2023年matlab实验报告新编.pdf

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1、数学实验报告一、实验问题：有一形状较为复杂，但表面很光滑的曲面工件.通过科学手段，将其放置于某一空间坐标系下，测得曲面上若干个点的坐标如下：-5-4-3-2-1012345-513.6-8.214.86,61.40-3.81.413.616.80-4-8.2-15.8-7.92.23.800.67.31 0.10-16.83-14.8-7.92.55.82.302.75.1010.1-13.7-26.62.25.93-0.301.90 5.1-7.3-1.4-11.43.82.3-0.3-0.900-1.7-2.7-0.63.80000000000001-3.80.62.71.7000.90.

2、32.3-3.8-1.421.47.35.10-1.700.3-3.1-5.8-2.26.6313.610.10-5.1-2.70-2.3-5.8-2.57.914.8416.80-10.1-7.3-0.60 3.8-2.27.915.88.2501 6.313.6-1 .43.80-1.46.614.88.2一 13.6规定：(1)、画出该曲面工件的图形.(2)、在已知相邻的横、纵坐标之间插入三个分点，用 interp 2 命令计算出所有点处的竖坐标，画出相应的插值曲面.(3 )、分别用不同的方法求出该曲面工件表面积的近似值.二、问题分析:、由x=-5:l:5；y=5:1:5产生“格点”矩阵

3、，再用已知的各“格点”的纵坐标z,用surf(x,y,z)命令即可画出未进行插值的工件表面图形。(2)、要在已知相邻的横、纵坐标之间插入三个分点，则要用xc=-5:0.25：5;yc=-5:0.25:5产生另一个“格点”矩阵，然后使用interp2命令计算所有“格点”处的纵坐标z,然后再用surf(x,y,z)命令即可画出该插值曲面。(3)、该工件是一个曲面，规定其表面积的近似值,可以想到的用“分”，“匀”,“和”，“精”的思想，将工件曲面提成n个在xoy平面上的投影是边长为d的矩形的曲面四边形(从第(2)题画出的曲面可以一目了然的看出)，分别求出各个曲面四边形的面积再求和，n取的越大，d越小

4、，越接近准确值。对于如何求每一个曲面四边形的面积：方法1:如图所示，曲面面积微元S近似等于以OP 1和0 P2为邻边的平行四边形的面积S=|0P1 x 0P2 II，只要n取的值较大,d足够小，误差会较小。方法2：由第一型面积分公式:S=ff(a)J l+Fa+Fdxdy,曲面面积微元S等于J l+己+耳d x d y.由上述分割工件曲面的思想，dxdy即等于d 2.问题是如何求得曲面方程的对x、y的偏导数?通过查找资料，发现Matlab软件中有求梯度的命令g rad i ent,因此，曲面的面积微元S可以求得，并且与方法一类似，当d取足够小时，误差可以忽略不计。三、问题求解:(1)、使用Ma

5、 t I a b 软件编写如下程序：x=5：1：5;y=-5:1 :5；xb,yb=m e shg r i d(x,y);zb=13.6,-8.2,-1 4.8,-6.6,1,4,0,-3.8,1.4,13.6,16.8,0;-8.2,-15.8,-7.9,2.2,3,8,0,0.6,7.3,10.1 ,0,-16.8;一 14.8,-7.9,2,5,5.8,2.3,0,2.7,5.1 ,0,-1 0.1,-13.7;-6.6,2.2,5.9,3.0,-0.3,0,1.9,0,5.1,-7.3,1 .4;1.4,3.8,2.3,-0.3,-0.9,0,0,-1.7,-2.7,-0.6,3.8;

6、0,0,0,0,0,0,0,0,0,0,0；-3.8,0.6,2.7,1.7,0,0,0.9,0.3,-2.3,-3.8,-1.4;1.4,7.3,5.lz0,-l.7,0,0.3,-3.1,-5.8,-2.2,6.6;1 3.6,1 0.1,0,-5.1,-2.7,0,-23,-5.8,-2.5,7.9,14.8；1 6.8,0,-10.1,-7.3,-0.6,0,3.8,-2.2,7.9,15.8,8.2;0,16.3,-13.6,-1.4,3.8,0,-1.4,6.6,14.8,8.2,-13.6；surf(xb,yb,zb)图 1、由已知坐标点画出的工件表面图形J Figure No.

