Heejin's 3-D plot and tangential plane example.
In order to plot a tangential plane of a 3-D plot at a nominal
point, you need to determine thegradients in each direction (i.e.,
x and y direction) and translate to the nominal point.
Thetranslation equation is
z zo f x xo y yo, ( )=The example I showed in the class
coincidently had the same value of offset that would beprovided by
translating in x, y, and z direction. The correct solution is
presented in thefollowing.
z x y, ( ) x2
3y2
2+:=
axz x y, ( )d
dsubstitute x 2=, y 1=, 4
3:=
byz x y, ( )d
dsubstitute x 2=, y 1=, 1:=
This is what I did in the class: Tangential plane with correct
translation:
zz x y, ( ) a x b y+ z 2 1, ( ):= zzz x y, ( ) a x 2( ) b y 1(
)+ z 2 1, ( )+:=
z 2 1, ( ) 1.833= 2 a 1b z 2 1, ( )+ 1.833=
z zz, z zzz,
If you still don't understand my point, please send me an email
to [email protected] or comeby my office in Room 312, Carpenter.
