Triangulation of simple arbitrarily shaped polyhedra by cutting off one vertex at a time

Zhang Qi‐Hua; Lin Shao‐Zhong; Ding Xiu‐Li; Wu Ai‐Qing

摘要

Summary > We describe a heuristic method of triangulating arbitrarily shaped polyhedra without the addition of Steiner points. The polyhedra are simple, with each vertex connected to at least 3 other vertices (ie, coplanarity and colinearity are not considered). They may, however, be convex or concave and consist of dozens or even hundreds of facets. This makes the treatment universal enough to well meet the requirements of models used to simulate fractured rock masses. Certain concepts are defined in the work, eg, adjacent vertices, polygon of adjacent vertices, and closed cone of a vertex. A polygon of adjacent vertices of an apex can be subdivided into a set of nonoverlapping triangles without adding any vertices. These triangles, together with the apex, form tetrahedra whose union is the closed cone of the apex. The polyhedron is thus the union of the closed cones. Subsequently, we triangulate the polyhedron by gradually removing the closed cones of its vertices. The number of vertices of the polyhedron decreases by one each time a closed cone is removed. A block with <fi>n</fi> vertices can produce no more than <fi>n</fi> ?3 tetrahedra. We present the analysis procedure and discuss the core issues of the method proposed. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”> <title type =“main”>摘要</ title> >我们描述在没有添加施坦纳点的情况下三晶的多面体三角化的启发式方法。多面体很简单，每个顶点连接到至少3个其他顶点（即，不考虑共面，共面和离坡性）。然而，它们可能是凸或凹入的，由数十个甚至数百个方面组成。这使得治疗方法足以满足用于模拟裂缝岩体的模型的要求。某些概念在工作中定义，例如相邻顶点，相邻顶点的多边形，以及顶点的封闭锥体。在不添加任何顶点的情况下，可以将顶点的相邻顶点的多边形细分为一组非转印三角形。这些三角形与顶点一起形成四面体，其工会是顶点的封闭锥体。因此，多面体是封闭锥体的结合。随后，我们通过逐渐去除其顶点的封闭锥来三角模拟多面体。每次移除闭合锥时，多面体的顶点的数量减小了一个。具有<fi> n </ fi>顶点的块不能超过<fi> n </ fi>？3四面体。我们提出了分析程序并讨论了所提出的方法的核心问题。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20801/'>《International Journal for Numerical Methods in Engineering》</a> <b style="margin: 0 2px;">|</b><span>2018年第5期</span><b style="margin: 0 2px;">|</b><span>共18页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Zhang Qi‐Hua&option=202" target="_blank" rel="nofollow">Zhang Qi‐Hua;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Lin Shao‐Zhong&option=202" target="_blank" rel="nofollow">Lin Shao‐Zhong;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ding Xiu‐Li&option=202" target="_blank" rel="nofollow">Ding Xiu‐Li;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Ai‐Qing&option=202" target="_blank" rel="nofollow">Wu Ai‐Qing;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Yangtze River Scientific Research InstituteWuhan China;</p> <p>Yangtze River Scientific Research InstituteWuhan China;</p> <p>Yangtze River Scientific Research InstituteWuhan China;</p> <p>Yangtze River Scientific Research InstituteWuhan China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/6940.html" title="工程数学">工程数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=closed cone&option=203" rel="nofollow">closed cone;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=discrete fracture network&option=203" rel="nofollow">discrete fracture network;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=polygon of adjacent vertices&option=203" rel="nofollow">polygon of adjacent vertices;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Steiner points&option=203" rel="nofollow">Steiner points;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=triangulation of polyhedra&option=203" rel="nofollow">triangulation of polyhedra;</a> </p> <div class="translation"> 机译：封闭的锥;离散骨折网络;相邻顶点的多边形;施泰纳点;多面体的三角测量; 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