7、1-lalxiFile Edit View Insert Tools Window HelpD G S J H e k A 7/您分(2 卜使用Matla b 软件编写如下程序：x=-5：1：5;y=-5：1:5；x b,y b =mes h g r i d(x,y);zb=13.6,-8.2,-143,-6.6,1.4,0,-3.8,1.4,13.6,1 6.8,0；-8.2,-15.8,-7.9,2.2,3.8,0,0.6,7.3,10.1,0,-l 6.8;-14.8,-7.9,2.5,5.8,23,0,2.7,5.1,0 1 0.1,-13.7;-6.6,2,2,5.9,3.0,-0.

8、3,0,1.9,0,-5,-7.3,-1.4;1.4,3,8,2.3,-0.3,-0.9,0,0,-1.7,-2.7,-0.6,3.8;0,0,0,0,0,0,0,0,0,0,0;-3.8,0.6,2.7,1.7,0,0,0.9,0.3,-2.3,-3.8,-1.4;1.4,7.3,5.1,0,-1.7,0,0.3,-3.1,-5.8,-2.2,6.6;13.6,10.lA-5.1,-2.7,0r2.3,-5.8,-2.5,7.9 ,14.8；1 6.8,0,10.1,-7.3r0.6,0,一3.8,-2.2,7.9,15.8,8.2;0,16.3,-13.6,一1.4,3.8,0,-1 .4

9、,6.6,14.8,8.2,-13.6;x c=-5：0.25:5;yc=-5:0.2 5：5;x c b,yc b=meshg r i d(x c,yc)；z c b=in t er p 2(xb,y b,z b,x c b,ycb,s p lin e)s urf(x cb,ycb,zc b)图2、插值计算出的所有点的纵坐标值（截取了一部分）Command Window0.9998 t r n r r r r0.8320-OTTTOT0.6272U.ZUZI-0.41530.2263 DTOTTJrr-0.0855u*uou-0.0005u.uuuu-0.029700.08670.21260

10、 31.43691.12100.77800.45000.1792-0.0002-0.0860-0.084000.15550.35240 51.70001.21760.74120.31920-0.1792-0.2263-0.160200.23060.48910 71.70521.05780.4738-0.0006-0.3192-0.4497-0.4153-0.253000.30340.60300 81.42900.6446-0.0023-0.4761-0.7412-0.7777-0.6278-0.349200.36130.67260 80.8634-0.0022-0.6490-1.0598-1.

11、2176-1.1213-0.8337-0.433700.39130.67590 70-0.8629-1.4281-1.7043-1.7000-1.4387-1.0032-0.491100.38020.59090 5-1.1459-1.9015-2.2919-2.3577-2.1397-1.6902-1.1092-0.508600.31840.40320 2-2.4659-3.0178-3.1538-2.9510-2.4865-1.8442-1.1364-0.481900.21020.1291-02-3.8279-4.0951-3.9176-3.4107-2.6901-1.8716-1.0722

12、-0.409300.0638-0.2076-07-5.1000-5.0172-4.4869-3.6632-2.7000-1.7429-0.9044-0.28870-0.1129-0.5831-13-6.1605-5.6779-4.7775-3.6481-2.4784-1.4391-0.6271-0.12120-0.3105-0.9725-18-6.9280-6.0138-4.7522-3.3559-2.0378-0.9825-0.26190.08020-0.5144-1.3475-23-7.3316-5.9718-4.3857-2.7905-1.4033-0.40580.16290.29940

13、-0.7085-1.6786-27-7.3000-5.4987-3.6527-1.9553-0.60000.25840.61920.52040-0.8769-1.9364-29-6.7622-4.5416-2.5279-0.85400.34710.97741.07850.72720-1.0035-2.0916-30-5.6470-3.0474-0.98610.50971.41281.71861.51280.90380-1.0723-2.1146-29-3.8833-0.96290.99822.13242.57222.44941.89371.03420-1.0673-1.9761-25-1.40

14、001.76483.45014.01033.80003.13712.19291.10230-0.9725-1.6468-18Columns 25 through36-3.8000-3.5462-2.5802-0.92411.40004.31787.546910.752513.600015.787417.142717.5-2.5439-1.8350-0.47071.46393.88326.66109.506412.087914.073515.180015.317614.4-1.3805-0.34391.26273.30465.64698.126310.466512.362313.509013.6

15、59212.795710.9图3、插值曲面Q Figure 1I H 回File Edit View Insert Tools Desktop Window Help、0 中 p 昌 I 玲 I e 争 B Q(3)、求工件表面面积：运用方法一求面积微元：x=-5：1：5;y=-5:1：5；xb,yb=me s hgri d(x,y)；z b=13.6,-8.2,-1 4.8,-6.6,1.4,0,-3.8,1.4,1 3.6,1 6.8,0;-8.2,-15.8,-7.9,2.2,3.8,0,0.6,7.3,1 0.1 ,0,-1 6.8;-1 4.8,-7.9,2.5,5.8,2.3,0,

