Drawing Algorithms Research Articles

$st$-Orientations with Few Transitive Edges

The problem of orienting the edges of an undirected graph such that the resulting digraph is acyclic and has a single source $s$ and a single sink $t$ has a long tradition in graph theory and is central to many graph drawing algorithms. Such an orientation is called an $st$-orientation. We address the problem of computing $st$-orientations of undirected graphs with the minimum number of transitive edges. We prove that the problem is NP-hard in the general case. For planar graphs we describe an ILP (Integer Linear Programming) model that is fast in practice, namely it takes on average less than 1 second for graphs with up to 100 vertices, and about 10 seconds for larger instances with up to 1000 vertices. We experimentally show that optimum solutions significantly reduce (35% on average) the number of transitive edges with respect to unconstrained $st$-orientations computed via classical $st$-numbering algorithms. Moreover, focusing on popular graph drawing algorithms that apply an $st$-orientation as a preliminary step, we show that reducing the number of transitive edges leads to drawings that are much more compact (with an improvement between 30% and 50% for most of the instances).

Tightening Curves on Surfaces Monotonically with Applications

We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number of crossings in the curve is not allowed to increase at any time during the process. The best known upper bound before was exponential, which can be obtained by combining the algorithm of De Graaf and Schrijver [ J. Comb. Theory Ser. B , 1997] together with an exponential upper bound on the number of possible surface maps. To obtain the new upper bound, we apply tools from hyperbolic geometry, as well as operations in graph drawing algorithms—the cluster and pipe expansions—to the study of curves on surfaces. As corollaries, we present two efficient algorithms for curves and graphs on surfaces. First, we provide a polynomial-time algorithm to convert any given multicurve on a surface into minimal position. Such an algorithm only existed for single closed curves, and it is known that previous techniques do not generalize to the multicurve case. Second, we provide a polynomial-time algorithm to reduce any k -terminal plane graph (and more generally, surface graph) using degree-1 reductions, series-parallel reductions, and Δ Y -transformations for arbitrary integer k . Previous algorithms only existed in the planar setting when k ≤ 4, and all of them rely on extensive case-by-case analysis based on different values of k . Our algorithm makes use of the connection between electrical transformations and homotopy moves and thus solves the problem in a unified fashion.

Toward Building a Functional Image of the Design Object in CAD

The paper proposes an approach to the classification of lifecycle support automation systems for engineering objects, with the proposed structure of the description of the designed object, using a triple description approach: functional, mathematical, and physical. Following this approach, an algorithm for drawing up a functional description of the lifecycle is described, which is based on the principle of unity of analysis and synthesis of the created system in the design process. The proposed solutions are considered using the traditional aircraft shaping methodology with the application of the airplane make-up algorithm as an example. Furthermore, the architecture of a multiagent platform for structural–parametric synthesis of the object was presented; for convenient usage of this architecture, it was proposed to use classification of design tasks in the form of a design cube. The proposed approach allows obtaining an accurate description of the designed object and the subtasks needed to create it, which can reduce the time of the project. Unfortunately, not all decisions can be automated at the given stage of technical development, but what is possible to automate is enough to achieve a reduction in terms of realization and an acceleration of the prototyping process, as shown in the considered example. The actual reduction throughout the lifecycle of the product ranges from 10% to 21% of the planned time.

