{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"基于遗传算法的三角网格折叠简化"}]},{"lang":"en","data":[{"name":"text","data":"Collapsing simplification of triangular mesh based on genetic algorithm"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"段","givenname":"黎明","namestyle":"eastern","prefix":""},{"lang":"en","surname":"DUAN","givenname":"Li-ming","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":["corresp","first-author"],"corresp":[{"rid":"cor1","lang":"en","text":"DUAN Li-ming, E-mail: duanliming163@163.com","data":[{"name":"text","data":"DUAN Li-ming, E-mail: duanliming163@163.com"}]}],"bio":[{"lang":"zh","text":["段黎明(1964-), 男, 四川营山人, 教授, 博士生导师。1985年于成都科技大学获得学士学位, 1988年、1998年于重庆大学分别获得硕士、博士学位, 主要从事工业CT技术及应用, 基于工业CT的逆向设计, 网格重建与处理等研究。E-mail:duanliming163@163.com"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"段黎明"}]},{"name":"text","data":"(1964-), 男, 四川营山人, 教授, 博士生导师。1985年于成都科技大学获得学士学位, 1988年、1998年于重庆大学分别获得硕士、博士学位, 主要从事工业CT技术及应用, 基于工业CT的逆向设计, 网格重建与处理等研究。E-mail:"},{"name":"text","data":"duanliming163@163.com"}]]}],"email":"duanliming163@163.com","deceased":false},{"name":[{"lang":"zh","surname":"杨","givenname":"尚朋","namestyle":"eastern","prefix":""},{"lang":"en","surname":"YANG","givenname":"Shang-peng","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":[],"bio":[{"lang":"zh","text":["杨尚朋(1990-), 男, 山东滕州人, 硕士研究生。2013年于山东理工大学取得学士学位, 主要研究方向为三角网格处理, 基于工业CT的逆向工程。E-mail:yangshangpeng163@163.com"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"杨尚朋"}]},{"name":"text","data":"(1990-), 男, 山东滕州人, 硕士研究生。2013年于山东理工大学取得学士学位, 主要研究方向为三角网格处理, 基于工业CT的逆向工程。E-mail:"},{"name":"text","data":"yangshangpeng163@163.com"}]]}],"email":"yangshangpeng163@163.com","deceased":false},{"name":[{"lang":"zh","surname":"张","givenname":"霞","namestyle":"eastern","prefix":""},{"lang":"en","surname":"ZHANG","givenname":"Xia","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff3","text":"3"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"任","givenname":"华桥","namestyle":"eastern","prefix":""},{"lang":"en","surname":"REN","givenname":"Hua-qiao","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"沈","givenname":"宽","namestyle":"eastern","prefix":""},{"lang":"en","surname":"SHEN","givenname":"Kuan","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"重庆大学 光电技术及系统教育部重点实验室ICT研究中心, 重庆 400044","data":[{"name":"text","data":"重庆大学 光电技术及系统教育部重点实验室ICT研究中心, 重庆 400044"}]},{"lang":"en","label":"1","text":"The ICT Research Center of the Key Laboratory of Optoelectronic Technology and Systems of Chongqing University, Chongqing 400044, China","data":[{"name":"text","data":"The ICT Research Center of the Key Laboratory of Optoelectronic Technology and Systems of Chongqing University, Chongqing 400044, China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"重庆大学 机械工程学院, 重庆 400044","data":[{"name":"text","data":"重庆大学 机械工程学院, 重庆 400044"}]},{"lang":"en","label":"2","text":"Mechanical Engineering College, Chongqing University, Chongqing 400044, China","data":[{"name":"text","data":"Mechanical Engineering College, Chongqing University, Chongqing 400044, China"}]}]},{"id":"aff3","intro":[{"lang":"zh","label":"3","text":"中国科学院 重庆绿色智能技术研究院, 重庆 400044","data":[{"name":"text","data":"中国科学院 重庆绿色智能技术研究院, 重庆 400044"}]},{"lang":"en","label":"3","text":"Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400044, China","data":[{"name":"text","data":"Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400044, China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"针对处理大数据量的三角网格模型会给计算机带来较大压力的问题，本文提出了一种基于遗传算法的三角形折叠简化方法。先求取三角形重心，用重心的三个坐标值与初始化的三个步长进行计算，得到新点坐标，重复多次得到顶点种群，利用遗传算法求取适应度值最小点，修正后得到最优折叠点，最后依照简化误差对三角形排序并根据输入的简化比进行折叠简化。本文方法的适应度函数采用简化误差和三角形规范化系数之商。采用本文方法对花朵和瓶子的三角网格模型进行简化，体积变化率分别为0.010 6%和0.2%，规范化系数分别提高了11.0%和4.56%，优于其他方法。实验结果表明本文方法在有效简化模型的同时，既能保形又能提升三角形的质量。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"To solve the problem that the triangular mesh model which deals with large amount of data will bring great pressure to the computer, a triangle collapsing simplification method based on genetic algorithm was proposed in this paper. In this method, the gravity of the triangles was first derived, the new coordinates were calculated by using the three coordinates of the gravity and the three initialized step lengths, the vertex population was obtained through repeating the above operation several times, the minimum point of fitness value was calculated by using genetic algorithm, the optimal collapsing point was obtained after appropriate amendment, and finally, the sequence of the triangles and collapsing simplification were made according to the simplified error and the proportion of input simplification, respectively. The fitness function adopted in this paper was the quotient of the simplified error and the triangle normalization coefficient. The proposed method was used to achieve the simplification of the triangular mesh model of the flower and the vase, whose volume change rates were 0.0106% and 0.2%, respectively. Besides, their normalized coefficients increased by 11.0% and 4.56%, respectively, which were better than the other methods. The experimental results show that the method proposed can not only simplify the model effectively but also remain its shape as well as improve the quality of the triangular."