问题
matlab处理网格时,有时需要将网格细分
思路参考:https://hanspond.github.io//11/27/%E7%AE%80%E5%8D%95%E7%BD%91%E6%A0%BC%E7%BB%86%E5%88%86%201to4%20Mesh%20Subdivision/index.html
将每一个面的每一条边取中点并连接,形成新的三角形,原来一个面细分成四个面
原博主的代码只适合封闭曲面的细分,如果曲面是不封闭的,则拓扑结构会乱,如:
代码:
%% created by H_P 1119: subdivide mesh into 4 smaller meshes in a simple mannerfunction [ Divided_faces, Divided_vertices ] = sub_test( faces, vertices )%SUB_TEST 此处显示有关此函数的摘要% 此处显示详细说明mesh_length_Large=length(faces); Divided_faces=1:mesh_length_Large*4*3;Divided_faces=(reshape(Divided_faces,[3,mesh_length_Large*4]))';Divided_vertices=repelem(vertices,4,1);for n_for=1:mesh_length_Largev1=faces(n_for,1);v2=faces(n_for,2);v3=faces(n_for,3);new_1=(vertices(v1,:)+vertices(v2,:))/2;new_2=(vertices(v3,:)+vertices(v2,:))/2;new_3=(vertices(v1,:)+vertices(v3,:))/2;Divided_vertices((n_for-1)*12+2,:)= new_1;Divided_vertices((n_for-1)*12+3,:)= new_3;Divided_vertices((n_for-1)*12+4,:)= new_1;Divided_vertices((n_for-1)*12+6,:)= new_2;Divided_vertices((n_for-1)*12+7,:)= new_2;Divided_vertices((n_for-1)*12+8,:)= new_3;Divided_vertices((n_for-1)*12+10,:)= new_1;Divided_vertices((n_for-1)*12+11,:)= new_2;Divided_vertices((n_for-1)*12+12,:)= new_3;endend
调用:
>> [v,f]=read_obj('test.obj');>> [ Divided_faces, Divided_vertices ] = sub_test( f', v');>> writeOBJ('test_sub.obj',Divided_vertices,Divided_faces);
结果:
细分前:
细分后:
解决
我将代码改进了一下,将分割条件改为网格面积大于阈值就分割,否则不分割
代码:
function [ divided_vertices ,divided_faces ] = subdivide_mesh01( vertices,faces ,threshold )%SUBDIVIDE_MESH 将曲面简单细分为1to4% 输入:% vertices:细分前的点集n*3% faces:细分前的面集m*3% threshold:网格面积小于这个就细分% 输出:% divided_vertices:细分后的点集% divided_faces:细分后的面集tic%403秒size_faces=size(faces,1);delete_flag=[];for m=1:size_facesinx1=faces(m,1);inx2=faces(m,2);inx3=faces(m,3);v1=vertices(inx1,:);v2=vertices(inx2,:);v3=vertices(inx3,:);s=my_area(v1,v2,v3);if s>thresholddelete_flag=[delete_flag;m];%细分new1=(v1+v2)/2;new2=(v2+v3)/2;new3=(v3+v1)/2;[inx_new1,vertices]=my_index(new1,vertices);[inx_new2,vertices]=my_index(new2,vertices);[inx_new3,vertices]=my_index(new3,vertices);faces_temp=[inx3,inx_new2,inx_new3;inx_new1,inx_new2,inx_new3;inx_new1,inx_new2,inx2;inx_new3,inx_new1,inx1];faces=[faces;faces_temp];endendtocfaces(delete_flag,:)=[];%删除细分过后的原始面divided_vertices=vertices;divided_faces=faces;endfunction [dist]=my_dist(v1,v2)%输入两个点,得到它们之间的距离dist=power( (v1-v2)*((v1-v2)'),1/2);endfunction [area]=my_area(v1,v2,v3)%输入三个点,得到由它们构成的三角形的面集a=my_dist(v1,v2);b=my_dist(v2,v3);c=my_dist(v1,v3);p=(a+b+c)/2;area=power(p*(p-a)*(p-b)*(p-c),1/2);endfunction [inx,vertices]=my_index(v,vertices)%输入一个点,返回该点在点集中的索引行%如果该点存在,返回索引行,如果该点不存在,插入该点,返回索引行mem = ismember(vertices,v,'rows');inx=find(mem==1);if isempty(inx)%如果inx为空vertices=[vertices;v];inx=size(vertices,1);endend
调用:
>> [ divided_vertices ,divided_faces ] = subdivide_mesh01( v',f' ,0.06 );时间已过 4.625456 秒。>> writeOBJ('test_sub02.obj',divided_vertices,divided_faces);
结果:
细分前:
细分后:
优化
将元素运算换成矩阵运算,见文章
【matlab教程】21、matlab优化一:将对单个元素的操作转换成矩阵之间的运算
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