scholarly journals Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes

2020 ◽  
Vol 9 (11) ◽  
pp. 680
Author(s):  
Elżbieta Lewandowicz ◽  
Paweł Flisek
Keyword(s):  
Base Point ◽  
Vector Data ◽  
Triangulated Irregular Network ◽  
Base Points ◽  
Complex Polygon ◽  
Selection Of

This article presents the Base Point Split (BPSplit) algorithm to generate a complex polygon skeleton based on sets of vector data describing lakes and rivers. A key feature of the BPSplit algorithm is that it is dependent on base points representing the source or mouth of a river or a stream. The input values of base points determine the shape of the resulting skeleton of complex polygons. Various skeletons can be generated with the use of different base points. Base points are applied to divide complex polygon boundaries into segments. Segmentation supports the selection of triangulated irregular network (TIN) edges inside complex polygons. The midpoints of the selected TIN edges constitute a basis for generating a skeleton. The algorithm handles complex polygons with numerous holes, and it accounts for all holes. This article proposes a method for modifying a complex skeleton with numerous holes. In the discussed approach, skeleton edges that do not meet the preset criteria (e.g., that the skeleton is to be located between holes in the center of the polygon) are automatically removed. An algorithm for smoothing zigzag lines was proposed.

scholarly journals Base Point Split Algorithm for Generating Polygon Skeleton Lines

2020 ◽  
Author(s):  
Elżbieta Lewandowicz ◽  
Paweł Flisek
Keyword(s):  
Simple Algorithm ◽  
Base Point ◽  
Vector Data ◽  
Base Points ◽  
Selection Of

The article presents the Base Point Split (BPSplit) algorithm for generating a polygon skeleton based on sets of vector data describing lakes and rivers. A key feature of the BPSplit algorithm is that it is dependent on base points representing the source or mouth of a river or a stream. The input values of base points determine the shape of the resulting skeleton. Various skeletons can be generated with the use of different base points. Base points are applied to divide polygon boundaries into segments. Segmentation supports the selection of TIN edges inside polygons. The midpoints of selected TIN edges constitute a basis for generating a skeleton. The algorithm handles polygons with numerous holes, and it accounts for all holes. This article proposes a method for modifying a complex skeleton with numerous holes. In the discussed approach, skeleton edges that do not meet the preset criteria (e.g. that the skeleton is to be located between holes in the center of the polygon), are automatically removed. A simple algorithm for smoothing zigzag lines was proposed.

scholarly journals A Method for Generating the Centerline of an Elongated Polygon on the Example of a Watercourse

2020 ◽  
Vol 9 (5) ◽  
pp. 304
Author(s):  
Elżbieta Lewandowicz ◽  
Paweł Flisek
Keyword(s):  
River Flow ◽  
Medial Axis ◽  
Hydraulic Structures ◽  
Vector Data ◽  
Triangulated Irregular Network ◽  
University Center ◽  
Medial Axis Transformation ◽  
Base Points ◽  
The City

The centerlines of polygons can be generated with the use of various methods. The aim of this study was to propose an algorithm for generating the centerline of an elongated polygon based on the transformation of vector data. The proposed method involves the determination of base points denoting the direction of river flow. These points were also used to map two polygon boundaries. A Triangulated Irregular Network (TIN) was created based on the polygon’s breakpoints. Edges that intersect the river channel in a direction perpendicular to river flow (across) were selected from a set of TIN edges. The polygon was partitioned into segments with the use of the selected TIN edges. The midpoints of selected TIN edges were used to generate the polygon’s centerline based on topological relations. The presented methodology was tested on a polygon representing a 15-km-long section of a river intersecting the city of Olsztyn (a university center). The analyzed river is a highly meandering watercourse, and its channel is narrowed down by hydraulic structures. The river features an island and distributary channels. The generated centerline effectively fits the polygon, and, unlike the solution modeled with the Medial Axis Transformation (MAT) algorithm, it does not feature branching streams.

scholarly journals Optimal base point selection method based on convex hull construction technology

2021 ◽  
Vol 245 ◽  
pp. 02034
Author(s):  
Jian Dong ◽  
Zhiqiang Zhang ◽  
Lulu Tang ◽  
Rencan Peng ◽  
Hongchao Ji
Keyword(s):  
Convex Hull ◽  
Base Point ◽  
Selection Method ◽  
Optimal Selection ◽  
Construction Technology ◽  
Point Selection ◽  
Base Points ◽  
Selection Of ◽  
The Ideal ◽  
Hull Construction

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.

scholarly journals Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180761 ◽  
Author(s):  
Matteo Petrera ◽  
Jennifer Smirin ◽  
Yuri B. Suris
Keyword(s):  
Vector Field ◽  
Base Point ◽  
Hamiltonian Vector ◽  
Geometric Condition ◽  
Hamiltonian Vector Field ◽  
Cubic Curves ◽  
Birational Map ◽  
Base Points ◽  
Finite Base ◽  
Pass Through

Kahan discretization is applicable to any quadratic vector field and produces a birational map which approximates the shift along the phase flow. For a planar quadratic canonical Hamiltonian vector field, this map is known to be integrable and to preserve a pencil of cubic curves. Generically, the nine base points of this pencil include three points at infinity (corresponding to the asymptotic directions of cubic curves) and six finite points lying on a conic. We show that the Kahan discretization map can be represented in six different ways as a composition of two Manin involutions, corresponding to an infinite base point and to a finite base point. As a consequence, the finite base points can be ordered so that the resulting hexagon has three pairs of parallel sides which pass through the three base points at infinity. Moreover, this geometric condition on the base points turns out to be characteristic: if it is satisfied, then the cubic curves of the corresponding pencil are invariant under the Kahan discretization of a planar quadratic canonical Hamiltonian vector field.

