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两张相交的球面

2013-04-26 18:14:44| 分类：高等数学图形动画 | 标签： |举报 |字号大中小订阅

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with(plots):R:=3:r:=2:

qumian:=plot3d([r*sin(phi)*cos(theta),r*sin(phi)*sin(theta),R+r*cos(phi)],phi=Pi/2+arcsin(r/R/2)..Pi,theta=0..2*Pi,color=green):

qumian1:=plot3d([r*sin(phi)*cos(theta),r*sin(phi)*sin(theta),R+r*cos(phi)],phi=0..Pi/2+arcsin(r/R/2),theta=0..2*Pi,color=yellow):

qumian2:=plot3d([R*sin(phi)*cos(theta),R*sin(phi)*sin(theta),R*cos(phi)],phi=0..Pi,theta=0..2*Pi,color=blue,style=wireframe):

x_axis:=plot3d([u,0,0],u=-R-1..R+1,v=0..0.01,thickness=3):

y_axis:=plot3d([0,u,0],u=-R-1..R+1,v=0..0.01,thickness=3):

z_axis:=plot3d([0,0,u],u=-R-1..R+r+1,v=0..0.01,thickness=3):

display(qumian,qumian1,qumian2,x_axis,y_axis,z_axis,scaling=constrained); 两张相交的球面 - calculus - 徐小湛的博客

with(plots):R:=3:r:=2:

qumian:=plot3d([r*sin(phi)*cos(theta),r*sin(phi)*sin(theta),R+r*cos(phi)],phi=Pi/2+arcsin(r/R/2)..Pi,theta=0..2*Pi,color=red):

qumian1:=plot3d([r*sin(phi)*cos(theta),r*sin(phi)*sin(theta),R+r*cos(phi)],phi=0..Pi/2+arcsin(r/R/2),theta=0..2*Pi,color=green,style=wireframe):

qumian2:=plot3d([R*sin(phi)*cos(theta),R*sin(phi)*sin(theta),R*cos(phi)],phi=0..Pi,theta=0..2*Pi,color=blue,style=wireframe):

x_axis:=plot3d([u,0,0],u=-R-1..R+1,v=0..0.01,thickness=3):

y_axis:=plot3d([0,u,0],u=-R-1..R+1,v=0..0.01,thickness=3):

z_axis:=plot3d([0,0,u],u=-R-1..R+r+1,v=0..0.01,thickness=3):

display(qumian,qumian1,qumian2,x_axis,y_axis,z_axis,scaling=constrained);

面积最大的情形 r:=R*4/3:

with(plots):R:=3:r:=R*4/3:

qumian:=plot3d([r*sin(phi)*cos(theta),r*sin(phi)*sin(theta),R+r*cos(phi)],phi=Pi/2+arcsin(r/R/2)..Pi,theta=0..2*Pi,color=red):

qumian1:=plot3d([r*sin(phi)*cos(theta),r*sin(phi)*sin(theta),R+r*cos(phi)],phi=0..Pi/2+arcsin(r/R/2),theta=0..2*Pi,color=green,style=wireframe):

qumian2:=plot3d([R*sin(phi)*cos(theta),R*sin(phi)*sin(theta),R*cos(phi)],phi=0..Pi,theta=0..2*Pi,color=blue,style=wireframe):

x_axis:=plot3d([u,0,0],u=-R-1..R+1,v=0..0.01,thickness=3):

y_axis:=plot3d([0,u,0],u=-R-1..R+1,v=0..0.01,thickness=3):

z_axis:=plot3d([0,0,u],u=-R-1..R+r+.31,v=0..0.01,thickness=3):

display(qumian,qumian1,qumian2,x_axis,y_axis,z_axis,scaling=constrained);

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