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狗鞍面

2012-04-24 09:49:54| 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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狗鞍面 (dog saddle)

狗鞍面的方程为：z=x*y^3-y*x^3。这是一个4次曲面。

(见Stewart《Calculus》p.900)

狗鞍面的图形如下：

狗鞍面 dog saddle - calculus - 徐小湛的博客

狗鞍面有四个缺口，狗的四条腿可以从缺口伸下。

with(plots):
implicitplot3d(z=x*y^3-y*x^3,x=-2..2,y=-2..2,z=-1..1,
grid=[20,20,20],lightmodel=light2,style=patchnogrid);

狗鞍面 dog saddle - calculus - 徐小湛的博客

狗鞍面 - calculus - 徐小湛的博客

with(plots):

for i from 1 to 60 do:

qumian[i]:=implicitplot3d(z=x*y^3-y*x^3,x=-2..2,y=-2..2,z=-1..1,
orientation=[90+6*i,55],grid=[20,20,20]):od:

display(seq(qumian[i],i=1..60),insequence=true,lightmodel=light2,style=patch);

参考资料：http://www.math.uiowa.edu/~stroyan/CTLC3rdEd/ctlcOldcd/estroyan/cd/19/index.htm

http://books.google.com.hk/books?id=906FPCXJg9UC&pg=PA904&lpg=PA904&dq=dog+saddle+calculus&source=bl&ots=mhZxN-Unek&sig=EAQtKgz3ZyCoZ-lO5Vs9QpvWPps&hl=en&sa=X&ei=W_GZT6aLHoetiQei2KDpDg&ved=0CEQQ6AEwBQ#v=onepage&q&f=true 904页

http://books.google.com.hk/books?id=906FPCXJg9UC&pg=PA904&lpg=PA904&dq=dog+saddle+calculus&source=bl&ots=mhZxN-Unek&sig=EAQtKgz3ZyCoZ-lO5Vs9QpvWPps&hl=en&sa=X&ei=W_GZT6aLHoetiQei2KDpDg&ved=0CEQQ6AEwBQ#v=onepage&q&f=true

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