Isoline families in the space with rectilinear distances
The paper is devoted to planar linear sets generated by linear conditions which are realized for rectangular or Manhattan metrics. The aim of this paper is to give an approach to researching the properties of linear conditions defined on Manhattan plane. Linear conditions are written as a finit...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Omsk State Technical University, Federal State Budgetary Educational Institution of Higher Education
2022-04-01
|
| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%202%20(182)%20(%D0%9E%D0%9D%D0%92)/17-20%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdf |
| _version_ | 1818207972915937280 |
|---|---|
| author | V. Yu. Yurkov |
| author_facet | V. Yu. Yurkov |
| author_sort | V. Yu. Yurkov |
| collection | DOAJ |
| description | The paper is devoted to planar linear sets generated
by linear conditions which are realized for rectangular
or Manhattan metrics. The aim of this paper is to
give an approach to researching the properties of
linear conditions defined on Manhattan plane. Linear
conditions are written as a finite sum of products
Manhattan distances and real numerical factors. The
paper presents a constructive method to solve the next
general geometric problem. Let finite sets of linear
figures (segments of line, polygons) are given on
Manhattan plane at general positions. Find a planar
set corresponding to given linear condition based on
the given sets. The set of broken lines corresponding
to given conditions generates a family of isolines for
given sets. Constructive algorithm to build the family
is suggested. The algorithm is based on the rectangular
Hanan lattice and calculation numerical values in
each cell. Some theorems applied to these cases are
formulated in the paper. |
| first_indexed | 2024-12-12T04:37:25Z |
| format | Article |
| id | doaj.art-e10e040a2f3a478cb27ca679b481f04f |
| institution | Directory Open Access Journal |
| issn | 1813-8225 2541-7541 |
| language | English |
| last_indexed | 2024-12-12T04:37:25Z |
| publishDate | 2022-04-01 |
| publisher | Omsk State Technical University, Federal State Budgetary Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj.art-e10e040a2f3a478cb27ca679b481f04f2022-12-22T00:37:56ZengOmsk State Technical University, Federal State Budgetary Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412022-04-012 (182)172010.25206/1813-8225-2022-182-17-20Isoline families in the space with rectilinear distancesV. Yu. Yurkov0Omsk State Technical UniversityThe paper is devoted to planar linear sets generated by linear conditions which are realized for rectangular or Manhattan metrics. The aim of this paper is to give an approach to researching the properties of linear conditions defined on Manhattan plane. Linear conditions are written as a finite sum of products Manhattan distances and real numerical factors. The paper presents a constructive method to solve the next general geometric problem. Let finite sets of linear figures (segments of line, polygons) are given on Manhattan plane at general positions. Find a planar set corresponding to given linear condition based on the given sets. The set of broken lines corresponding to given conditions generates a family of isolines for given sets. Constructive algorithm to build the family is suggested. The algorithm is based on the rectangular Hanan lattice and calculation numerical values in each cell. Some theorems applied to these cases are formulated in the paper. https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%202%20(182)%20(%D0%9E%D0%9D%D0%92)/17-20%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdfrectangular metricsdistancelinear conditionshanan latticeisoline familiespolygons |
| spellingShingle | V. Yu. Yurkov Isoline families in the space with rectilinear distances Омский научный вестник rectangular metrics distance linear conditions hanan lattice isoline families polygons |
| title | Isoline families in the space with rectilinear distances |
| title_full | Isoline families in the space with rectilinear distances |
| title_fullStr | Isoline families in the space with rectilinear distances |
| title_full_unstemmed | Isoline families in the space with rectilinear distances |
| title_short | Isoline families in the space with rectilinear distances |
| title_sort | isoline families in the space with rectilinear distances |
| topic | rectangular metrics distance linear conditions hanan lattice isoline families polygons |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%E2%84%96%202%20(182)%20(%D0%9E%D0%9D%D0%92)/17-20%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdf |
| work_keys_str_mv | AT vyuyurkov isolinefamiliesinthespacewithrectilineardistances |