The topological drawing of a graph: Construction methods

Kurapov, S.V.; Tolok, A. V.

doi:10.1134/s0005117913090063

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…Therefore, in order to achieve a zero value of the MacLane functional, it is necessary to remove some part of the cycles. We can use the operation of differentiating the structural number W of isometric cycles [8,9] to model the the process of removing cycles by the gradient descent method. We illustrate the process of constructing the planar part of a non-planar nonseparable graph with specific examples, as during explanation it is necessary to introduce new nonconventional terms and definitions.…”

Section: Isometric Cycles and Matroidsmentioning

confidence: 99%

Generating a topological drawing of the flat part of a nonplanar graph

Kurapov¹,

Davidovsky²,

Tolok³

2020

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In this article, we consider the issues of applying the diakoptic approach to constructing a topological drawing of the planar part of a non-planar graph. It is demonstrated that the first stage of constructing a topological drawing is based on the matroid properties of the set of graph isometric cycles. In the article, we propose a method for constructing a topological drawing of the planar part of a non-planar graph using the methods of structure numbers algebra. The initial solution is based on the set of graph isometric cycles that allows application of discrete optimization methods. The second stage of joining the cycles is based on the methods of vector algebra of intersections. In the article we describe the essential mathematical concepts and structures for solving the problem of constructing a planar topological drawing of a non-planar graph. The presentation is supported by detailed illustrative examples.

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Section: Isometric Cycles and Matroidsmentioning

confidence: 99%

Generating a topological drawing of the flat part of a nonplanar graph

Kurapov¹,

Davidovsky²,

Tolok³

2020

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“…При таком графическом образе для формы трасс характерно максимальное приближение к форме самого препятствия, из-за чего зачастую не обеспечивается плавность обхода, однако опорные точки такой траектории удобно использовать при построении рисунка графа [26], с последующим применением алгоритмов поиска кратчайшего пути [27]. Рельеф поверхности функции на графическом образе (рисунок 9в) формирует скелет общего контура описания сцены, широко применимый при анализе его формы и ко многим другим прикладным задачам [28,29].…”

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Route Planning in 3d Environment with a Multivariant Model

Васильев¹,

Loktev²,

Толок³

et al. 2016

Тр. СПИИРАН

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А. К планированию маршрутов в 3D-среде с многовариантной моделью. Аннотация. В данной статье излагаются результаты исследований по планированию маршрутов автономных подвижных объектов на априорно сформированной многовариантной модели маршрута (МММ) как множестве альтернативных путей из начальной точки в целевую. Построение МММ основывается на компьютерном методе функционально-воксельного моделирования, сочетающем аналитическую форму описания 3D-сцены с воксельным представлением ее локальных геометрических характеристик. Синтез управления движением и стабилизация траектории движения обеспечиваются представлением объекта управления в форме многорежимной модели и применением к ней метода редукции. Ключевые слова: Многовариантная модель маршрута, R-функциональное моделирова-ние, функционально-воксельное моделирование, метод редукции. Vassilyev S.N., Loktev M.A., Tolok A.V., Tolok N.B., Ulyanov S.A. Route Planning in 3dEnvironment with Multivariant Model. Abstract. We present results of the research on the planning of routes of unmanned vehicles (autonomous moving objects). The routing is based on the multivariant route model (MRM) formed a priori as a set of alternative paths from an initial point to the target. The MRM construction is done using the computer method of functional voxel modeling, combining the analytical form of describing a 3D-environment with the voxel representation of its local geometrical characteristics. Synthesis of the motion control and stabilization of the path trajectory are done by representing the control object as a multimode model and applying the reduction method to it.

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Construction of a Topological Drawing of the Most Planar Subgraph of the Non-planar Graph

Kurapov

Tolok

2018

Autom Remote Control

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The topological drawing of a graph: Construction methods

Cited by 3 publications

References 6 publications

Generating a topological drawing of the flat part of a nonplanar graph

Generating a topological drawing of the flat part of a nonplanar graph

Route Planning in 3d Environment with a Multivariant Model

Construction of a Topological Drawing of the Most Planar Subgraph of the Non-planar Graph

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