Collection Of Line Segments Research Articles

Joint Resource Allocation and Trajectory Optimization for Completion Time Minimization for Energy-Constrained UAV Communications

An unmanned-aerial-vehicle (UAV)-aided communication scenario is studied in this research, where a UAV with constrained on-board battery capacity communicates with multiple ground users (GUs) during the flying process. We investigate the UAV trajectory as well as the resource allocation to minimize the time consumption of the specific task. The formulated problem is non-convex with innumerable variables. To make this problem tractable, a collection of line segments are utilized to represent the real trajectory through discretization. The reformulated problem is solved by applying the block coordinate descent (BCD) algorithm. To be specific, the reformulated problem is decoupled into two subproblems, i.e., resource allocation and trajectory optimization subproblems. The subproblems are both non-convex, which are efficiently resolved with the successive convex approximation (SCA) method. Then the result is obtained with an iterative algorithm. The simulation results reveal that, in comparison to benchmark schemes, the system performance has a significant improvement.

Optimal planar facility location with dense demands along a curve

This paper studies a multi-facility location problem with demand distributed continuously along a curve (MFLCD) in a planar space. We first model a single facility location problem in this setting. When the curve is approximated by a collection of line segments, an exact algorithm is proposed to solve the problem. Then we extend the model to the multi-facility case and propose an “alternate location and allocation” (ALA) based algorithm. Extensive computational experiments are conducted to justify the proposed models and algorithms. We show that using the proposed model to deal with continuous demand directly is much more effective than using other models with discrete demand generated by demand aggregation. As a by-product, some sufficient conditions that ensure an error-free demand aggregation from continuous demand to discrete demand are provided. Computational results are in support of the solution quality and computational efficiency of the proposed ALA-based algorithm for solving MFLCD problems. Our sensitivity analysis also offers some insights and suggestions.

Scratch iridescence

The surface of metal, glass and plastic objects is often characterized by microscopic scratches caused by manufacturing and/or wear. A closer look onto such scratches reveals iridescent colors with a complex dependency on viewing and lighting conditions. The physics behind this phenomenon is well understood; it is caused by diffraction of the incident light by surface features on the order of the optical wavelength. Existing analytic models are able to reproduce spatially unresolved microstructure such as the iridescent appearance of compact disks and similar materials. Spatially resolved scratches, on the other hand, have proven elusive due to the highly complex wave-optical light transport simulations needed to account for their appearance. In this paper, we propose a wave-optical shading model based on non-paraxial scalar diffraction theory to render this class of effects. Our model expresses surface roughness as a collection of line segments. To shade a point on the surface, the individual diffraction patterns for contributing scratch segments are computed analytically and superimposed coherently. This provides natural transitions from localized glint-like iridescence to smooth BRDFs representing the superposition of many reflections at large viewing distances. We demonstrate that our model is capable of recreating the overall appearance as well as characteristic detail effects observed on real-world examples.

Focal point computation and homogeneous geometrical transformation for linear curves

Summary In computer graphics, computer aided design, solid modelling and robotics and pattern recognition evaluation of focal point for a collection of line segments is the bottleneck problem. In the computer era the significant importance is given to this problem in present research world, however resolving its complexity has persisted imperceptible. This paper presents an efficient and optimal algorithm to evaluate intersection point in Euclidean space by evolving the mathematical analysis. Analysis of mathematics of the algorithm is rather seems to be intricate but implementation of algorithm is simple and straightforward.

α-Visibility

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility, weak and complete segment visibility, and the construction of the visibility graph. We also investigate the natural query versions of these problems, when α is either fixed or specified at query time.

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.

Coverage with k-transmitters in the presence of obstacles

For a fixed integer k≥0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower and upper bounds for the number of k-transmitters that are necessary and sufficient to cover a given collection of line segments, polygonal chains and polygons.

Power Control and Channel Training for MIMO Channels: A DMT Perspective

The achievable diversity and multiplexing tradeoff (DMT) in MIMO fading channels with channel training is analyzed in this paper. We first consider a typical training scenario, where the transmitter transmits training symbols followed by data symbols, and the receiver performs channel estimation using the training symbols and then uses the imperfect channel estimates to decode the data symbols. From the DMT perspective, our results show that as long as the training power is equal to the data power, the obtained DMT result based on imperfect channel state information at receiver (CSIR) is the same as the original DMT result with perfect CSIR given in Zheng and Tse's seminal work . We extend the analysis to two-way training scenarios, with single and multiple training rounds. Our results show that two-way training together with power control can substantially improve the achievable diversity gain. Specifically, the achievable DMT with multiple training rounds can be described as a single straight line; while in the case of single training round, the achievable DMT is much lower and can be described as a single straight line or a collection of line segments, depending on the underlying training strategy and channel qualities.

