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徐小湛的博客

高等数学课件、函数图形动画、数学软件应用

 
 
 

日志

 
 

用二重积分计算旋转体体积的几何解释  

2012-07-05 09:22:43|  分类: 高等数学图形动画 |  标签: |举报 |字号 订阅

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用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
 
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
 
 

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客

 

 

两个Maple程序(备用)

程序1

with(plots):
xzhou:=spacecurve([x,0,0], x=-2..2, thickness=1,color=black):
yzhou:=spacecurve([0,y,0], y=-2..2, thickness=1,color=black):
zzhou:=spacecurve([0,0,z], z=-2..4, thickness=1,color=black):
a:=0:b:=3:R:=1:r:=0.1:
yuan:=spacecurve([0,a+R*cos(t),b+R*sin(t)], t=0..2*Pi, thickness=3,color=red):
a0:=0:a2:=0.2:a4:=0.4:a6:=0.6:a8:=0.8:a_2:=-0.2:a_4:=-0.4:a_6:=-0.6:a_8:=-0.8:
b0:=3:b2:=3.2:b4:=3.4:b6:=3.6:b8:=3.8:b_2:=3-0.2:b_4:=3-0.4:b_6:=3-0.6:b_8:=3-0.8:
y00:=spacecurve([0,a0+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y02:=spacecurve([0,a0+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y04:=spacecurve([0,a0+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y06:=spacecurve([0,a0+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y08:=spacecurve([0,a0+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y0_2:=spacecurve([0,a0+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y0_4:=spacecurve([0,a0+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y0_6:=spacecurve([0,a0+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y0_8:=spacecurve([0,a0+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y20:=spacecurve([0,a2+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y22:=spacecurve([0,a2+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y24:=spacecurve([0,a2+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y26:=spacecurve([0,a2+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y28:=spacecurve([0,a2+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y2_2:=spacecurve([0,a2+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y2_4:=spacecurve([0,a2+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y2_6:=spacecurve([0,a2+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y2_8:=spacecurve([0,a2+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y40:=spacecurve([0,a4+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y42:=spacecurve([0,a4+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y44:=spacecurve([0,a4+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y46:=spacecurve([0,a4+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y48:=spacecurve([0,a4+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y4_2:=spacecurve([0,a4+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y4_4:=spacecurve([0,a4+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y4_6:=spacecurve([0,a4+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y4_8:=spacecurve([0,a4+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y60:=spacecurve([0,a6+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y62:=spacecurve([0,a6+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y64:=spacecurve([0,a6+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y66:=spacecurve([0,a6+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y6_2:=spacecurve([0,a6+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y6_4:=spacecurve([0,a6+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y6_6:=spacecurve([0,a6+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y80:=spacecurve([0,a8+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y82:=spacecurve([0,a8+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y84:=spacecurve([0,a8+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y8_2:=spacecurve([0,a8+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y8_4:=spacecurve([0,a8+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y8_6:=spacecurve([0,a8+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_20:=spacecurve([0,a_2+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_22:=spacecurve([0,a_2+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_24:=spacecurve([0,a_2+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_26:=spacecurve([0,a_2+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y_28:=spacecurve([0,a_2+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y_2_2:=spacecurve([0,a_2+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_2_4:=spacecurve([0,a_2+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_2_6:=spacecurve([0,a_2+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_2_8:=spacecurve([0,a_2+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y_40:=spacecurve([0,a_4+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_42:=spacecurve([0,a_4+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_44:=spacecurve([0,a_4+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_46:=spacecurve([0,a_4+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y_48:=spacecurve([0,a_4+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y_4_2:=spacecurve([0,a_4+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_4_4:=spacecurve([0,a_4+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_4_6:=spacecurve([0,a_4+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_4_8:=spacecurve([0,a_4+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y_60:=spacecurve([0,a_6+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_62:=spacecurve([0,a_6+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_64:=spacecurve([0,a_6+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_66:=spacecurve([0,a_6+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y_6_2:=spacecurve([0,a_6+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_6_4:=spacecurve([0,a_6+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_6_6:=spacecurve([0,a_6+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_80:=spacecurve([0,a_8+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_82:=spacecurve([0,a_8+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_84:=spacecurve([0,a_8+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_8_2:=spacecurve([0,a_8+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_8_4:=spacecurve([0,a_8+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_8_6:=spacecurve([0,a_8+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
h00:=plot3d([(b0+r*cos(t))*sin(u),a0+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h02:=plot3d([(b2+r*cos(t))*sin(u),a0+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h04:=plot3d([(b4+r*cos(t))*sin(u),a0+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h06:=plot3d([(b6+r*cos(t))*sin(u),a0+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h08:=plot3d([(b8+r*cos(t))*sin(u),a0+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h0_2:=plot3d([(b_2+r*cos(t))*sin(u),a0+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h0_4:=plot3d([(b_4+r*cos(t))*sin(u),a0+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h0_6:=plot3d([(b_6+r*cos(t))*sin(u),a0+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h0_8:=plot3d([(b_8+r*cos(t))*sin(u),a0+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h20:=plot3d([(b0+r*cos(t))*sin(u),a2+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h22:=plot3d([(b2+r*cos(t))*sin(u),a2+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h24:=plot3d([(b4+r*cos(t))*sin(u),a2+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h26:=plot3d([(b6+r*cos(t))*sin(u),a2+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h28:=plot3d([(b8+r*cos(t))*sin(u),a2+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h2_2:=plot3d([(b_2+r*cos(t))*sin(u),a2+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h2_4:=plot3d([(b_4+r*cos(t))*sin(u),a2+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h2_6:=plot3d([(b_6+r*cos(t))*sin(u),a2+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h2_8:=plot3d([(b_8+r*cos(t))*sin(u),a2+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h40:=plot3d([(b0+r*cos(t))*sin(u),a4+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h42:=plot3d([(b2+r*cos(t))*sin(u),a4+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h44:=plot3d([(b4+r*cos(t))*sin(u),a4+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h46:=plot3d([(b6+r*cos(t))*sin(u),a4+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h48:=plot3d([(b8+r*cos(t))*sin(u),a4+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h4_2:=plot3d([(b_2+r*cos(t))*sin(u),a4+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h4_4:=plot3d([(b_4+r*cos(t))*sin(u),a4+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h4_6:=plot3d([(b_6+r*cos(t))*sin(u),a4+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h4_8:=plot3d([(b_8+r*cos(t))*sin(u),a4+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h60:=plot3d([(b0+r*cos(t))*sin(u),a6+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h62:=plot3d([(b2+r*cos(t))*sin(u),a6+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