Parametric Paraboloid In Polar Coordinates

[Lancelot59]

I just want to see if my logic is sound here. If we have the paraboloid z=x²+y² from z=0 to z=1, and I wanted a parametric form of that I think this should work for polar coordinates:

$$\vec{r}(u,v)=(vcosu,vsinu,v^{2})$$
$$u:[0..2\pi],v:[0..1]$$

Does this make sense?

 

[lanedance]

not really i think you are still defining cartesian coords, though its not exactly clear what you are trying to do

 

[HallsofIvy]

Thise are perfectly good parametric equations for the paraboloid, using "polar coordinates" in the xy-plane as parameters (actually you are using v= r, $u= \theta$).

 

[lanedance]

ok, so parameterise in terms of 2D polar coords, that makes more sense

 

[Lancelot59]

Then it isn't in 3D anymore...I meant to say cylindrical coordinates, so that's my bad with the terminology.