终于调试好了Catmull-Clark细分（CC细分）的全部程序，将之前只适用于的程序进行了完善
主要一段代码来自于，这个博主的很多篇博文都写的非常好，但是经常丢三落四的，像在这篇博文中他就用到了函数outline.m用来计算网格的边界，但是博主却没有给出outline函数，我自己重新编写了这个函数，并且能够成功执行^^，现在我贴出完整代码
1 function [VV, FF, S] = CCSubdivision(V, F, iter) 2 % Catmull_Clark subdivision 3 if ~exist('iter','var') 4 iter = 1; 5 end 6 VV = V; 7 FF = F; 8 9 for i = 1:iter 10 11 nv = size(VV,1); 12 nf = size(FF,1); 13 14 O = outline(FF); 15 16 original = 1:nv; 17 boundary = O(:,1)'; 18 interior = original(~ismember(original, boundary)); 19 20 no = length(original); 21 nb = length(boundary); 22 ni = length(interior); 23 24 %% Sv 25 Etmp = sort([FF(:,1) FF(:,2);FF(:,2) FF(:,3);FF(:,3) FF(:,4);FF(:,4) FF(:,1)],2); 26 [E, ~, idx] = unique(Etmp, 'rows'); 27 28 Aeven = sparse([E(:,1) E(:,2)], [E(:,2) E(:,1)], 1, no, no); 29 Aodd = sparse([FF(:,1) FF(:,2)], [FF(:,3) FF(:,4)], 1, no, no); 30 Aodd = Aodd + Aodd'; 31 32 val_even = sum(Aeven,2); 33 beta = 3./(2*val_even); 34 35 val_odd = sum(Aodd,2); 36 gamma = 1./(4*val_odd); 37 38 alpha = 1 - beta - gamma; 39 40 Sv = sparse(no,no); 41 Sv(interior,:) = ... 42 sparse(1:ni, interior, alpha(interior), ni, no) + ... 43 bsxfun(@times, Aeven(interior,:), beta(interior)./val_even(interior)) + ... 44 bsxfun(@times, Aodd(interior,:), gamma(interior)./val_odd(interior)); 45 Sboundary = ... 46 sparse([O(:,1);O(:,2)],[O(:,2);O(:,1)],1/8,no,no) + ... 47 sparse([O(:,1);O(:,2)],[O(:,1);O(:,2)],3/8,no,no); 48 Sv(boundary,:) = Sboundary(boundary,:); 49 50 %% Sf 51 Sf = 1/4 .* sparse(repmat((1:nf)',1 ,4), FF, 1); 52 i0 = no + (1:nf)'; 53 54 %% Se 55 flaps = sparse([idx;idx], ... 56 [FF(:,3) FF(:,4);FF(:,4) FF(:,1);FF(:,1) FF(:,2);FF(:,2) FF(:,3)], ... 57 1); 58 onboundary = (sum(flaps,2) == 2); 59 flaps(onboundary,:) = 0; 60 61 ne = size(E,1); 62 Se = sparse( ... 63 [1:ne 1:ne]', ... 64 [E(:,1); E(:,2)], ... 65 [onboundary;onboundary].*1/2 + ~[onboundary;onboundary].*3/8, ... 66 ne, ... 67 no) + ... 68 flaps*1/16; 69 70 %% new faces & new vertices 71 i1 = no + nf + (1:nf)'; 72 i2 = no + 2*nf + (1:nf)'; 73 i3 = no + 3*nf + (1:nf)'; 74 i4 = no + 4*nf + (1:nf)'; 75 76 FFtmp = [i0 i4 FF(:,1) i1; ... 77 i0 i1 FF(:,2) i2; ... 78 i0 i2 FF(:,3) i3; ... 79 i0 i3 FF(:,4) i4]; 80 81 reidx = [(1:no)'; no+(1:nf)'; no+nf+idx]; 82 FF = reidx(FFtmp); 83 84 S = [Sv; Sf; Se]; 85 VV = S*VV; 86 end 87 end 其中outline函数如下
1 function out = outline( FF ) 2 %OUTLINE Summary of this function goes here 3 % Detailed explanation goes here 4 Etmp = sort([FF(:,1) FF(:,2);FF(:,2) FF(:,3);FF(:,3) FF(:,4);FF(:,4) FF(:,1)],2); 5 [~, ~, idx] = unique(Etmp, 'rows'); 6 7 oriEtmp = [FF(:,1) FF(:,2);FF(:,2) FF(:,3);FF(:,3) FF(:,4);FF(:,4) FF(:,1)]; 8 hh=sortrows([oriEtmp,idx],3); 9 10 x2=diff(sortrows(idx));11 vector = all(x2==0, 2);12 13 index1=find(vector);14 index2=index1+1;15 index=[index1;index2];16 17 hh(index,:)=[];18 out=hh(:, 1:2);19 20 end
对于任意四边形网格是适用的，下面是我们的测试代码
1 [V,F]=obj__read('six.obj'); 2 V=V';F=F'; 3 iter=4; 4 [VV, FF] = CCSubdivision(V, F, iter); 5 %[VV, FF] = CCsub(V, F, iter); 6 obj_write('six1.obj',VV',FF'); 7 8 [V,F]=obj__read('torus.obj'); 9 V=V';F=F';10 iter=4;11 [VV, FF] = CCSubdivision(V, F, iter);12 %[VV, FF] = CCsub(V, F, iter);13 obj_write('torus1.obj',VV',FF'); 最后贴上细分效果
| 开放四边形网格 |  |  |
| 六面开口盒子 | 四次细分 | |
| 封闭四边形网格 |  |  |
| 四边形框 | 四次细分 |
搞定哈哈^^