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"网格简化"}],[{"name":"text","data":"三角形折叠"}],[{"name":"text","data":"遗传算法"}],[{"name":"text","data":"三角形质量"}]]},{"lang":"en","data":[[{"name":"text","data":"mesh simplification"}],[{"name":"text","data":"triangle collapsing"}],[{"name":"text","data":"genetic algorithm"}],[{"name":"text","data":"triangular quality"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"1"}],"title":[{"name":"text","data":"引言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"三角网格模型是一种常用的几何模型数字化表示方法"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"，在3D打印制造、有限元分析及娱乐行业等有着广泛的应用"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"2","type":"bibr","rid":"b2","data":[{"name":"text","data":"2"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。数据量庞大的模型会在传输、处理等操作时给计算机带来较大压力"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"3","type":"bibr","rid":"b3","data":[{"name":"text","data":"3"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"4","type":"bibr","rid":"b4","data":[{"name":"text","data":"4"}]}}],"rid":["b3","b4"],"text":"3-4","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。因此，有必要在尽可能逼近原始模型的前提下进行简化。"}]},{"name":"p","data":[{"name":"text","data":"网格简化的实质是删除不必要的点和面，用数量更少的新元素重新构造模型"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"5","type":"bibr","rid":"b5","data":[{"name":"text","data":"5"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"，从而达到简化的目的。吕书明"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"6","type":"bibr","rid":"b6","data":[{"name":"text","data":"6"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"的方法是先边折叠再进行细分，但易丢失细节。Turk"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"7","type":"bibr","rid":"b7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"以新顶点连接起来的表面逼近原平面，但处理不平坦区域时容易累计误差。袁小翠等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"8","type":"bibr","rid":"b8","data":[{"name":"text","data":"8"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"结合全局聚类、主成分分析法和自适应均值漂移法对点云进行操作，但精简非封闭曲面会丢失一部分边界信息。Ozaki等人"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"9","type":"bibr","rid":"b9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"使用二次误差测量方法对模型进行最小区域采样，随后使用数据进行点云聚类，在数据量大时效率高，但不易保存特征。计忠平等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"10","type":"bibr","rid":"b10","data":[{"name":"text","data":"10"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"为了保持细节特征，用局部体积误差和顶点离散曲率作为折叠代价，效果一般。Keeneth等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"11","type":"bibr","rid":"b11","data":[{"name":"text","data":"11"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"引入辐射函数因子，但简化效率不高。Pan等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"12","type":"bibr","rid":"b12","data":[{"name":"text","data":"12"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"引入二次误差测量算法，有效减少了累积误差，但拓扑结构不稳定。周元峰等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"13","type":"bibr","rid":"b13","data":[{"name":"text","data":"13"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"采用体积平方度量下的简化方法，但对细节特征的保持效果一般。吴志芳等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"14","type":"bibr","rid":"b14","data":[{"name":"text","data":"14"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"利用投影法预测新顶点，存在不易选取长度阈值和角度阈值，表面连续性较差的问题。易兵等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"15","type":"bibr","rid":"b15","data":[{"name":"text","data":"15"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"结合二次误差简化算法和张量投票理论，算法较为复杂。"}]},{"name":"p","data":[{"name":"text","data":"针对上述各方法存在误差大、三角形质量低等问题，本文提出了一种基于遗传算法的三角网格三角形折叠简化方法，并通过多组实验的对比和分析，实验结果表明本文方法在有效简化模型的同时，既能保形又能提升三角形的质量。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"遗传算法的应用"}],"level":"1","id":"s2"}},{"name":"p","data":[{"name":"text","data":"遗传算法用于寻找最优折叠点，三角形折叠方法则根据折叠点完成模型的简化。两者的结合能找到使折叠后区域体积误差最小、三角形质量最好的点，从而在逼近原模型的前提下，简化模型的同时又能提升三角网格质量。"}]},{"name":"p","data":[{"name":"text","data":"遗传算法模拟遗传信息的演化过程，用适应度函数模仿自然界的淘汰机制，基因经过进化产生优于上一代的新种群，最终得到理想个体"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"16","type":"bibr","rid":"b16","data":[{"name":"text","data":"16"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。"}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.1"}],"title":[{"name":"text","data":"基因编码"}],"level":"2","id":"s2-1"}},{"name":"p","data":[{"name":"text","data":"本文方法中基因编码对象是17位的二进制数串。