MATLAB如何计算三维曲面面积？要代码

Question

比如这个图像，X=[1 2 3 4 5 6 7 81 2 3 4 5 6 7 81 2 3 4 5 6 7 81 2 3 4 5 6 7 81 2 3 4 5 6 7 81 2 3 4 5 6 7 8]
Y=[1 1 1 1 1 1 1 12 2 2 2 2 2 2 23 3 3 3 3 3 3 34 4 4 4 4 4 4 45 5 5 5 5 5 5 56 6 6 6 6 6 6 6]
Z=[432.335403737374 487.979245214646 462.223786161616 496.483356408810 534.923548535353 670.066019835859 233.417181388889 653.049925820707567.425643308081 575.089659154040 625.151120315657 566.141669520202 504.884559974747 604.961804103535 310.957122045455 598.248766047980393.577876047980 229.604557840909 692.243790252525 496.483356408810 660.751814444444 362.776172866162 671.130324633838 359.425213825758472.677966325758 703.757622196970 330.584034343434 418.634868156566 348.371081287879 550.397900252525 490.834348434343 316.517100252525306.456190972222 510.946483055555 512.250451363636 405.154832954545 572.853131376263 622.464512487374 525.989615530303 392.633634545454563.875009797980 338.221265795455 498.112456325758 496.483356408810 534.488043181818 535.793587689394 506.465988989899 687.905708005050]
其它数据插值给定。怎么求曲面面积？？？？？？？？？

Answer 1

dX1=diff(X,1,1);dX2=diff(X,1,2);
dY1=diff(Y,1,1);dY2=diff(Y,1,2);
dZ1=diff(Z,1,1);dZ2=diff(Z,1,2);

a=[reshape(dX1(:,1:end-1),[],1),reshape(dY1(:,1:end-1),[],1),reshape(dZ1(:,1:end-1),[],1)];
b=[reshape(dX2(1:end-1,:),[],1),reshape(dY2(1:end-1,:),[],1),reshape(dZ2(1:end-1,:),[],1)];
c=[reshape(dX1(:,2:end),[],1),reshape(dY1(:,2:end),[],1),reshape(dZ1(:,2:end),[],1)];
d=[reshape(dX2(2:end,:),[],1),reshape(dY2(2:end,:),[],1),reshape(dZ2(2:end,:),[],1)];
s1=cross(a,b,2);
s2=cross(c,d,2);
s=sum(sqrt(dot(s1,s1,2)))/2+sum(sqrt(dot(s2,s2,2)))/2;

实际上就是将网格中的每个网格的面积算出来

而一个网格是空间中的四个点，将其分为两个三角形来计算
当然这是数值计算的近似值
如果网格划分越精细，误差会越小