocessing. However, it was limited to lattice structures with uniform beam radii. Furthermore, existing algorithms rely on explicit convex-hull construction which is known to be numerically unstable. In this paper, a combinatorial stitching strategy is proposed where tessellated open cylinders of arbitrary radii are stitched together using topological operations. The convex hull construction is handled through a simple and robust projection method, avoiding expensive exact-arithmetic calculations and improving the computational efficiency. This is demonstrated through several examples involving millions of triangles. On a typical eight-core desktop, the proposed algorithm can construct approximately up to a million cylinders per second.

Bivariate Residual Plots With Simulation Polygons

When using univariate models, goodness of fit can be assessed through many different methods, including graphical tools such as half-normal plots with a simulation envelope. This is straightforward due to the notion of ordering of a univariate sample, which can readily reveal possible outliers. In the bivariate case, however, it is often difficult to detect extreme points and verify whether a sample of residuals is a reasonable realization from a fitted model. We propose a new framework, implemented as the bivrp R package, available on CRAN. Our framework uses the same principles of the simulation envelope in a half-normal plot, but as a simulation polygon for each point in a bivariate sample. By using algorithms of convex hull construction and polygon area reduction, we describe how our method works and illustrate its functionality with examples using simulated bivariate normal data and real bivariate count data. We show how different model diagnostics can produce different results and pinpoint potential drawbacks of our approach, such as the limitations in terms of computational burden. Supplementary materials for this article are available online.

Secondary Fans and Secondary Polyhedra of Punctured Riemann Surfaces

A famous construction of Gel'fand, Kapranov and Zelevinsky associates to each finite point configuration a polyhedral fan, which stratifies the space of weight vectors by the combinatorial types of regular subdivisions of A. That fan arises as the normal fan of a convex polytope. In a completely analogous way, we associate to each hyperbolic Riemann surface ℛ with punctures a polyhedral fan. Its cones correspond to the ideal cell decompositions of ℛ that occur as the horocyclic Delaunay decompositions which arise via the convex hull construction of Epstein and Penner. Similar to the classical case, this secondary fan of ℛ turns out to be the normal fan of a convex polyhedron, the secondary polyhedron of ℛ.

A new local search heuristic based on nearest insertion into the convex hull for solving Euclidean TSP

The travelling salesman problem (TSP) is probably the most famous and extensively studied problem in the field of combinatorial optimisation. This problem is in the fields of logistics, transportation, and distribution. Since the TSP is NP-hard, many heuristics for the TSP have been developed. In this paper, we developed a novel local search heuristic, based on nearest insertion into the convex hull construction heuristic for solving Euclidean TSP. The proposed method, nearest insertion into the convex hull local search (NICH-LS) is used to improve the initial tour, which is taken from a tour construction heuristic, multi-agent reinforcement learning (MARL) heuristic, by locally manipulating the order of nodes in the consecutive partial tours of the initial tour. Changing the order of nodes in a partial tour is done via constructing the NICH tour of these nodes and replacing the partial tour with the modified partial tour, if its length is reduced. The proposed novel local search heuristic is applied to 29 benchmark instances from TSPLIB. The computational results show the efficiency of the proposed local search compared with five state-of-the-art heuristics.

Fine-scale movement of juvenile Atlantic sturgeon (Acipenser oxyrinchus oxyrinchus) during aggregations in the lower Saint John River Basin, New Brunswick, Canada

Juvenile Atlantic sturgeon (Acipenser oxyrinchus oxyrinchus) form seasonal aggregations near the salt wedge in their natal river systems. We used an array of Vemco positioning system acoustic receivers to track fine-scale movement within aggregation sites in two rivers in the Saint John River Basin. We used the t-LoCoH convex hull construction algorithm to map space use and aggregation behavior and nonmetric multidimensional scaling to test for differences among rivers, seasons, and photoperiods. Aggregation sites consisted of small core areas, where juvenile Atlantic sturgeon remained for long periods, that are adjacent to foraging grounds. This structure was largely consistent between rivers and seasons. Directional movement within aggregation sites differed between rivers. In areas of high flow velocity, directional movement was parallel to flow and largely restricted to littoral areas, whereas areas of low flow exhibited no distinct patterns in directional movement. This indicates flow may be an important driver of fine-scale distribution within aggregation sites. Studies of fine-scale space use can inform future investigations of rearing capacity, aid in the identification of critical habitat, and inform management decisions.