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两个抛物面的交线

2009-08-13 21:39:45| 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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抛物面 z=2*x^2+3*y^2 和 z=4-2*x^2-y^2 相交的交线方程就是将这两个方程联立：

with(plots):
z1:=(x,y)->2*x^2+3*y^2: z2:=(x,y)->4-2*x^2-y^2:
qumian1:=plot3d([u*cos(t)/sqrt(2), u*sin(t)/sqrt(3), u^2],u=0..2, t=0..2*Pi,color=yellow):
qumian2:=plot3d([u*cos(t)/sqrt(2), u*sin(t), 4-u^2],u=0..2,t=0..2*Pi, color=green):
quxian:=spacecurve([cos(t),sin(t),z1(cos(t),sin(t))],t=0..2*Pi,thickness=5,color=red):
display(qumian1,qumian2,quxian,scaling=constrained,orientation=[40,60]);

可以看出这个交线是一条空间曲线。

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