Zone diagrams in compact subsets of uniformly convex normed spaces

A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matousek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the existence of zone diagrams with respect to finitely many pairwise disjoint compact sites contained in a compact and convex subset of a uniformly convex normed space, provided that either the sites or the convex subset satisfy a certain mild condition. The proof is based on the Schauder fixed point theorem, the Curtis-Schori theorem regarding the Hilbert cube, and on recent results concerning the characterization of Voronoi cells as a collection of line segments and their geometric stability with respect to small changes of the corresponding sites. Along the way we obtain the continuity of the Dom mapping as well as interesting and apparently new properties of Voronoi cells.

Cluster-fusion recognition method for rivet lines based on Fisher discriminant criterion function

A cluster-fusion recognition method for rivet lines was proposed based on Fisher discriminant criterion function.The edge points were extracted using Canny operator,and processed by morphology in order to get the location of the centroid.Then,any two centroids were combined to construct the collection of line segments which were classified by Fisher criterion.According to the principle that the distance from the segments on one rivet line to origin point is similar,the segment-vectors were fused to fit the rivet line.The experimental results show that its accuracy and robustness are improved,which can meet the requirements of real-time detection.

Building Segment-Based Maps Without Pose Information

Most map building methods employed by mobile robots are based on the assumption that an estimate of robot poses can be obtained from odometry readings or from observing landmarks or other robots. In this paper we propose methods to build a global geometric map by integrating scans collected by laser range scanners without using any knowledge about the robots' poses. We consider scans that are collections of line segments. Our approach increases the flexibility in data collection, since robots do not need to see each other during mapping, and data can be collected by multiple robots or a single robot in one or multiple sessions. Experimental results show the effectiveness of our approach in different types of indoor environments.

On Reconfiguring Radial Trees

A linkage is a collection of line segments, called bars, possibly joined at their ends, called joints. We consider flattening a tree-like linkage, that is, a continuous motion of their bars from an initial configuration to a final configuration looking like a straight line segment, preserving the length of each bar and not crossing any two bars. Inthis paper, we introduce a new class of linkages, called trees, and show that there existsa radial tree which cannot be flattened.

Rational Geometry in Space

The objects and motions of geometrical modelling, graphics and robotics are most often described by rational (or close to rational) data in R 3 . This leads naturally to a notion of rational geometry (as opposed to the classical notion of Euclidean geometry) where two objects are considered equal if there exists a rational rigid motion from one to the other. We show here that although the notion of equality in rational geometry differs from that of Euclidean geometry for lines and planes, the two notions coincide on collections of line segments, in particular for polyhedra. Next, by an explicit symbolic calculation and the use of a simple technique of classical number theory, we obtain a rational parameterization of the subgroup of all rational linear movements of the space which keep a given point fixed. Finally we study the equivalence relation of Q -equality among segments in the space Q 3 , and give a representation of the space of equivalence classes, i.e. of the quotient space Q 3 /O(3, Q) .

Computing Simple Circuits from a Set of Line Segments is NP-Complete

Given a collection of line segments in the plane, the segments are connected by their endpoints to construct a simple circuit. (A simple circuit is the boundary of a simple polygon.) However, there are collections of line segments where this cannot be done. In this note it is proved that deciding whether a set of line segments admits a simple circuit is NP-complete. The NP-completeness proof relies on the fact that line segments may intersect at their endpoints. Deciding whether a set of horizontal line segments can be connected with horizontal and vertical line segments to construct an orthogonal simple circuit is also shown to be NP-complete.

Fuzzy approach to solve the recognition problem of handwritten chinese characters

A method based on the concept of fuzzy set for handwritten Chinese character (HCC) recognition is proposed in this paper. Chinese characters can be viewed as a collection of line segments, called strokes. Since the strokes under consideration here are fuzzy in nature, the concept of fuzzy set is utilized in the similarity measure. Two membership functions are defined for the location measure and type measure between two strokes, and a function of fuzzy entropy is used in information measure. Although the recognition problem can be reduced to the assignment problem, some modifications are still necessary. All the similarities between the corresponding strokes can be chosen by solving the assignment problem using the cost function of fuzzy entropy, and then are averaged to derive the score of similarity between two Chinese characters. 881 classes of Chinese characters in ETL-8 (160 variations/class) are used as the test patterns, and the recognition rate is about 96%. In addition, experiments about the effects of the membership function based on the class separability are also discussed in this paper.