Event‐based Dynamic Graph Drawing without the Agonizing Pain

AbstractTemporal networks can naturally model real‐world complex phenomena such as contact networks, information dissemination and physical proximity. However, nodes and edges bear real‐time coordinates, making it difficult to organize them into discrete timeslices, without a loss of temporal information due to projection. Event‐based dynamic graph drawing rejects the notion of a timeslice and allows each node and edge to retain its own real‐valued time coordinate. While existing work has demonstrated clear advantages for this approach, they come at a running time cost. We investigate the problem of accelerating event‐based layout to make it more competitive with existing layout techniques. In this paper, we describe the design, implementation and experimental evaluation of MultiDynNoS, the first multi‐level event‐based graph layout algorithm. We consider three operators for coarsening and placement, inspired by Walshaw, GRIP and FM3, which we couple with an event‐based graph drawing algorithm. We also propose two extensions to the core algorithm: AutoTau and Bend Transfer. We perform two experiments: first, we compare MultiDynNoS variants to existing state‐of‐the‐art dynamic graph layout approaches; second, we investigate the impact of each of the proposed algorithm extensions. MultiDynNoS proves to be competitive with existing approaches, and the proposed extensions achieve their design goals and contribute in opening new research directions.

Granger causality procedeture to diagnosis and failture in industrial systems

Industrial process supervision is an important subject now days due to the increased requirement for safer processes for operators and effective for companies. Control loops affected by disturbs, are grouped with PCA, based on their increased variability and the causal relationships between them are detected via Granger causality. A graph drawing algorithm allows indicating the source of the disturbance. The procedure is applied to data from a simulated chemical process CSTR. The proposed procedeture correctly indicated the sources of disturbances.

Drawing Halin-graphs with small height

In this paper, we study how to draw Halin-graphs, i.e., planar graphs that consist of a tree $T$ and a cycle among the leaves of that tree. Based on tree-drawing algorithms and the pathwidth $pw(T) $, a well-known graph parameter, we find poly-line drawings of height at most $6pw(T)+3\in O(\log n)$. We also give an algorithm for straight-line drawings, and achieve height at most $12pw(T)-1$ for Halin-graphs, and smaller if the Halin-graph is cubic. We show that the height achieved by our algorithms is optimal in the worst case (i.e. for some Halin-graphs).

The algorithms for drawing up annual plans of inspections performed by Rospotrebnadzor’s regional organizations within the framework of risk-based model

The existing model of control and surveillance activities is based on a procedure that involves assigning activities performed by juridical persons or private entrepreneurs and (or) production facilities used by them in these activities into a specific risk category or a specific hazard class (category). The goal of the present work was to develop and improve algorithms for drawing up annual plans of inspections performed by Rospotrebnadzor’s territorial organizations within the framework of the risk-based model. For the first time, we have formulated conceptual and mathematical statement of the problem of planning control and surveillance activities performed by Rospotrebnadzor. This allowed us, among other things, to consider history of violations (integrity of a given subject) over a specific period and availability of objects for inspections. The latter is described with several parameters that include both regional peculiarities (a distance between objects, quality of road networks) and “complexity” of checking a particular object. When analyzing the mathematical statement, we identified certain model parameters that had the greatest influence on a solution to the problem, that is, the most sensitive parameters that should be regulated with special care if we want to make control and surveillance activities more effective. We have created planning algorithms with preset parameter values (scenario forecasting programs) and tested them at the regional level. We have developed three criteria for comparing these algorithms: coverage of a number of subjects that are to be inspected; coverage of a number of objects that are to be inspected; coverage by the total risk. The testing results indicate that the combined algorithm has higher coverage rates since in this case not all objects are inspected when a given subject is being checked. Consequently, this allows reducing overall labor costs required to perform an inspection. The suggested approaches give an opportunity to achieve more effective distribution and use of resources allocated by Rospotrebnadzor for scheduled inspections.

