Straight-line Edges Research Articles

An Ultrawideband Compact Magneto-Electric Dipole Antenna and Its Coupled Array

A novel magneto-electric dipole antenna with compact structure and unidirectional radiation is proposed. The electrical connection between the U-shaped floor and the electric dipole (E-dipole) was cut off to reduce the profile height, and the straight-line edges of the original dipoles were replaced with an arc-shaped one to stabilize the VSWR. Furthermore, when the antenna element is employed as the coupled array unit, the altering of the element number and the way the array is assembled has no significant impact on the radiation performance, which is almost the same as that of a single antenna. The modified prototype of a 2×2 array with the dimension of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.33 \lambda_{L} \times 0.28 \lambda_{L} \times 0.10 \lambda_{L}$</tex-math></inline-formula> is fabricated and measured. Results indicate that the antenna array exhibits a band ratio of 30.9 with VSWR≤ 2.3 in 98 MHz-3.03 GHz, realized gain of 4.1-14.9 dBi and unidirectional pattern with SLL<-10 dB from 98 to 700 MHz.

Traveling edge states in massive Dirac equations along slowly varying edges

Abstract Topologically protected wave motion has attracted considerable research interest due to its chirality and potential applications in many applied fields. We construct quasi-traveling wave solutions to the 2D Dirac equation with a domain wall mass in this work. It is known that the system admits exact and explicit traveling wave solutions, which are termed edge states if the interface is a straight line. By modifying such explicit solutions, we construct quasi-traveling-wave solutions if the interface is nearly straight. The approximate solutions in two scenarios are given. One is the circular edge with a large radius, and the second is a straight line edge with the slowly varying along the perpendicular direction. We show the quasi-traveling wave solutions are valid in a long lifespan by energy estimates. Numerical simulations are provided to support our analysis both qualitatively and quantitatively.

Computer Vision Method for In Situ Measuring Forming Accuracy of 3D Sand Mold Printing

The three-dimensional sand mold printing technology (3DSP) for casting sand molds via a binding jet is a breakthrough in the casting mold-making process. It is a favorable combination of digital forming technology and sand casting, which is a significantly interesting research area in the foundry industry. This study has proposed an edge extraction approach for the forming region in the sand bed image. With the edge information, the study measures the forming accuracy of the printed molds, which offers a basis for assessing the forming quality after 3DSP. The extracted edges essentially match the original image through the validation of cube printing. The error between the measured and actual size is below 0.6 mm, and the standard deviation of the straight line edge is below 0.170 mm, which fulfills the accuracy requirements for 3D sand mold printing.

The Complexity of Drawing a Graph in a Polygonal Region

We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal region, with some vertices of the graph assigned to points on the boundary of the region, place the remaining vertices to create a planar straight-line drawing of the graph inside the region. This establishes a wider context for the NP-hardness result by Patrignani on extending partial planar graph drawings. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open in the case of a simply connected region. We also show that, even for integer input coordinates, it is possible that drawing a graph in a polygonal region requires some vertices to be placed at irrational coordinates. By contrast, the coordinates are known to have bounded bit complexity for the special case of a convex region, or for drawing a path in any polygonal region. In addition, we prove a Mnëv-type universality result - loosely speaking, that the solution spaces of instances of our graph drawing problem are equivalent, in a topological and algebraic sense, to bounded algebraic varieties.

Modeling and prediction of tool influence function under complex edge in sub-aperture optical polishing.

Edge mis-figures are regarded as one of the most difficult technical issues in optical fabrication. At present, only the near straight-line edge tool influence function (TIF) can be fitted by a polynomial function, but it is difficult to unify a 2-D analytical model suitable for complex edge workpieces and various tools, due to the lack of the scientific understanding of the edge removal behavior. In this paper, a comprehensive mathematical model is proposed to reveal the mechanism of the edge effect and accurately predict the complex edge TIF. The concept of a nonlinear edge kernel is first proposed and verified that the nonlinear pressure can be characterized by convoluting the kernel with the edge contour, which can be easily adapted to complex edge cases; besides, the edge kernel obtaining algorithm is established. The linear pressure part is verified to be constrained by the moment balance formula, which occurs in universal joint tool. Besides, the basic pressure distribution is presented to compensate the pressure distortion caused by the uneven form of the tool pad. The introducing of these three parts makes the complex edge pressure modeled efficiently and matched perfectly with the FEA results. In addition, a series of TIF experiments were carried out on various complex edge workpieces and different tools, which could be well predicted by the proposed model in 2-D view.