h64:=plot3d([(b4+r*cos(t))*sin(u),a6+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h66:=plot3d([(b6+r*cos(t))*sin(u),a6+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h6_2:=plot3d([(b_2+r*cos(t))*sin(u),a6+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h6_4:=plot3d([(b_4+r*cos(t))*sin(u),a6+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h6_6:=plot3d([(b_6+r*cos(t))*sin(u),a6+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h80:=plot3d([(b0+r*cos(t))*sin(u),a8+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h82:=plot3d([(b2+r*cos(t))*sin(u),a8+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h84:=plot3d([(b4+r*cos(t))*sin(u),a8+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h8_2:=plot3d([(b_2+r*cos(t))*sin(u),a8+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h8_4:=plot3d([(b_4+r*cos(t))*sin(u),a8+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_20:=plot3d([(b0+r*cos(t))*sin(u),a_2+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_22:=plot3d([(b2+r*cos(t))*sin(u),a_2+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_24:=plot3d([(b4+r*cos(t))*sin(u),a_2+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_26:=plot3d([(b6+r*cos(t))*sin(u),a_2+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_28:=plot3d([(b8+r*cos(t))*sin(u),a_2+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_2_2:=plot3d([(b_2+r*cos(t))*sin(u),a_2+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_2_4:=plot3d([(b_4+r*cos(t))*sin(u),a_2+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_2_6:=plot3d([(b_6+r*cos(t))*sin(u),a_2+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_2_8:=plot3d([(b_8+r*cos(t))*sin(u),a_2+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_40:=plot3d([(b0+r*cos(t))*sin(u),a_4+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_42:=plot3d([(b2+r*cos(t))*sin(u),a_4+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_44:=plot3d([(b4+r*cos(t))*sin(u),a_4+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_46:=plot3d([(b6+r*cos(t))*sin(u),a_4+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_48:=plot3d([(b8+r*cos(t))*sin(u),a_4+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_4_2:=plot3d([(b_2+r*cos(t))*sin(u),a_4+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_4_4:=plot3d([(b_4+r*cos(t))*sin(u),a_4+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_4_6:=plot3d([(b_6+r*cos(t))*sin(u),a_4+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_4_8:=plot3d([(b_8+r*cos(t))*sin(u),a_4+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_60:=plot3d([(b0+r*cos(t))*sin(u),a_6+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_62:=plot3d([(b2+r*cos(t))*sin(u),a_6+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_64:=plot3d([(b4+r*cos(t))*sin(u),a_6+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_66:=plot3d([(b6+r*cos(t))*sin(u),a_6+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_6_2:=plot3d([(b_2+r*cos(t))*sin(u),a_6+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_6_4:=plot3d([(b_4+r*cos(t))*sin(u),a_6+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_6_6:=plot3d([(b_6+r*cos(t))*sin(u),a_6+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_80:=plot3d([(b0+r*cos(t))*sin(u),a_8+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_82:=plot3d([(b2+r*cos(t))*sin(u),a_8+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_84:=plot3d([(b4+r*cos(t))*sin(u),a_8+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_8_2:=plot3d([(b_2+r*cos(t))*sin(u),a_8+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
h_8_4:=plot3d([(b_4+r*cos(t))*sin(u),a_8+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=0..2*Pi):
display(xzhou,yzhou,zzhou,yuan,
y00,y02,y04,y06,y08,y0_2,y0_4,y0_6,y0_8,
y20,y22,y24,y26,y28,y2_2,y2_4,y2_6,y2_8,
y40,y42,y44,y46,y48,y4_2,y4_4,y4_6,y4_8,
y60,y62,y64,y66,y6_2,y6_4,y6_6,
y80,y82,y84,y8_2,y8_4,
y_20,y_22,y_24,y_26,y_28,y_2_2,y_2_4,y_2_6,y_2_8,
y_40,y_42,y_44,y_46,y_48,y_4_2,y_4_4,y_4_6,y_4_8,
y_60,y_62,y_64,y_66,y_6_2,y_6_4,y_6_6,
y_80,y_82,y_84,y_8_2,y_8_4,
h00,h02,h04,h06,h08,h0_2,h0_4,h0_6,h0_8,
h20,h22,h24,h26,h28,h2_2,h2_4,h2_6,h2_8,
h40,h42,h44,h46,h48,h4_2,h4_4,h4_6,h4_8,
h60,h62,h64,h66,h6_2,h6_4,h6_6,
h80,h82,h84,h8_2,h8_4,
h_20,h_22,h_24,h_26,h_28,h_2_2,h_2_4,h_2_6,h_2_8,
h_40,h_42,h_44,h_46,h_48,h_4_2,h_4_4,h_4_6,h_4_8,
h_60,h_62,h_64,h_66,h_6_2,h_6_4,h_6_6,
h_80,h_82,h_84,h_8_2,h_8_4,
scaling=constrained);

