三个半径相同的圆柱体两两垂直相交,怎么用MATLAB画出三立体相交部分 三个相同的圆柱 两两垂直相交,求相交部分的体积,给出过程

\u4e09\u4e2a\u534a\u5f84\u76f8\u540c\u7684\u5706\u67f1\u4f53\u4e24\u4e24\u5782\u76f4\u76f8\u4ea4\uff0c\u600e\u4e48\u7528mathematica\u753b\u51fa\u4e09\u7acb\u4f53\u76f8\u4ea4\u90e8\u5206\uff0c\u5e76\u628a\u9762\u6807\u6ce8\u989c\u8272\uff0c\u6c42\u5927\u795e\uff01\uff01\uff01

\u8fd9\u4e2a\u5f88\u5bb9\u6613\u554a\uff1a
RegionPlot3D[ x^2 + y^2 <= 1 && x^2 + z^2 <= 1 && y^2 + z^2 <= 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}]



\u554a\uff0c\u4e0d\u8fc7\u6211\u4e3a\u4ec0\u4e48\u8981\u6765\u7b54\u8fd9\u4e2a\u95ee\u9898\u5462\uff0c\u697c\u4e3b\u663e\u7136\u5df2\u7ecf\u629b\u5f03\u4e86\u4ed6\u7684\u95ee\u9898\uff0c\u4e00\u4e2a\u4e0d\u5408\u8981\u6c42\u7684\u7b54\u6848\u4e5f\u5df2\u7ecf\u88ab\u9009\u6210\u4e86\u63a8\u8350\uff0c\u6211\u8fd9\u4e0d\u662f\u81ea\u964d\u91c7\u7eb3\u7387\u5417\u2026\u2026

\u70ae\u5f39\u5927\u4ed9\u548cSMW_forever\u8ba4\u4e3a\uff0c\u76f8\u4ea4\u90e8\u5206\u662f\u4e00\u4e2a\u7403\u4f53
\u7528\u8ba1\u7b97\u7403\u4f53\u7684\u516c\u5f0f\u5c31\u53ef\u4ee5\u4e86
\u6240\u4ee5\uff0c\u6b64\u8bf4\u6cd5\u662f\u6b63\u786e\u7684\u3002

我只能用 wolfram mathematica 来画出了,不太了解 MATLAB ,不过函数的原理都一样,画出三个圆柱来,用函数方程组来指定圆柱范围:

d = ContourPlot3D[

z^2 == 100 - y^2 , {x, -11, 11}, {y, -11, 11}, {z, -11, 11}, 

RegionFunction -> 

Function[{x, y, z}, And[x^2 + y^2 <= 100 , x^2 + z^2 <= 100]], 

BoxRatios -> Automatic];

e = ContourPlot3D[

z^2 == 100 - x^2 , {x, -11, 11}, {y, -11, 11}, {z, -11, 11}, 

RegionFunction -> 

Function[{x, y, z}, And[x^2 + y^2 <= 100 , y^2 + z^2 <= 100]], 

BoxRatios -> Automatic];

f = ContourPlot3D[

x^2 == 100 - y^2 , {x, -11, 11}, {y, -11, 11}, {z, -11, 11}, 

RegionFunction -> 

Function[{x, y, z}, And[z^2 + y^2 <= 100 , x^2 + z^2 <= 100]], 

BoxRatios -> Automatic];

Show[d, e, f, PlotRange -> All, BoxRatios -> Automatic]





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