扩展形成选项线性表面

N. Sal'kov
{"title":"扩展形成选项线性表面","authors":"N. Sal'kov","doi":"10.12737/2308-4898-2024-12-1-3-11","DOIUrl":null,"url":null,"abstract":"When solving large geometric problems, in some cases there is a need to solve smaller auxiliary problems. So, when expanding the options for forming ruled surfaces, a solution arose for constructing a plane or a straight line at certain angles of inclination to the planes of projections or to some given plane of general position. The article presents this related task of constructing a plane, as well as building a straight line using a sphere. The basis for constructing a plane and a straight line at certain angles to the projection planes is the application of a contiguous cone of rotation to an arbitrarily specified sphere. The same method is already used to construct a straight line and a plane to a given plane of general position, taking into account that this plane is tangent to some given surface. All constructions of linear surfaces are based on the principle of specifying three guides and three conditions limiting each of the generators in relation to the specified guides. The condition of passing the guide at certain angles to the surfaces expands the possibilities of designing ruled surfaces almost indefinitely.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"47 19","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Expansion of Formation Options Linear Surfaces\",\"authors\":\"N. Sal'kov\",\"doi\":\"10.12737/2308-4898-2024-12-1-3-11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"When solving large geometric problems, in some cases there is a need to solve smaller auxiliary problems. So, when expanding the options for forming ruled surfaces, a solution arose for constructing a plane or a straight line at certain angles of inclination to the planes of projections or to some given plane of general position. The article presents this related task of constructing a plane, as well as building a straight line using a sphere. The basis for constructing a plane and a straight line at certain angles to the projection planes is the application of a contiguous cone of rotation to an arbitrarily specified sphere. The same method is already used to construct a straight line and a plane to a given plane of general position, taking into account that this plane is tangent to some given surface. All constructions of linear surfaces are based on the principle of specifying three guides and three conditions limiting each of the generators in relation to the specified guides. The condition of passing the guide at certain angles to the surfaces expands the possibilities of designing ruled surfaces almost indefinitely.\",\"PeriodicalId\":426623,\"journal\":{\"name\":\"Geometry & Graphics\",\"volume\":\"47 19\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Graphics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12737/2308-4898-2024-12-1-3-11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Graphics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12737/2308-4898-2024-12-1-3-11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在解决大型几何问题时,有时需要解决较小的辅助问题。因此,在扩展形成规则曲面的选项时,出现了一种解决方案,即在与投影平面或给定的一般位置平面成一定倾斜角的情况下构建平面或直线。本文介绍了构建平面以及使用球面构建直线的相关任务。构建与投影面成一定角度的平面和直线的基础是对任意指定的球面应用连续的旋转锥。同样的方法也可用于构造与给定平面一般位置的直线和平面,同时考虑到该平面与给定曲面相切。所有线性曲面的构造都基于以下原则:指定三个导轨和三个条件,限制每个生成器与指定导轨的关系。导轨与曲面成一定角度的条件几乎无限地扩展了尺规曲面设计的可能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Expansion of Formation Options Linear Surfaces
When solving large geometric problems, in some cases there is a need to solve smaller auxiliary problems. So, when expanding the options for forming ruled surfaces, a solution arose for constructing a plane or a straight line at certain angles of inclination to the planes of projections or to some given plane of general position. The article presents this related task of constructing a plane, as well as building a straight line using a sphere. The basis for constructing a plane and a straight line at certain angles to the projection planes is the application of a contiguous cone of rotation to an arbitrarily specified sphere. The same method is already used to construct a straight line and a plane to a given plane of general position, taking into account that this plane is tangent to some given surface. All constructions of linear surfaces are based on the principle of specifying three guides and three conditions limiting each of the generators in relation to the specified guides. The condition of passing the guide at certain angles to the surfaces expands the possibilities of designing ruled surfaces almost indefinitely.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信