Drawing graphs on few lines and few planes

We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many relations to other challenging graph-drawing problems such as small-area or small-volume drawings,layered or track drawings, and drawing graphs with low visual complexity. While some facts about our problem are implicit in previous work, this is the first treatment of the problem in its full generality. Our contribution is as follows. We show lower and upper bounds for the numbers of lines and planes needed for covering drawings of graphs in certain graph classes. In some cases our bounds are asymptotically tight; in some cases we are able to determine exact values. We relate our parameters to standard combinatorial characteristics of graphs (such as the chromatic number, treewidth, or arboricity) and to parameters that have been studied in graph drawing (such as the track number or the number of segments appearing in a drawing). We pay special attention to planar graphs. For example, we show that there are planar graphs that can be drawn in 3-space on asymptotically fewer lines than in the plane.

Minimizing the continuous diameter when augmenting a geometric tree with a shortcut

We augment a tree T with a shortcut pq to minimize the largest distance between any two points along the resulting augmented tree T+pq. We study this problem in a continuous and geometric setting where T is a geometric tree in the Euclidean plane, a shortcut is a line segment connecting any two points along the edges of T, and we consider all points on T+pq (i.e., vertices and points along edges) when determining the largest distance along T+pq. The continuous diameter is the largest distance between any two points along edges. We establish that a single shortcut is sufficient to reduce the continuous diameter of a geometric tree T if and only if the intersection of all diametral paths of T is neither a line segment nor a point. We determine an optimal shortcut for a geometric tree with n straight-line edges in O(nlog⁡n) time.

Persistence-based resolution-independent meshes of superpixels

The over-segmentation problem is to split a pixel-based image into a smaller number of superpixels that can be treated as indecompasable regions to speed up higher level image processing such as segmentation or object detection. A traditional superpixel is a potentially disconnected union of square pixels, which can have complicated topology (with holes) and geometry (highly zigzag boundaries). This paper contributes to new resolution-independent superpixels modeled as convex polygons with straight-line edges and vertices with real coordinates not restricted to a fixed pixel grid. Any such convex polygon can be rendered at any resolution higher than in original images, hence superpixels are resolution-independent.The key difficulty in obtaining resolution-independent superpixels is to find continuous straight-line edges, while classical edge detection focuses on extracting only discrete edge pixels. The recent Persistent Line Segment Detector (PLSD) avoids intersections and small angles between line segments, which are hard to fix before a proper polygonal mesh can be constructed. The key novelty is an automatic selection of strongest straight-line segments by using the concept of persistence from Topological Data Analysis, which allows to rank segments by their strength. The PLSD performed well in comparison with the only past Line Segment Detector Algorithm (LSDA) on the Berkeley Segmentation Database of 500 real-life images. The PLSD is now extended to the Persistent Resolution-Independent Mesh (PRIM).

Plane and planarity thresholds for random geometric graphs

A random geometric graph, [Formula: see text], is formed by choosing [Formula: see text] points independently and uniformly at random in a unit square; two points are connected by a straight-line edge if they are at Euclidean distance at most [Formula: see text]. For a given constant [Formula: see text], we show that [Formula: see text] is a distance threshold function for [Formula: see text] to have a connected subgraph on [Formula: see text] points. Based on this, we show that [Formula: see text] is a distance threshold for [Formula: see text] to be plane, and [Formula: see text] is a distance threshold to be planar. We also investigate distance thresholds for [Formula: see text] to have a non-crossing edge, a clique of a given size, and an independent set of a given size.

Structural Low-Level Dynamic Response Analysis Using Deviations of Idealized Edge Profiles and Video Acceleration Magnification

The development of high-speed camera systems and image processing techniques has promoted the use of vision-based methods as a practical alternative for the analysis of non-contact structural dynamic responses. In this study, a deviation extraction method is introduced to obtain deviation signals from structural idealized edge profiles. Given that the deviation temporal variations can reflect the structural vibration characteristics, a method based on singular-value decomposition (SVD) is proposed to extract valuable vibration signals from the matrix composed of deviations from all video frames. However, this method exhibits limitations when handling low-level motions that reflect high-frequency vibration components. Hence, a video acceleration magnification algorithm is employed to enhance low-level deviation variations before the extraction. The enhancement of low-level deviation variations is validated by a light-weight cantilever beam experiment and a noise barrier field test. From the extracted waveforms and their spectrums from the original and magnified videos, subtle deviations of the selected straight-line edge profiles are magnified in the reconstructed videos, and low-level high-frequency vibration signals are successfully enhanced in the final extraction results. Vibration characteristics of the test beam and the noise barrier are then analyzed using signals obtained by the proposed method.