16、2.7,5.1,0,-10.1,-13.7;-6.6,2,2,5,9,3.0,0.3,0,1.9,0,-5.l,-7.3,-1.4;1.4,3.8,23,-0.3 0.9,0,0,-1.77-2.7,-0.6,3.8;0,0,0；0,0,0,0,0,0,0,0；-3 .8,0.6,2.7 ,1.7,0,0,0.9,0.3,-2.3,-3.8,-1.4；1.4,7,3,5.1,0 1.7,0,0.3-3.1-5.8,-2.2,6.6；13.6,1 0.1,0,-5.1,-2.7,0,-2.3,-5.8,-2.5,7.9Z 1 4.8;1 6.8,0,-1 0.1,-7.3,一0.6,0,-3.8

17、厂2.2,7.9,1 5.8,8.2;0,16.3,13.6,-1.4,3.8,0,-l.4,6.6,14.8,8.2,-13.6；d=0.25;%改变d 的值即可改变曲面四边形的个数nx c=-5：d：5;yc=-5:d:5;xcb,y c b=mes h grid(x c,y c);z c b=i n t e r p2(xb,yb,zb,x cb,ycb/spl i ne);p=l;q=i；ss=0；whi 1 e p10/d+1wh i Ie q 10/d+1s=sqr t(d*d*(zcb(p,q+l)-zc b(p,q)A 2+d*d*(cb(p+l,q)-zcb(p,q)A 2+d

18、 A4);%s为每一个曲面四边形的面积ss=s+s s;%对 s 循环相加q=q+l；e ndq=i;P=P+1;en d（步长d 取 0.2 5 时得工件表面积约为ss=670.01 8 4）使用方法二求面积微元：x=-5:1:5;y=-5：1 :5；xb,yb=mes h gri d(x,y);zb=13.6,-8.2,-14.8,-6.6,1.4,0,-3.8,1.4,1 3.6,1 6.8,0;-8.2,-1 5 8-7.9,2.2,3.8,0,0.6,7.3,10.1,0,-16.8；-14.8,-7.9,2.5,5.8,2.3,0,2.7,5.1,0,-1 0.1,-13.7;-6

19、.6,2.2,5.9,3.0,-0.3,0,1.9,0,-5.1,-7.3,-1 .4;1.4,3.8,2.3,-0.3,-0.9,0,0,-1.7,-2.7,-0.6,3.8;0,0,0,0,0,0,0,0,0,0,0;-3.8,0,6,2.7,1,7,0,0z0,9,0.3,-2.3,-3.8,1.4;1.4,7.3,5.1,0,-1.7,0,0.3,3 1,-5.8,22,6.6;1 3.6,10.1,0,-5.1,-2.7,0,-2.3,-5.8,-2.5,7.9,14.8;16.8,0,-1 0.l,-7.3,-0.6,0,-3.8,-2.2,7.9,15.8,8.2;0,1 6.3

20、,1 3.6,1.4,3,8,0,-l.4,6.6,14.8,8.2,-13.6;d=0.25;%改变d 的值即可改变曲面四边形的个数nx c=5:d:5;yc=-5：d:5;xcb,ycb=meshgri d(xc,yc)；z c b=interp2(xb,yb,zb,xcb,y c b/s p line);Fx,Fy=gr a d i ent(z c bz d,d);P=1 ；q=i；ss=0;w h il e q10/d+1while pl 0/d+1s=sqrt(l+F x(p,q)A2+Fy(p,q)A2)*d*d；%s 为每一个曲面四边形的面积s s =s+s s;%对$循环相加p

21、=p+1;e n dP=l；q=q+1；e n ds s（步长d取0.2 5时得工件表面积约为s s =6 6 1.1 8 78）两种方法的比较:d的取值方法一的s S方法二的s S0.2 5 06 70.0 1 8 46 6 1.1 8 780.2 0 06 7 1.3 2 4 26 6 5.4 3 3 60 .1 0 06 73.9 6 8 06 7 2.1 5 3 80.0 5 06 75.0 7 8 86 74.5 2 0 40 .0 2 06 7 5.7 0 5 96 75.5 6 8 50.0 1 06 7 5.9 0 7 56 75.8 5 3 40.0 0 56 7 6.0 0 6 96 7 5.9 8 3 6可以看出，两种方法算得的工件表面面积最终都逼近到6 7 6左右，因此,可以认为工件表面面积约为6 7 6。还可以看出，当d取的值不是很大的情况下,方法一的结果更接近准确值，方法一误差相对较小。