找到三角网格中的孔洞

大致上还是沿用了loop细分中寻找边界的思路，将其中的一部分代码截出来形成了新的算法，如果一条边只被索引了一次就是边界，而空洞一定是由这些边界组成的。所以目标就是找到边界，主要的函数如下find_holes_in_triangle_mesh.m，输入点和面的信息，输出的是一个n*n的数组（n表示点的个数），如果i行j列上的元素是1，表示ij连线是边界

function edge =  find_holes_in_triangle_mesh(vertices, faces)  
% find_holes_in_triangle_mesh  
%  
%  Dimensions:  
%    vertices: 3xnVertices  
%    faces:    3xnFaces  
%    
%  Author: zhenyu 
  

    global edgeVertice;  

  
    nVertices = size(vertices,2);  
    nFaces    = size(faces,2);  
    edgeVertice = zeros(nVertices, nVertices, 3);

    edge=zeros(nVertices,nVertices);
   
      
    for i=1:nFaces  
        [vaIndex, vbIndex, vcIndex] = deal(faces(1,i), faces(2,i), faces(3,i));  
          
        addEdgeVertice(vaIndex, vbIndex);  
        addEdgeVertice(vbIndex, vcIndex);  
        addEdgeVertice(vaIndex, vcIndex);  
           
    end;            
    
    for i=1:nVertices
        for j=1:nVertices
            if (edgeVertice(i, j, 1) ~= 0)&&(edgeVertice(i, j, 3)==0)
            edge(i, j)=1;
            end
        end
    end
    
end  
  
% ---------------------------------------------------------------------------- %  
function addEdgeVertice(v1Index, v2Index)  
    global edgeVertice;  
  
    if (v1Index>v2Index) % setting: v1 <= v2  
        vTmp = v1Index;  
        v1Index = v2Index;  
        v2Index = vTmp;  
    end;  
      
    if (edgeVertice(v1Index, v2Index, 1)==0)  % new vertex   
        edgeVertice(v1Index, v2Index, 1) = 1;  
        edgeVertice(v1Index, v2Index, 2) = 1;  
    else  
        edgeVertice(v1Index, v2Index, 3) = 1;  
    end;  
  
  
    return;  
end  

之后利用trans_matrix_to_arrow函数将edge里的边界找出，形成edges矩阵，是一个2*m，第i列表示第i条边的两个点的索引值

function edges = trans_matrix_to_arrow( edge)
%TRANS_MATRIX_TO_ARROW Summary of this function goes here
%   Detailed explanation goes here
n=size(edge,1);
x=[];
y=[];

for i=1:n
    for j=1:n
        if (edge(i,j)~=0)
            x(end+1)=i;
            y(end+1)=j;
        end
    end
end 

n=size(x,2);
edges=zeros(2,n);
edges(1,:)=x;
edges(2,:)=y;

end

最后是一段测试代码，我们先将正方体挖去两个面，再找出其边界

[V,F]=obj__read('cube.obj');
edge = find_holes_in_triangle_mesh(V, F);

F=F';V=V';
edges=trans_matrix_to_arrow(edge);

trep=triangulation(F,V);
n=size(edges,2);

for i=1:n
    plot3(V(edges(:,i),1),V(edges(:,i),2),V(edges(:,i),3),'Color','blue','linewidth',2);hold on;
end
trisurf(trep,'edgecolor','k','facecolor','w');

最后是演示效果，用蓝色显示出空洞

好像有点简单吼[奸笑]