An accurate intersection method based on irregular triangular networks and its application in 3D geological modeling

LI Yida; ZHU Shuang; ZHENG Guizhou

doi:10.19509/j.cnki.dzkq.tb20240105

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LI Yida，ZHU Shuang，ZHENG Guizhou. An accurate intersection method based on irregular triangular networks and its application in 3D geological modeling[J]. Bulletin of Geological Science and Technology，2026，45（1）：1-10 doi: 10.19509/j.cnki.dzkq.tb20240105

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An accurate intersection method based on irregular triangular networks and its application in 3D geological modeling

doi: 10.19509/j.cnki.dzkq.tb20240105

School of Geography and Information Engineering， China University of Geosciences， WuHan 430074， China

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E-mail：2789827918@qq.com
Corresponding author: E-mail：zhenggz@cug.edu.cn
Received Date: 20 Mar 2024
Accepted Date: 31 Jul 2024
Rev Recd Date: 30 Jul 2024

Available Online: 04 Dec 2025

Abstract

Abstract

<p>Aiming at the problems of low accuracy and numerical calculation errors in the current intersection methods for 3D geological models, this paper proposes a precise intersection algorithm for geological bodies based on the <bold>Irregular Triangular Network (TIN)</bold> and integrating floating-point precision with exact precision. The specific process is as follows: First, a hierarchical tree of Oriented Bounding Boxes (OBB) for the TIN is constructed, and a set of <bold>effectively intersecting triangle pairs</bold> is screened out through fast collision detection, which greatly reduces the scope of subsequent calculations. Second, the intersecting triangle pairs are decomposed into edge-triangle intersection units, and an intersection position relationship structure is established. This structure includes the spatial position states of intersections (<bold>onVertex</bold>: on the vertex, <bold>onEdge</bold>: on the edge, <bold>inTriangle</bold>: inside the face) and the IDs of corresponding entities (points, edges, faces). It not only eliminates redundant calculations of intersection coordinates but also accurately identifies duplicate intersections by matching position states with entity IDs (e.g., matching vertex IDs in the <bold>onVertex</bold> state and edge IDs in the <bold>onEdge</bold> state). Finally, the precision mode is dynamically selected according to the requirements of topological correctness: if floating-point precision can maintain topological correctness, the <bold>Constrained Delaunay Triangulation (CDT)</bold> based on projection dimension reduction is used to complete retriangulation; if deviations such as intersection position offsets (e.g., an in-face point projected outside the edge), point coincidence, or false intersection of intersection line segments occur, the algorithm switches to exact precision represented by rational numbers. Retriangulation is realized through <bold>constrained point insertion</bold> (an in-face point splits a triangle into three new triangles, and an on-edge point splits adjacent triangles into four new triangles) and <bold>constrained line segment insertion</bold> (processing intersecting line segments and implementing edge swap rules: direct edge swapping for convex quadrilaterals and queued edge swapping for concave quadrilaterals), so as to ensure the topological consistency of the reconstructed results. <bold>Experimental results</bold> show that the intersection algorithm proposed in this paper can effectively support the intersection operation of triangular networks. The algorithm requires fewer conversions to exact precision, and has good computational efficiency and high robustness. The average time consumption of the algorithm is <bold>better than</bold> that of GOCAD, and it can meet the needs of intersection calculation between most complex geological models based on irregular triangular networks.</p></sec><p style="line-height: 12px;"> </p> </div> <ul class="article-keyword article-info-en"> <b>Keywords:</b> <li><a class="underHigh mainColor" href="javascript:void(0);" onclick="searchLike('keywordEn','Geological Body')">Geological Body</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" onclick="searchLike('keywordEn','3D Geological Modeling')">3D Geological Modeling</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" onclick="searchLike('keywordEn','Irregular Triangular Network')">Irregular Triangular Network</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" onclick="searchLike('keywordEn','Triangular Network Intersection')">Triangular Network Intersection</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" onclick="searchLike('keywordEn','Double Triangulation')">Double Triangulation</a></li> </ul> </li>  <div class="footnotes" > </div>  <div val="FullText" class="html-text phone-title phone-mark"> <a class="mainColor" articleId='ef4600a1-20ba-4b96-8282-882febc59d12' href="javascript:void(0);">FullText(HTML)</a> </div> <li id="FullText" class="articleListBox FullText-all html-text"> <img style="display:block;margin:10px auto;" src="//dzkjtb.cug.edu.cn/style/web/images/public/1.gif" alt="loading" /> </li>  <div class="phone-title" rel="ref" val="References"> <a class="mainColor" data-navId="References" href="javascript:void(0);"> References<num>(40)</num> </a> </div> <li id="References" class="articleListBox"> <h3 class="navTitle" id="References-list">References</h3> <div class="References-wrap"> <table class="reference-tab"> <tr class="document-box" id="b1"> <td valign="top" class="td1">[1]</td> <td class="td2"> <div class="reference-cn">陈麒玉, 荀磊, 崔哲思, 等. 三维地质建模技术的最新进展和发展趋势[J]. 地质科技通报, 2025, 44(3): 373-387.</div> <p class="mar6"></p><div class="reference-en">CHEN Q Y, XUN L, CUI Z S, et al. 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class="triangle"></span></a> </div> <div class="picbox"> <ul class="piclist"> </ul> <div id="big_play_prev" class="home-picprev thePrev"></div> <div id="big_play_next" class="home-picnext theNext"></div> </div> <div class="picsmallbox"> <a href="javascript:;" id="play_prev" class="play_prev"> <span class="imgShowIcon imgShowIcon-prev"></span> </a> <div class="picboxpic"> <ul id="picsmall" class="picsmall clear"> </ul> </div> <a href="javascript:;" id="play_next" class="play_next"> <span class="imgShowIcon imgShowIcon-next"></span> </a> </div> </div> <ul id="miniImgs_title" hidden> <li> Figure 1. Intersection of two triangles</li> <li> Figure 2. Retriangulating based on floating point number</li> <li> Figure 3. Triangle splited by insert point</li> <li> Figure 4. edge swap rules</li> <li> Figure 5. Retriangulating based on rational number</li> <li> Figure 6. Intersection of two cubes</li> <li> Figure 7. Intersection of geological model</li> <li> Figure 8. Intersection and detail of geological layer model</li> <li> Figure 9. Geological 3D modeling</li> </ul> </body> </html>