 

程序2

with(plots):
xzhou:=spacecurve([x,0,0], x=-2..2, thickness=1,color=black):
yzhou:=spacecurve([0,y,0], y=-2..2, thickness=1,color=black):
zzhou:=spacecurve([0,0,z], z=-2..4, thickness=1,color=black):
a:=0:b:=3:R:=1:r:=0.1:
yuan:=spacecurve([0,a+R*cos(t),b+R*sin(t)], t=0..2*Pi, thickness=3,color=red):
a0:=0:a2:=0.2:a4:=0.4:a6:=0.6:a8:=0.8:a_2:=-0.2:a_4:=-0.4:a_6:=-0.6:a_8:=-0.8:
b0:=3:b2:=3.2:b4:=3.4:b6:=3.6:b8:=3.8:b_2:=3-0.2:b_4:=3-0.4:b_6:=3-0.6:b_8:=3-0.8:
y00:=spacecurve([0,a0+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y02:=spacecurve([0,a0+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y04:=spacecurve([0,a0+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y06:=spacecurve([0,a0+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y08:=spacecurve([0,a0+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y0_2:=spacecurve([0,a0+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y0_4:=spacecurve([0,a0+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y0_6:=spacecurve([0,a0+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y0_8:=spacecurve([0,a0+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y20:=spacecurve([0,a2+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y22:=spacecurve([0,a2+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y24:=spacecurve([0,a2+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y26:=spacecurve([0,a2+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y28:=spacecurve([0,a2+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y2_2:=spacecurve([0,a2+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y2_4:=spacecurve([0,a2+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y2_6:=spacecurve([0,a2+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y2_8:=spacecurve([0,a2+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y40:=spacecurve([0,a4+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y42:=spacecurve([0,a4+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y44:=spacecurve([0,a4+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y46:=spacecurve([0,a4+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y48:=spacecurve([0,a4+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y4_2:=spacecurve([0,a4+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y4_4:=spacecurve([0,a4+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y4_6:=spacecurve([0,a4+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y4_8:=spacecurve([0,a4+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y60:=spacecurve([0,a6+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y62:=spacecurve([0,a6+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y64:=spacecurve([0,a6+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y66:=spacecurve([0,a6+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y6_2:=spacecurve([0,a6+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y6_4:=spacecurve([0,a6+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y6_6:=spacecurve([0,a6+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y80:=spacecurve([0,a8+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y82:=spacecurve([0,a8+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y84:=spacecurve([0,a8+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y8_2:=spacecurve([0,a8+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y8_4:=spacecurve([0,a8+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y8_6:=spacecurve([0,a8+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_20:=spacecurve([0,a_2+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_22:=spacecurve([0,a_2+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_24:=spacecurve([0,a_2+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_26:=spacecurve([0,a_2+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y_28:=spacecurve([0,a_2+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y_2_2:=spacecurve([0,a_2+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_2_4:=spacecurve([0,a_2+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_2_6:=spacecurve([0,a_2+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_2_8:=spacecurve([0,a_2+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y_40:=spacecurve([0,a_4+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_42:=spacecurve([0,a_4+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_44:=spacecurve([0,a_4+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_46:=spacecurve([0,a_4+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y_48:=spacecurve([0,a_4+r*cos(t),b8+r*sin(t)], t=0..2*Pi,color=blue):
