| 高冀峰,王晨阳,卢光福,叶中豹,陈务军.识别平面图形最小封闭区域的边双向搜索算法[J].安徽建筑大学学报,2025,33(6):46-52 |
| 识别平面图形最小封闭区域的边双向搜索算法 |
| A Bidirectional Edge-based Search Algorithm for Identifying the Minimum Enclosed Region in Planar Figures |
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| DOI： |
| 中文关键词: 平面图形 最小封闭区域 识别算法 鞋带公式 DXF |
| 英文关键词: planar figure minimum enclosed region recognition algorithm shoelace formula DXF |
| 基金项目:国家自然科学基金面上项目（52278191）；安徽省高等学校自然科学研究重点项目（2022AH050245）；安徽建筑大学引进人才（博士）科研启动项目（2022QDZ33） |
| 作者 | 单位 | | 高冀峰 | College of Civil Engineering,Anhui Jianzhu University,Hefei 230601,China | | 王晨阳 | College of Civil Engineering,Anhui Jianzhu University,Hefei 230601,China | | 卢光福 | College of Civil Engineering,Anhui Jianzhu University,Hefei 230601,China | | 叶中豹 | College of Civil Engineering,Anhui Jianzhu University,Hefei 230601,China | | 陈务军 | Space Structures Research Center,Shanghai Jiao Tong University,Shanghai 200240,China |
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| 中文摘要: |
| 平面图形在工程领域中的应用具有重要作用。针对平面图形的最小封闭区域识别，提出了基于图形边的自动搜索算法。采用DXF文件记录平面图形点与边信息，读取文件中的边数据，计算当前路径与分支边之间的顺时针夹角，选择夹角最小的分支边为前进方向，沿着每条边的两个方向开始逆时针搜索，并各完成一次封闭区域识别。辅以鞋带公式排除重复搜索区域。无需判断封闭图形间的包含关系，能搜索出平面图形中的所有最小封闭区域。通过识别六个复杂平面图形结果，证明了该算法的准确性。 |
| 英文摘要: |
| The application of planar graphics plays a vital role in various engineering fields. To address the problem of identifying the minimum enclosed regions in planar figures, an automatic recognition algorithm based on edge traversal is proposed. The geometric data, including points and edges, are extracted from DXF files. The algorithm calculates the clockwise angle between the current path and each branching edge, selects the branch with the smallest angle as the forward direction, and performs a counterclockwise search in both directions along each edge to complete the identification of closed regions. The shoelace formula is employed to eliminate duplicate regions. This approach avoids the need to determine inclusion relationships among closed shapes and is capable of identifying all minimum enclosed regions within a planar figure. The algorithm’s accuracy is demonstrated through its successful application to six complex planar graphics. |
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