{"id":1060,"date":"2021-01-15T20:03:16","date_gmt":"2021-01-15T18:03:16","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=1060"},"modified":"2021-03-23T12:55:06","modified_gmt":"2021-03-23T10:55:06","slug":"%d0%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%87%d0%bd%d0%b5-%d0%bc%d0%be%d0%b4%d0%b5%d0%bb%d1%8e%d0%b2%d0%b0%d0%bd%d0%bd%d1%8f-%d0%b2-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d1%96-%d1%82%d1%80%d0%b0","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=1060","title":{"rendered":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0432 \u0437\u0430\u0434\u0430\u0447\u0456 \u0442\u0440\u0430\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0445 \u0456\u043d\u0436\u0435\u043d\u0435\u0440\u043d\u0438\u0445 \u0441\u043f\u043e\u0440\u0443\u0434"},"content":{"rendered":"

\u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0415 \u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u0412 \u0417\u0410\u0414\u0410\u0427\u0406 \u0422\u0420\u0410\u0421\u0423\u0412\u0410\u041d\u041d\u042f \u041b\u0406\u041d\u0406\u0419\u041d\u0418\u0425 \u0406\u041d\u0416\u0415\u041d\u0415\u0420\u041d\u0418\u0425 \u0421\u041f\u041e\u0420\u0423\u0414<\/p>\n

GEOMETRIC MODELING IN THE TRACING PROBLEM LINEAR ENGINEERING STRUCTURES<\/p>\n

<\/a> \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 279-285. \u041d\u043e\u043c\u0435\u0440: \u21161, 2020 (281)<\/strong>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0410.\u0412. \u0428\u0415\u0412\u0427\u0415\u041d\u041a\u041e
\n\u0412\u0456\u043d\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\n\u0410.\u0410. \u0412\u0418\u0414\u041c\u0418\u0428, \u0410.\u0410. \u0428\u0422\u0423\u0426\u042c
\n\u0412\u0456\u043d\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0430\u0433\u0440\u0430\u0440\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nA. SHEVCHENKO
\nVinnytsia National Technical University
\n\u0410. VIDMYSH, A. STUTS
\nVinnytsia National Agrarian University
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2020-281-1-279-285<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review :<\/strong> 20. 01.2020 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 14.02.2020 \u0440.<\/p>\n

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\u0441\u043f\u043e\u0441\u0456\u0431 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u043f\u043e\u0447\u0430\u0442\u043a\u043e\u0432\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u0438\u0436\u0435\u043d\u043d\u044f \u0442\u0440\u0430\u0441\u0438 \u0437 \u0443\u0440\u0430\u0445\u0443\u0432\u0430\u043d\u043d\u044f\u043c \u0432\u0438\u043c\u043e\u0433\u0438 \u0434\u043e \u0457\u0457 \u043c\u0456\u043d\u0456\u043c\u0430\u043b\u044c\u043d\u043e\u0457 \u043f\u0440\u043e\u0442\u044f\u0436\u043d\u043e\u0441\u0442\u0456. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043e\u00a0 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456 \u043e\u0446\u0456\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u043a\u0440\u0438\u0432\u0438\u043d\u0438 \u043f\u0440\u043e\u0441\u0442\u043e\u0440\u043e\u0432\u043e\u0457 \u043b\u0456\u043d\u0456\u0457 \u0442\u0440\u0430\u0441\u0438.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u043e-\u0430\u043d\u0430\u043b\u0456\u0442\u0438\u0447\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c, \u043f\u0440\u043e\u0441\u0442\u043e\u0440\u043e\u0432\u0430 \u043b\u0456\u043d\u0456\u044f, \u0442\u0440\u0430\u0441\u0443\u0432\u0430\u043d\u043d\u044f, \u0442\u0440\u0430\u0441\u0430, \u043f\u0440\u043e\u0442\u044f\u0436\u043d\u0456\u0441\u0442\u044c, \u043a\u0440\u0438\u0432\u0438\u043d\u0430.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The tracing of linear structures consists in determining on the locality of their axis, the planned and altitude position, characterized by a plan and a longitudinal profile. In terms of the route is a straight line segments of different directions, interconnecting circular or transition curves. In the longitudinal profile, the route consists of lines of different slope, which are joined by vertical curves. The gradients of the route are set depending on the purpose and characteristics of the structures. When compiling a longitudinal profile, the vertical scale is 10 times or larger than the horizontal scale. The terrain along the route is characterized by cross-sections that are equal in horizontal and vertical scales. Linear tracing involves locating and locating the optimal route for the route. The optimal location of the route on the terrain is chosen as a result of comparing several feasible options on maps of scale 1: 1000000 – 1: 25000. Depending on the destination of the route and the stage of designing the route may be a cameral or field. Constructing diagrams of change of curves along the line of the track, then the shape of the resulting curve characterizes its spatial smoothness: the visual smoothness of the curve change curve is a sign of the smoothness of the curve in space. Only the curvature of its longitudinal profile can be used to estimate the curvature of a route. If it is described by some function z = z (x), then the curvature is calculated using a known mathematical apparatus through the first and second derivatives and finite differences, or as a value inverse of the radius of a circle passing through three adjacent points of the track profile, which is not lie in one line. The paper presents a geometric-analytical model of search on a given terrain of spatial lines whose geometry satisfies the requirements of tracing of linear structures – highways (AS), railways, pipelines, etc. for use in CAD. A method of simulating the initial approximation of a route with the requirement for its minimum length is developed. Geometric models for estimating the curvature of a spatial line of a route are presented.
\nKeywords:<\/strong> geometric-analytical model, spatial line, trace, route, length, curvature.<\/em><\/p>\n

References<\/strong><\/p>\n

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    \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0415 \u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u0412 \u0417\u0410\u0414\u0410\u0427\u0406 \u0422\u0420\u0410\u0421\u0423\u0412\u0410\u041d\u041d\u042f \u041b\u0406\u041d\u0406\u0419\u041d\u0418\u0425 \u0406\u041d\u0416\u0415\u041d\u0415\u0420\u041d\u0418\u0425 \u0421\u041f\u041e\u0420\u0423\u0414 GEOMETRIC MODELING IN THE TRACING PROBLEM LINEAR ENGINEERING STRUCTURES \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 279-285. \u041d\u043e\u043c\u0435\u0440: \u21161, 2020 (281) \u0410\u0432\u0442\u043e\u0440\u0438: \u0410.\u0412. \u0428\u0415\u0412\u0427\u0415\u041d\u041a\u041e \u0412\u0456\u043d\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0410.\u0410. \u0412\u0418\u0414\u041c\u0418\u0428, \u0410.\u0410. \u0428\u0422\u0423\u0426\u042c \u0412\u0456\u043d\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0430\u0433\u0440\u0430\u0440\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 A. SHEVCHENKO Vinnytsia National Technical University \u0410. VIDMYSH, A. STUTS Vinnytsia National Agrarian University DOI: https:\/\/www.doi.org\/10.31891\/2307-5732-2020-281-1-279-285 \u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[13],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/1060"}],"collection":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1060"}],"version-history":[{"count":3,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/1060\/revisions"}],"predecessor-version":[{"id":5164,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/1060\/revisions\/5164"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}