y_4_2:=spacecurve([0,a_4+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_4_4:=spacecurve([0,a_4+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_4_6:=spacecurve([0,a_4+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_4_8:=spacecurve([0,a_4+r*cos(t),b_8+r*sin(t)], t=0..2*Pi,color=blue):
y_60:=spacecurve([0,a_6+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_62:=spacecurve([0,a_6+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_64:=spacecurve([0,a_6+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_66:=spacecurve([0,a_6+r*cos(t),b6+r*sin(t)], t=0..2*Pi,color=blue):
y_6_2:=spacecurve([0,a_6+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_6_4:=spacecurve([0,a_6+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_6_6:=spacecurve([0,a_6+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
y_80:=spacecurve([0,a_8+r*cos(t),b0+r*sin(t)], t=0..2*Pi,color=blue):
y_82:=spacecurve([0,a_8+r*cos(t),b2+r*sin(t)], t=0..2*Pi,color=blue):
y_84:=spacecurve([0,a_8+r*cos(t),b4+r*sin(t)], t=0..2*Pi,color=blue):
y_8_2:=spacecurve([0,a_8+r*cos(t),b_2+r*sin(t)], t=0..2*Pi,color=blue):
y_8_4:=spacecurve([0,a_8+r*cos(t),b_4+r*sin(t)], t=0..2*Pi,color=blue):
y_8_6:=spacecurve([0,a_8+r*cos(t),b_6+r*sin(t)], t=0..2*Pi,color=blue):
h00:=plot3d([(b0+r*cos(t))*sin(u),a0+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..6.6):
h02:=plot3d([(b2+r*cos(t))*sin(u),a0+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.3):
h04:=plot3d([(b4+r*cos(t))*sin(u),a0+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.56..6.4):
h06:=plot3d([(b6+r*cos(t))*sin(u),a0+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.31):
h08:=plot3d([(b8+r*cos(t))*sin(u),a0+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.2..6.29):
h0_2:=plot3d([(b_2+r*cos(t))*sin(u),a0+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1..2*Pi):
h0_4:=plot3d([(b_4+r*cos(t))*sin(u),a0+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.59..6.33):
h0_6:=plot3d([(b_6+r*cos(t))*sin(u),a0+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..5.2):
h0_8:=plot3d([(b_8+r*cos(t))*sin(u),a0+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=1..6.3):
h20:=plot3d([(b0+r*cos(t))*sin(u),a2+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.5):
h22:=plot3d([(b2+r*cos(t))*sin(u),a2+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.26):
h24:=plot3d([(b4+r*cos(t))*sin(u),a2+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h26:=plot3d([(b6+r*cos(t))*sin(u),a2+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1..2*Pi):
h28:=plot3d([(b8+r*cos(t))*sin(u),a2+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.8..6.26):
h2_2:=plot3d([(b_2+r*cos(t))*sin(u),a2+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..6.5):
h2_4:=plot3d([(b_4+r*cos(t))*sin(u),a2+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..6.31):
h2_6:=plot3d([(b_6+r*cos(t))*sin(u),a2+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..6.34):
h2_8:=plot3d([(b_8+r*cos(t))*sin(u),a2+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.57..6.25):
h40:=plot3d([(b0+r*cos(t))*sin(u),a4+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h42:=plot3d([(b2+r*cos(t))*sin(u),a4+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.2):
h44:=plot3d([(b4+r*cos(t))*sin(u),a4+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.2..2*Pi):
h46:=plot3d([(b6+r*cos(t))*sin(u),a4+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h48:=plot3d([(b8+r*cos(t))*sin(u),a4+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.1..2*Pi):
h4_2:=plot3d([(b_2+r*cos(t))*sin(u),a4+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..2*Pi):
h4_4:=plot3d([(b_4+r*cos(t))*sin(u),a4+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h4_6:=plot3d([(b_6+r*cos(t))*sin(u),a4+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h4_8:=plot3d([(b_8+r*cos(t))*sin(u),a4+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.2):
h60:=plot3d([(b0+r*cos(t))*sin(u),a6+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.7..6.4):
h62:=plot3d([(b2+r*cos(t))*sin(u),a6+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h64:=plot3d([(b4+r*cos(t))*sin(u),a6+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.2):
h66:=plot3d([(b6+r*cos(t))*sin(u),a6+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h6_2:=plot3d([(b_2+r*cos(t))*sin(u),a6+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h6_4:=plot3d([(b_4+r*cos(t))*sin(u),a6+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..2*Pi):
