Surface parametrization


by chaotixmonjuish
Tags: parametrization
chaotixmonjuish
chaotixmonjuish is offline
#1
Nov6-10, 01:55 AM
P: 287
I'm having problems understanding surface parametrization from differential geometry.

We are given two general forms for parametrization:
[tex]\alpha[/tex](u,v) = (u,v,0)
and x(u,v)=(u,v,f(u,v))


This is one I'm especially stuck on:

y=Cosh(x) about the x-axis

[tex]\alpha[/tex](u,v)=(u, Cosh[v],0)

x(u,v) = (u, Cosh[v]cos(u), Cosh[v]sin(u))

I think that's right.
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
arkajad
arkajad is offline
#2
Nov6-10, 04:29 AM
P: 1,412
I do not understand the notation in these "general forms". Which textbook are you using?
tiny-tim
tiny-tim is offline
#3
Nov6-10, 05:00 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
hi chaotixmonjuish!

(have an alpha: α and a theta: θ )
Quote Quote by chaotixmonjuish View Post
y=Cosh(x) about the x-axis

[tex]\alpha[/tex](u,v)=(u, Cosh[v],0)

x(u,v) = (u, Cosh[v]cos(u), Cosh[v]sin(u))
are you talking about the surface of revolution obtained by rotating y = coshx about the x-axis?

if so, if one of your parameters (u) is equal to x, then the other sensible paramter to choose would be θ, an angle round the x-axis

(so you'll get a nice "square-ish" (x,θ) grid on the surface)

anyway, your y will always be cosh(u), won't it, not cosh of some other parameter v ?


Register to reply

Related Discussions
Surface area parametrization Calculus & Beyond Homework 0
Parametrization help? Calculus & Beyond Homework 5
surface parametrization Calculus & Beyond Homework 4
surface parametrization Calculus & Beyond Homework 2
parametrization? Introductory Physics Homework 3