首先随机生成基因(0或1)，17位基因组成一条染色体，即一组二进制数串，该数串是交叉、变异的操作对象，通过计算转为十进制数用作步长。初始点的三坐标加上或者减去各随机生成的长度得到新点。不断重复上述操作得到点群。"}]},{"name":"p","data":[{"name":"text","data":"本文设定精度为小数点后6位，即相当于把长度为1的区间分成10"},{"name":"sup","data":[{"name":"text","data":"6"}]},{"name":"text","data":"个子区间。由于2"},{"name":"sup","data":[{"name":"text","data":"16"}]},{"name":"text","data":" 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3"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"本文方法步骤流程图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 3"}],"title":[{"name":"text","data":"Flow chart of procedures of the method proposed in this paper"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1712164&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1712164&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1712164&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"步骤3是为了寻找出最优折叠点。在初始化步长时以初始折叠点"},{"name":"italic","data":[{"name":"text","data":"v"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":")为例，随机生成"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"三轴上的步长"},{"name":"italic","data":[{"name":"text","data":"L"},{"name":"sub","data":[{"name":"text","data":"rxi"}]}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"L"},{"name":"sub","data":[{"name":"text","data":"ryi"}]}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"L"},{"name":"sub","data":[{"name":"text","data":"rzi"}]}]},{"name":"text","data":"(正负符号随机)，进而生成第一代新点"},{"name":"italic","data":[{"name":"text","data":"v"}]},{"name":"sub","data":[{"name":"text","data":"0"},{"name":"italic","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"L"},{"name":"sub","data":[{"name":"text","data":"rxi"}]}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"L"},{"name":"sub","data":[{"name":"text","data":"ryi"}]}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"sub","data":[{"name":"text","data":"0"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"L"},{"name":"sub","data":[{"name":"text","data":"rzi"}]}]},{"name":"text","data":")，"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1, 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3…50；根据公式(6)和(7)计算简化误差Δ"},{"name":"italic","data":[{"name":"text","data":"V"}]},{"name":"text","data":"，根据公式(8)计算新点生成区域的三角形规范化系数"},{"name":"italic","data":[{"name":"text","data":"Q"}]},{"name":"text","data":"，并根据公式(2)以及Δ"},{"name":"italic","data":[{"name":"text","data":"V"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"Q"}]},{"name":"text","data":"计算第一代新点的适应度值"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"text","data":"。在使用遗传算法操作选取折叠点的过程中，需要利用适应度函数、选择算子、交叉算子及变异算子不断迭代，达到迭代次数时结束。适应度值"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"text","data":"越小越接近理想折叠点，选出适应度值"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"text","data":"最小的点利用公式(4)和公式(5)修正之后作为最优折叠点。"}]},{"name":"p","data":[{"name":"text","data":"在步骤4中，排序是将各三角形最优折叠点的简化误差、相对应的三角形按照误差由大到小的顺序进行排列，将最优折叠点和对应的三角形存入VC++的容器Vector中。"}]},{"name":"p","data":[{"name":"text","data":"在步骤5中，折叠三角形是指将最小的三角形折叠成点，并更新邻域信息。此外，对新生成的三角形需要重复进行步骤3~4。直到最优折叠点的简化误差和邻域信息存储完毕，进入下一步。"}]},{"name":"p","data":[{"name":"text","data":"在步骤6中，需要计算被简化的三角形数量占总三角形数的百分比，若不满足步骤1设定的简化百分比则重复步骤5，直至满足设定的百分比时结束全过程。"}]}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4"}],"title":[{"name":"text","data":"实验结果与讨论"}],"level":"1","id":"s4"}},{"name":"p","data":[{"name":"text","data":"本文方法在Visual 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methods"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1712222&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1712222&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1712222&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"本文将简化前后的模型导入CATIA软件得到相应的体积数据，并根据公式(11)计算得到模型总体的体积变化率"},{"name":"italic","data":[{"name":"text","data":"ξ"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"，对比情况如"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"所示。从"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"中体积变化率可以看出，本文方法产生的体积变化情况优于其他3种方法，说明经本文方法处理后的模型整体误差小。从"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"中可以看到根据计算得到的简化后三角网格模型平均规范化系数及其变化率(在表中括号内)，三角网格模型经本文方法处理后，与其他方法相比，三角形质量提升效果稳定、明显。"}]},{"name":"table","data":{"id":"Table1","caption":[{"lang":"zh","label":[{"name":"text","data":"表1"}],"title":[{"name":"text","data":"不同方法的简化效果对比"}]},{"lang":"en","label":[{"name":"text","data":"Table 1"}],"title":[{"name":"text","data":"Comparative analysis of simplification effect by different methods"}]}],"note":[],"table":[{"head":[[{"style":"class:table_top_border","data":[{"name":"text","data":"模型"}]},{"colspan":"5","style":"class:table_top_border","data":[{"name":"text","data":"花朵(108 816个三角形，简化90%)"}]},{"colspan":"5","style":"class:table_top_border","data":[{"name":"text","data":"瓶子(4 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