h6_6:=plot3d([(b_6+r*cos(t))*sin(u),a6+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.7..2*Pi):
h80:=plot3d([(b0+r*cos(t))*sin(u),a8+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.6):
h82:=plot3d([(b2+r*cos(t))*sin(u),a8+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..2*Pi):
h84:=plot3d([(b4+r*cos(t))*sin(u),a8+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h8_2:=plot3d([(b_2+r*cos(t))*sin(u),a8+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.5):
h8_4:=plot3d([(b_4+r*cos(t))*sin(u),a8+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h_20:=plot3d([(b0+r*cos(t))*sin(u),a_2+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h_22:=plot3d([(b2+r*cos(t))*sin(u),a_2+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h_24:=plot3d([(b4+r*cos(t))*sin(u),a_2+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1..2*Pi):
h_26:=plot3d([(b6+r*cos(t))*sin(u),a_2+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.25..6.4):
h_28:=plot3d([(b8+r*cos(t))*sin(u),a_2+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.1..2*Pi):
h_2_2:=plot3d([(b_2+r*cos(t))*sin(u),a_2+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..6.5):
h_2_4:=plot3d([(b_4+r*cos(t))*sin(u),a_2+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.2):
h_2_6:=plot3d([(b_6+r*cos(t))*sin(u),a_2+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..2*Pi):
h_2_8:=plot3d([(b_8+r*cos(t))*sin(u),a_2+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..6.2):
h_40:=plot3d([(b0+r*cos(t))*sin(u),a_4+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h_42:=plot3d([(b2+r*cos(t))*sin(u),a_4+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..2*Pi):
h_44:=plot3d([(b4+r*cos(t))*sin(u),a_4+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.7..2*Pi):
h_46:=plot3d([(b6+r*cos(t))*sin(u),a_4+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.58..2*Pi):
h_48:=plot3d([(b8+r*cos(t))*sin(u),a_4+r*sin(t),(b8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.53..6.3):
h_4_2:=plot3d([(b_2+r*cos(t))*sin(u),a_4+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.2):
h_4_4:=plot3d([(b_4+r*cos(t))*sin(u),a_4+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1..2*Pi):
h_4_6:=plot3d([(b_6+r*cos(t))*sin(u),a_4+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.31):
h_4_8:=plot3d([(b_8+r*cos(t))*sin(u),a_4+r*sin(t),(b_8+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..2*Pi):
h_60:=plot3d([(b0+r*cos(t))*sin(u),a_6+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h_62:=plot3d([(b2+r*cos(t))*sin(u),a_6+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.7..2*Pi):
h_64:=plot3d([(b4+r*cos(t))*sin(u),a_6+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=2..6.6):
h_66:=plot3d([(b6+r*cos(t))*sin(u),a_6+r*sin(t),(b6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.7..2*Pi):
h_6_2:=plot3d([(b_2+r*cos(t))*sin(u),a_6+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..2*Pi):
h_6_4:=plot3d([(b_4+r*cos(t))*sin(u),a_6+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.31):
h_6_6:=plot3d([(b_6+r*cos(t))*sin(u),a_6+r*sin(t),(b_6+r*cos(t))*cos(u)],t=0..2*Pi,u=1.7..2*Pi):
h_80:=plot3d([(b0+r*cos(t))*sin(u),a_8+r*sin(t),(b0+r*cos(t))*cos(u)],t=0..2*Pi,u=1.2..2*Pi):
h_82:=plot3d([(b2+r*cos(t))*sin(u),a_8+r*sin(t),(b2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.5..6.6):
h_84:=plot3d([(b4+r*cos(t))*sin(u),a_8+r*sin(t),(b4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.4..2*Pi):
h_8_2:=plot3d([(b_2+r*cos(t))*sin(u),a_8+r*sin(t),(b_2+r*cos(t))*cos(u)],t=0..2*Pi,u=1.6..2*Pi):
h_8_4:=plot3d([(b_4+r*cos(t))*sin(u),a_8+r*sin(t),(b_4+r*cos(t))*cos(u)],t=0..2*Pi,u=1.3..6.31):
display(xzhou,yzhou,zzhou,yuan,
y00,y02,y04,y06,y08,y0_2,y0_4,y0_6,y0_8,
y20,y22,y24,y26,y28,y2_2,y2_4,y2_6,y2_8,
y40,y42,y44,y46,y48,y4_2,y4_4,y4_6,y4_8,
y60,y62,y64,y66,y6_2,y6_4,y6_6,
y80,y82,y84,y8_2,y8_4,
y_20,y_22,y_24,y_26,y_28,y_2_2,y_2_4,y_2_6,y_2_8,
y_40,y_42,y_44,y_46,y_48,y_4_2,y_4_4,y_4_6,y_4_8,
y_60,y_62,y_64,y_66,y_6_2,y_6_4,y_6_6,
y_80,y_82,y_84,y_8_2,y_8_4,
h00,h02,h04,h06,h08,h0_2,h0_4,h0_6,h0_8,
h20,h22,h24,h26,h28,h2_2,h2_4,h2_6,h2_8,
h40,h42,h44,h46,h48,h4_2,h4_4,h4_6,h4_8,
h60,h62,h64,h66,h6_2,h6_4,h6_6,
h80,h82,h84,h8_2,h8_4,
h_20,h_22,h_24,h_26,h_28,h_2_2,h_2_4,h_2_6,h_2_8,
h_40,h_42,h_44,h_46,h_48,h_4_2,h_4_4,h_4_6,h_4_8,
h_60,h_62,h_64,h_66,h_6_2,h_6_4,h_6_6,
h_80,h_82,h_84,h_8_2,h_8_4,
scaling=constrained,orientation=[0,90]);

用二重积分计算旋转体体积的几何解释 - calculus - 徐小湛的博客
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