Hybridizing simulated annealing with variable neighborhood search for bipartite graph crossing minimization

Given a bipartite graph, the problem we address, called the bipartite graph crossing minimization problem (BGCMP), is to find an embedding the parts of the graph along two parallel lines so that the number of edge crossings is minimized. It is assumed that each edge is drawn as a straight line segment and edges sharing an end vertex do not cross. We propose an approach for the BGCMP, which combines a simulated annealing (SA) method with a variable neighborhood search (VNS) scheme. These two algorithms are executed iteratively. At each iteration, the solution produced by SA is submitted as input to the VNS component of the approach. Our VNS algorithm uses a local search technique which is based on a fast insertion neighborhood exploration procedure. We show that the time complexity of this procedure is O(n2), where n is the order of the graph. Another fast procedure is proposed for computing the gain in the objective function value obtained by swapping positions of two vertices. We experimentally compare our algorithm (called SA-VNS) against the tabu search algorithm as well as GRASP approach from the literature. Computational results are reported on four sets of bipartite graphs. The results demonstrate the superiority of SA-VNS over the state-of-the-art methods. The source code implementing SA-VNS is made publicly available as a benchmark for future comparisons.

Efficient Registration of Laser-Scanned Point Clouds of Bridges Using Linear Features

Efficient registration of point clouds from terrestrial laser scanners enables us to move from scanning to point cloud applications immediately. In this paper, a new efficient rough registration method of laser-scanned point clouds of bridges is proposed. Our method relies on straight-line edges as linear features, which often appear in many bridges. Efficient edge-line extraction and line-based registration methods are described in this paper. In our method, first, sampled regular point clouds based on the azimuth and elevation angles are created, and planar regions are extracted using the region growing on the regular point clouds. Then, straight lines of the edges of the planar regions are extracted as linear features. Next, vertical and horizontal line clusters are created according to the direction of the lines. To align the position and orientation of two point clouds, two corresponding nonparallel line pairs from line clusters are used. In the registration process, the RANSAC approach with a hash table of line pairs is used. In this process, the hash table is used for finding candidates of corresponding line pairs efficiently. Sampled points on the line pairs are used to align the line pairs, and occupied voxels and downsampled point clouds are used for efficient consensus calculation. The method is tested using three data sets of different types of bridges: a small steel bridge, a middle-size concrete bridge, and a high-pier concrete bridge. In our experiments, successful rates of our rough registration were 100%, and the processing time of rough registration for 19 point clouds was about 1 min.

Towards Visualizing Big Data with Large-Scale Edge Constraint Graph Drawing

Abstract Visualization plays an important role in enabling understanding of big data. Graphs are crucial tools for visual analytics of big data networks such as social, biological, traffic and security networks. Graph drawing has been intensively researched to enhance aesthetic features (i.e., layouts, symmetry, cross-free edges). Early physic-inspired techniques have focused on synthetic abstract graphs whose weights/distances of the edges are often ignored or assumed equal. Although recent approaches have been extended to sophisticated realistic networks, most are not designed to address very large-scale weighted graphs, which are important for visual analyses. The difficulty lies in the fact that the drawing process, governed by these physical properties, oscillates in large graphs and conflicts with specified distances leading to poor visual results. Our research attempts to alleviate these obstacles. This paper presents a simple graph visualization technique that aims to efficiently draw aesthetically pleasing large-scale straight-line weighted edge graphs. Our approach uses relevant physic-inspired techniques to promote aesthetic graphs and proposes a weak constraint-based approach to handle large-scale computing and competing goals to satisfy both weight requirements and aesthetic properties. The paper describes the approach along with experiments on both synthetic and real large-scale weighted graphs including that of over 10,000 nodes and comparisons with state-of-the-art approaches. The results obtained show enhanced and promising outcomes toward a general-purpose graph drawing technique for both big synthetic and real network data analytics.

一种利用大气散射模型实现图像去雾的方法

针对雾天图像清晰度不高的问题，我们采用大气散射模型进行图像去雾处理，利用Curvelet变换提取图像边缘，根据边缘相交的直线先计算灭点值，再由灭点计算景深值，得到含雾图像中入射光的辐射系数，即图像真实的颜色值，达到图像去雾的目的。在景深值计算中，分别对含雾图像的每个像素点都做一次景深计算，在一定程度上可以解决由于单一景深导致部分区域颜色失真的问题，使去雾后图像的颜色更自然。最后，通过实验验证了方法的有效性。 In view of the problem that the image under foggy days is not clear, the atmospheric scattering model is used to process the image dehazing. First, the Curvelet transform extracts the image edge and calculates the vanishing point on the basis of the intersection of straight line edges. Then it calculates the depth of field value according to the vanishing point. The radiation coefficient of incident light in the foggy image is obtained, which means that the real color value of the image is obtained and the image dehazing is finished. When calculating the depth of field value, it respectively calculates the depth of field value of every foggy image’s pixel at the same time, which solves the partial area color distortion problem that is caused by using single depth of field, and makes the processed image look more natural. Finally, the validity of the method is verified by experiments.