Алгоритмы формирования ежегодных планов проведения проверок территориальными органами и организациями Роспотребнадзора в рамках риск-ориентированной модели

The existing model of control and surveillance activities is based on a procedure that involves assigning activities performed by juridical persons or private entrepreneurs and (or) production facilities used by them in these activities into a specific risk category or a specific hazard class (category). The goal of the present work was to develop and improve algorithms for drawing up annual plans of inspections performed by Rospotrebnadzor’s territorial organizations within the framework of the risk-based model. For the first time, we have formulated conceptual and mathematical statement of the problem of planning control and surveillance activities performed by Rospotrebnadzor. This allowed us, among other things, to consider history of violations (integrity of a given subject) over a specific period and availability of objects for inspections. The latter is described with several parameters that include both regional peculiarities (a distance between objects, quality of road networks) and “complexity” of checking a particular object. When analyzing the mathematical statement, we identified certain model parameters that had the greatest influence on a solution to the problem, that is, the most sensitive parameters that should be regulated with special care if we want to make control and surveillance activities more effective. We have created planning algorithms with preset parameter values (scenario forecasting programs) and tested them at the regional level. We have developed three criteria for comparing these algorithms: coverage of a number of subjects that are to be inspected; coverage of a number of objects that are to be inspected; coverage by the total risk. The testing results indicate that the combined algorithm has higher coverage rates since in this case not all objects are inspected when a given subject is being checked. Consequently, this allows reducing overall labor costs required to perform an inspection. The suggested approaches give an opportunity to achieve more effective distribution and use of resources allocated by Rospotrebnadzor for scheduled inspections.

Computer Aided DIY Design of Stylized Generation of Random Needle Embroidery

Random stitch embroidery uses jagged and crossed lines to represent the painting and embroidery principles of an image. It requires the embroiderer to repeatedly scrutinize the embroidery techniques, operating steps, and predict the effects of embroidery. The embroidery has very personal artistic characteristics. In order to solve the problem of high difficulty in designing random stitch embroidery, long creation time, and difficulty in pre-viewing the effect, an interactive tool is proposed to assist users in DIY design of random stitch embroidery. By generating creation preview images and marked embroidery drafts, users can quickly embroider their own de-signs. Input the target image as a reference for random stitch embroidery, and divide the image into sub-regions based on the clustering algorithm for detailed drawing. Build a single stitch model and a multi-layer stitch model based on the texture characteristics of the object, and set the corresponding length, orientation, density, thickness and other parameters to the desired texture. Based on the image style, an interactive reconstruction using vector field rendering technology and lighting simulation technology are constructed for users to carry out DIY design and effect previews. Based on the CorelDraw platform, a DIY drawing system for random stitch embroidery and a draft generation system are developed, a human-computer interaction interface is designed, and case simulations are carried out. The experimental results show that proposed tool improves the efficiency and creativity of embroidery design. To generate a marked manuscript can also be provided to random needle embroidery beginners, to facilitate their rapid grasp of the random needle embroidery drawing methods and skills.

Clock Skew Compensation Algorithm Immune to Floating-Point Precision Loss

We propose a novel clock skew compensation algorithm based on Bresenham's line drawing algorithm. The proposed algorithm can avoid the effect of limited floating-point precision (e.g., 32-bit single precision) on clock skew compensation and thereby provide high-precision time synchronization even with resource-constrained sensor nodes in wireless sensor networks.

Toroidal Spectral Drawing

We give a deterministic drawing algorithm to draw a graph onto a torus, which is based on the usual spectral drawing algorithm. For most of the well-known toroidal vertex-transitive graphs, the result drawings give an embedding of the graphs onto the torus.

Real-time interactive visualization of large networks on a tiled display system

This paper introduces a methodology for visualizing large real-world (social) network data on a high-resolution tiled display system. Advances in network drawing algorithms enabled real-time visualization and interactive exploration of large real-world networks. However, visualization on a typical desktop monitor remains challenging due to the limited amount of screen space and ever increasing size of real-world datasets.To solve this problem, we propose an integrated approach that employs state-of-the-art network visualization algorithms on a tiled display system consisting of multiple screens. Key to our approach is to use the machine’s graphics processing units (GPUs) to their fullest extent, in order to ensure an interactive setting with real-time visualization. To realize this, we extended a recent GPU-based implementation of a force-directed graph layout algorithm to multiple GPUs and combined this with a distributed rendering approach in which each graphics card in the tiled display system renders precisely the part of the network to be displayed on the monitors attached to it.Our evaluation of the approach on a 12-screen 25 megapixels tiled display system with three GPUs, demonstrates interactive performance at 60 frames per second for real-world networks with tens of thousands of nodes and edges. This constitutes a performance improvement of approximately 4 times over a single GPU implementation. All the software developed to implement our tiled visualization approach, including the multi-GPU network layout, rendering, display and interaction components, are made available as open-source software.

