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两张抛物面的交线及所围成的立体

2013-04-26 10:55:19| 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):

u:=(x,y)->2*x^2+3*y^2: v:=(x,y)->4-x^2-2*y^2:

a:=2/sqrt(3): b:=2/sqrt(5):

qumian1:=plot3d([a*r*cos(t),b*r*sin(t),u(a*r*cos(t),b*r*sin(t))],t=0..2*Pi,r=0..1,color=yellow): 黄色抛物面

qumian2:=plot3d([a*r*cos(t),b*r*sin(t),v(a*r*cos(t),b*r*sin(t))],t=0..2*Pi,r=0..1,color=green): 绿色抛物面

quxian:=spacecurve([a*cos(t),b*sin(t),u(a*cos(t),b*sin(t))],t=0..2*Pi,color=red,thickness=4): 交线

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

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

z_axis:=plot3d([0,0,u],u=-.2..5,v=0..0.01,thickness=3): z轴

xyz:=display(x_axis,y_axis,z_axis,thickness=3):

display(qumian1,qumian2,quxian,xyz,scaling=constrained,orientation=[40,60]);

with(plots):

u:=(x,y)->2*x^2+3*y^2: v:=(x,y)->4-x^2-2*y^2:

a:=2/sqrt(3): b:=2/sqrt(5):

qumian1:=plot3d([a*r*cos(t),b*r*sin(t),u(a*r*cos(t),b*r*sin(t))],t=0..2*Pi,r=0..1,color=blue,style=wireframe):

qumian2:=plot3d([a*r*cos(t),b*r*sin(t),v(a*r*cos(t),b*r*sin(t))],t=0..2*Pi,r=0..1,color=black,style=wireframe):

quxian:=spacecurve([a*cos(t),b*sin(t),u(a*cos(t),b*sin(t))],t=0..2*Pi,color=red,thickness=4):

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

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

z_axis:=plot3d([0,0,u],u=-.2..5,v=0..0.01,thickness=3):

xyz:=display(x_axis,y_axis,z_axis,thickness=3):

display(qumian1,qumian2,quxian,xyz,scaling=constrained,orientation=[40,60]);

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