On the canonical systems of certain algebraic surfaces

1937 ◽  
Vol 33 (3) ◽  
pp. 311-314
Author(s):  
D. Pedoe
Keyword(s):  
Algebraic Surface ◽  
Base Point ◽  
Canonical System ◽  
Algebraic Surfaces ◽  
Simple Point ◽  
Canonical Systems ◽  
Base Points ◽  
Complete Linear System ◽  
Pass Through ◽  
Simple Points

A complete linear system of curves on an algebraic surface may have assigned base points. The canonical system, from its definition, has no assigned base points at simple points of the surface. But we may construct surfaces on which, all the same, the canonical system has “accidental base points” at simple points of the surface. The classical example, due to Castelnuovo, is a quintic surface with two tacnodes. On this surface the canonical system is cut out by the planes passing through the two tacnodes. These planes also pass through the simple point in which the join of the two tacnodes meets the surface again. This point is the accidental base point of the canonical system on the quintic surface.

scholarly journals Analysis of Water Bodies under Partial Cloud Conditions Using Satellite Images

2019 ◽  
Author(s):  
Rahul Neware ◽  
Mansi Thakare
Keyword(s):  
Remote Sensing ◽  
Shape Matching ◽  
Satellite Images ◽  
Feature Matching ◽  
Water Bodies ◽  
Vector Data ◽  
Water Reservoirs ◽  
Multi Scale ◽  
Water Surfaces ◽  
Complex Polygon

The technique of obtaining information or data about any feature or object from afar, called in technical parlance as remote sensing, has proven extremely useful in diverse fields. In the ecological sphere, especially, remote sensing has enabled collection of data or information about large swaths of areas or landscapes. Even then, in remote sensing the task of identifying and monitoring of different water reservoirs has proved a tough one. This is mainly because getting correct appraisals about the spread and boundaries of the area under study and the contours of any water surfaces lodged therein becomes a factor of utmost importance. Identification of water reservoirs is rendered even tougher because of presence of cloud in satellite images, which becomes the largest source of error in identification of water surfaces. To overcome this glitch, the method of the shape matching approach for analysis of cloudy images in reference to cloud-free images of water surfaces with the help of vector data processing, is recommended. It includes the database of water bodies in vector format, which is a complex polygon structure. This analysis highlights three steps: First, the creation of vector database for the analysis; second, simplification of multi-scale vector polygon features; and third, the matching of reference and target water bodies database within defined distance tolerance. This feature matching approach provides matching of one to many and many to many features. It also gives the corrected images that are free of clouds.

scholarly journals COMPARISON OF LINEAR AND VECTOR DATA NORMALIZATION TECHNIQUES IN DECISION MAKING FOR LEARNING QUOTA ASSISTANCE

2021 ◽  
Vol 4 (1) ◽  
pp. 22
Author(s):  
Edy Budiman ◽  
Ummul Hairah
Keyword(s):  
Decision Making ◽  
Online Learning ◽  
Data Normalization ◽  
Multi Criteria Decision Making ◽  
Vector Data ◽  
Vikor Method ◽  
Definite Answer ◽  
The Difference ◽  
Benefit Cost ◽  
Selection Of

Data normalization is essential for all kinds of decision-making problems, and a lot of effort has been spent on the development of normalization models in multi-criteria decision making (MCDM), but despite all this, there is no definite answer to the question: Which is the most appropriate technique?. This paper compares the popular normalization techniques: Linear Normalization (LN) and Vector Normalization (VN) using VIšekriterijumsko KOmpromisno Rangiranje (VIKOR) Method. The beneficiaries dataset of learning quota was collected of 399 students sample through observation (drive-test measurements and online questionnaires) to obtain information on criteria data including attributes in online learning during the Covid-19 pandemic. The ranking results for vector vs linear normalization show how ranking is affected. The difference in the selection of the best alternative (rank) shows that there are differences in vector and linear assessments that are influenced by the max-min criterion value which has an impact on the rank- sum results (benefit/cost). This test clearly shows how important it is to use an appropriate (normalized) representation of the model because there will often be a criterion where "the higher the better" while for others (cost) "the lower the better".

A Material Selection Method Based on Double Base Points

2014 ◽  
Vol 707 ◽  
pp. 509-513
Author(s):  
Shi Gang Chao
Keyword(s):  
Material Selection ◽  
Selection Method ◽  
Distance Measures ◽  
Entropy Weight ◽  
Base Points ◽  
Decision Making Problem ◽  
New Material ◽  
Double Base ◽  
Multiple Attributes Decision Making ◽  
Selection Of

The selection of the most desirable material contains many evaluation attributes, and thus leads to hard be solved. The material selection is actually a multiple attributes decision making problem, which has been studied by many authors. The aim of this study is to propose a new material selection method, which is an improved double base points method through defining the entropy weight and used the relative approach degree to measure the distance measures. The method may avoid the influence of subjective factors through the entropy weight, is very suitable for material selection problem. The applied example proves that the method is both effective and exercisable.

scholarly journals A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28 ◽  
Author(s):  
Yuji Liu ◽  
Bashir Ahmad
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Logistic Models ◽  
Base Point ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Base Points ◽  
Fractional Differential

We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models.

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