Improvement of Fuzzy Graph Drawing Using Partition Tree

Obtaining useful information from ambiguous information is a necessity in various fields. Ambiguous information can be handled quantitatively by using fuzzy theory, and representing it in an easy-to-understand manner is critical. One solution is to visualize an ambiguous relationship by using fuzzy graph representation, which has the essential characteristic of expressing variable relationships in between its nodes. We previously proposed an algorithm to draw intelligible and comprehensive fuzzy graphs. This study describes an improved drawing method for that graph drawing algorithm. As a result, highly related nodes were arranged closer to one another, and the display area was reduced. This method can be used as an effective means of expressing the results of ambiguous information analysis.

АЛГОРИТМ СКЛАДАННЯ ПОДАТКОВОЇ ДЕКЛАРАЦІЇ ПЛАТНИКА ЄДИНОГО ПОДАТКУ В УМОВАХ ВОЄННОГО СТАНУ

Introduction. Traditionally, the introduction of new taxes (for example, 2% of the single tax) led to the need to approve the appropriate form of tax declaration for both individuals and legal entities. It happened this time as well. The form of the tax declaration of payers of the single tax of the third group for the period of martial law and state of emergency in Ukraine was approved by the order of the Ministry of Finance of Ukraine dated April 26, 2022 No. 124 "On approval of the form of the tax declaration of the payer of the single tax of the third group for the period of martial law and state of emergency in Ukraine ". In general, the tax declaration of taxpayers of the single tax of the third group has a very simplified form, which consists of three parts and two appendices. At the same time, it is necessary to have an appropriate set of tools to correctly fill in the relevant lines of such a tax declaration. Such a tool can be an algorithm for drawing up a tax declaration of a single tax payer under martial law. Purpose. The purpose of the article is to develop an algorithm for drawing up a tax declaration of a single tax payer under martial law. Results. In the course of the research, the procedure for filling out the tax declaration of single tax payers under martial law conditions was identified. The proposed algorithm for filling out the lines of such a declaration made it possible to make it correctly, which in turn will be useful for all legal entities that prepare such a tax declaration, and the proposed algorithm will be useful for the authorities of the State Tax Service of Ukraine when conducting inspections of single tax payers. Discussion. In further scientific research, it is proposed to focus attention on the discussion regarding the study of the feasibility of the existence of a simplified taxation system, which on the one hand is a catalyst forthe development of small businesses, and on the other hand is a tool for minimizing tax payments to the state budget.

Lithological Patterns Based on Arc Fitting

Map of geological cross section is the most intuitive expression of strata in the vertical direction. Realizing automatic filling of lithologic patterns and reflecting the changes of stratum curvature are important contents of map of geological cross section drawing. The traditional lithologic pattern filling method can not show the change of rock stratum dip angle. To solve this problem, an algorithm of lithologic pattern drawing based on arc fitting is proposed. By analyzing the mathematical relationship between the dip angle of the rock stratum and the boundary line of the rock stratum, the data needed for drawing can be increased, and then the curve and lithologic pattern can be drawn according to the dip angle of the rock stratum.The application results show that the lithologic pattern compiled by the algorithm changes with the change of rock dip, and the first derivative of a single curve in the lithologic pattern is continuous and the segments are circular arcs.

Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, (SGD)2.

Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others. We propose a layout approach, Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, (SGD)2, that can handle multiple readability criteria. (SGD)2 can optimize any criterion that can be described by a differentiable function. Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other criteria which have not yet been explicitly optimized in such fashion (e.g., node resolution, angular resolution, aspect ratio). The approach is scalable and can handle large graphs. A variation of the underlying approach can also be used to optimize many desirable properties in planar graphs, while maintaining planarity. Finally, we provide quantitative and qualitative evidence of the effectiveness of (SGD)2: we analyze the interactions between criteria, measure the quality of layouts generated from (SGD)2 as well as the runtime behavior, and analyze the impact of sample sizes. The source code is available on github and we also provide an interactive demo for small graphs.

Circle Detection by an Improved Edge Drawing Algorithm

Circle Detection by an Improved Edge Drawing Algorithm

Research on Drawing Algorithm for Precise Lissajous Curves of Vibrations and its Application to Condition Monitoring/Diagnosis Technique

Visualization and characterization of changes in equipment conditions over time based on precise Lissajous curves are discussed. Enhancing the performance of condition monitoring and diagnostic technology based on vibration measurement requires the use of vibration phase information. The commercialized 3-axis high-precision digital vibration sensor, M-A342, combined with the proposed algorithm that suppresses the effects of external interference, make it possible to draw accurate and high SNR Lissajous curves. The trajectories of precise Lissajous curves corresponding to equipment vibrations are observed to be distributed in certain planes in many cases. We propose that the vibration surface angle (θv, φv), which is a vector perpendicular to the vibration surface expressed as an angular component in polar coordinates, can be used as an indicator. The standard deviation of the variation of θv, φv and the fluctuation of θv, φv well reflect changes in the equipment operating conditions over time, indicating the possibility of detecting changes in the operating conditions earlier than conventional methods such as using RMS values. Since these indicators are dimensionless quantities and can be calculated independently of the type and size of the equipment, direct and absolute value comparisons may be performed even if the equipment and measurement location are different.

Bresenham's Line and Circle Drawing Algorithm using FPGA

In Bresenham's line drawing algorithm, the points of an n-dimensional raster that have to be selected are determined forming a close approximation to a straight line existed between two points. It is widely used for drawing line primitives in a bitmap image (for example: on a computer screen), since only integer addition, subtraction and bit shifting are used. These three operations are cheap concerning standard computer architectures. In addition, it is an incremental error algorithm. It is among the oldest algorithms that have been developed in computer graphics. An extension to the original algorithm may lead to draw circles. This research deals with the Bresenham’s line and circle drawing algorithm based on FPGA hardware platform. The shapes on the VGA screen are displayed via internal VGA port that is built in the device.

A Point Cloud Vector Tracing Algorithm for Automatic Drawing of Interior Plan

Objectives According to the spatial attitude characteristics of the indoor walls, a point cloud vector tracking algorithm for automatically drawing the indoor plan was proposed. Methods Firstly, the indoor wall point cloud with a certain thickness was intercepted and projected onto the horizontal plane, and square grids were established on the projection plane. The plane points after projection were segmented and managed, and the point cloud in every grid was clustered by the eight neighborhood algorithm. Then the grid center of gravity method was used to generate sparse points, which were tracked and sorted according to the distance between points in the neighborhood and the angle of connection vector. The vector sequence of tracking direction was established, and the point cloud segmentation of different walls was completed combined with mutation of angle between adjacent values in the vector sequence. Finally, the least squares algorithm was used to fit the line of the same wall point cloud, and the intersection point of the adjacent wall line was obtained. Results The plane projection line segment of the house wall and its spatial connection relationship were established. The wall projection line segment was output in sequence. The drawing of the house plan was completed and the DXF format data exchange file was exported. Conclusions The proposed algorithm was verified by the analysis of indoor scanning data of a residential building. The results show that the proposed algorithm can accurately and quickly analyzed and processed the indoor laser scanning point cloud, and completed the drawing of interior plan.