A Census of Plane Graphs with Polyline Edges

We study vertex-labeled graphs that can be embedded on a given point set such that every edge is a polyline with $k$ bends per edge, where $k\in \mathbb{N}$. It is shown that on every $n$-element point set in the plane, at most $\exp(O(n\log(2+k)))$ labeled graphs can be embedded using polyline edges with $k$ bends per edge, and this bound is the best possible. This is the first exponential upper bound for the number of labeled plane graphs where the edges are polylines of constant complexity. Standard tools developed for the enumeration of straight-line graphs, such as triangulations and crossing numbers, do not seem applicable in this scenario. Furthermore, the exponential upper bound does not carry over to other popular relaxations of straight-line edges; for example, the number of labeled planar graphs that admit an embedding with $x$-monotone edges on $n$ points is superexponential.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case

This paper is the second part of a series of two. It follows [44], in which the positivity-preservation property of methods solving one-dimensional Lagrangian gas dynamics equations, from first-order to high-orders of accuracy, was addressed. This article aims at extending this analysis to the two-dimensional case. This study is performed on a general first-order cell-centered finite volume formulation based on polygonal meshes defined either by straight line edges, conical edges, or any high-order curvilinear edges. Such formulation covers the numerical methods introduced in [6], [32], [5], [41], [43]. This positivity study is then extended to high-orders of accuracy. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. It is important to point out that even if this paper is concerned with purely Lagrangian schemes, the theory developed is of fundamental importance for any methods relying on a purely Lagrangian step, as ALE methods or non-direct Euler schemes.

Recognizing and drawing IC-planar graphs

We give new results about the relationship between 1-planar graphs and RACgraphs. A graph is 1-planar if it has a drawing where each edge is crossed at most once. A graph is RAC if it can be drawn in such a way that its edges cross only at right angles. These two classes of graphs and their relationships have been widely investigated in the last years, due to their relevance in application domains where computing readable graph layouts is important to analyze or design relational data sets. We study IC-planar graphs, the sub-family of 1-planar graphs that admit 1-planar drawings with independent crossings (i.e., no two crossed edges share an endpoint). We prove that every IC-planar graph admits a straight-line RAC drawing, which may require however exponential area. If we do not require right angle crossings, we can draw every IC-planar graph with straight-line edges in linear time and quadratic area. We then study the problem of testing whether a graph is IC-planar. We prove that this problem is NP-hard, even if a rotation system for the graph is fixed. On the positive side, we describe a polynomial-time algorithm that tests whether a triangulated plane graph augmented with a given set of edges that form a matching is IC-planar.

Thickness and colorability of geometric graphs

The geometric thickness of a graph G is the smallest integer t such that there exist a straight-line drawing Γ of G and a partition of its straight-line edges into t subsets, where each subset induces a planar drawing in Γ. Over a decade ago, Hutchinson, Shermer, and Vince proved that any n-vertex graph with geometric thickness two can have at most 6n−18 edges, and for every n≥8 they constructed a geometric thickness-two graph with 6n−20 edges. In this paper, we construct geometric thickness-two graphs with 6n−19 edges for every n≥9, which improves the previously known 6n−20 lower bound. We then construct a thickness-two graph with 10 vertices that has geometric thickness three, and prove that the problem of recognizing geometric thickness-two graphs is NP-hard, answering two questions posed by Dillencourt, Eppstein and Hirschberg. Finally, we prove the NP-hardness of coloring graphs of geometric thickness t with 4t−1 colors, which strengthens a result of McGrae and Zito, when t=2.

Fourier–Mellin Transforms for Circular Domains

Generalized Fourier–Mellin transforms for analytic functions defined in simply connected circular domains are derived. Circular domains are taken to be those with boundaries that are a finite union of circular arcs, including straight line edges. The results are an extension to circular domains of the generalized Fourier transforms for convex polygons (having only straight line edges) derived by Fokas and Kapaev (IMA J Appl Math 68:355–408, 2003). First, a new, elementary derivation of the latter result for polygons is given based on Cauchy’s integral formula and a spectral representation of the Cauchy kernel. This rederivation extends in a natural way to the case of circular domains once an adapted spectral representation of the Cauchy kernel is established. Domains with boundaries that are a combination of circular arc and straight line edges can be treated similarly. The newly derived transforms are generalizations of the classical Fourier and Mellin transforms to general circular domains. It is shown by example how they can be used to solve boundary value problems for Laplace’s equation in such domains. The notions of spectral matrix and fundamental contour, which arise naturally in the formulation, are also introduced.

A note on 1-planar graphs

A graph is 1-planar if it can be drawn in the plane such that each of its edges is crossed at most once. We prove a conjecture of Czap and Hudák (2013) stating that the edge set of every 1-planar graph can be decomposed into a planar graph and a forest. We also provide simple proofs for the following recent results: (i) an n-vertex graph that admits a 1-planar drawing with straight-line edges has at most 4n−9 edges (Didimo, 2013); and (ii) every drawing of a maximally dense right angle crossing graph is 1-planar (Eades and Liotta, 2013).