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高等数学课件、函数图形动画、数学软件应用

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马鞍面

2009-07-13 11:41:43| 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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所有图形见：数学图形目录

马鞍面（双曲抛物面）(Saddle)

说明：这种曲面之所以称为“马鞍面”，是因为它在原点附近的图形很像一副马鞍。

曲面的Maple程序（用显函数绘制）：

with(plots): a:=2:

qumian:=plot3d(x*y,x=-a..a,y=-sqrt(a^2-x^2)..sqrt(a^2-x^2)):

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

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

z_axis:=plot3d([0,0,u],u=-1..1,v=0..0.01,color=blue):

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

display(qumian,xyz,tickmarks=[4,4,4], axes=none, grid=[40,40],lightmodel=light2);

with(plots): a:=3:b:=4:

qumian:=plot3d(x*y,x=-b..b,y=-b..b):

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

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

z_axis:=plot3d([0,0,u],u=-0..6,v=0..0.01,color=blue):

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

display(qumian,xyz,tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light2);

with(plots):

a:=1:b:=1:

qumian:=plot3d([a*lamda/2+a*t,b*lamda/2-b*t,2*lamda*t],t=-3..3,lamda=-3..3,scaling=unconstrained,lightmodel=light3,view=[-3..3,-3..3,-10..10],grid=[30,30]):

x_axis:=plot3d([u,0,0],u=-4..4,v=0..0.01,thickness=3):

y_axis:=plot3d([0,u,0],u=-4..4,v=0..0.01,thickness=3):

z_axis:=plot3d([0,0,u],u=-6..6,v=0..0.01,thickness=3):

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

display(qumian,xyz,tickmarks=[4,4,4],axes=none);

with(plots):

a:=1:b:=1:

x(u,v):=a*(u+v): y(u,v):=b*(u-v): z(u,v):=2*u*v:

A:=plot3d([x(u,v),y(u,v),z(u,v)],u=-2..2,v=-2..2):

display(A,scaling=unconstrained,lightmodel=light2,axes=normal);

用隐函数绘制

with(plots):

implicitplot3d(z=x*y,x=-2..2,y=-2..2,z=-1..1);

动画的Maple程序：

with(plots):
K:=60:for i from 1 to K do:
qumian[i]:=implicitplot3d(z=x*y,x=-2..2,y=-2..2,z=-1..1,orientation=[90+6*i,55]):od:
display(seq(qumian[i],i=1..K),insequence=true);

顺便去看看猴鞍面

返回：数学图形目录

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