parametric representation of a closed “Cylinder”

Multi tool use
up vote
0
down vote
favorite
Assume I have a parametric curve $r(t) = <X(t),Y(t)>$ that defines a closed curve (like a circle or a closed B-spline) on a 2D plane.
The cylinder can be defined as:
$f(u,v) = <X(u), Y(u), v>$
For bounded values of $u$ and $v$.
This however gives us a sleeve (there's holes on the top and the bottom). If $r(t)$ is any arbitrary, paramateric, closed curve defined in 2D, how can you close the top?
geometry differential-geometry manifolds parametric
add a comment |
up vote
0
down vote
favorite
Assume I have a parametric curve $r(t) = <X(t),Y(t)>$ that defines a closed curve (like a circle or a closed B-spline) on a 2D plane.
The cylinder can be defined as:
$f(u,v) = <X(u), Y(u), v>$
For bounded values of $u$ and $v$.
This however gives us a sleeve (there's holes on the top and the bottom). If $r(t)$ is any arbitrary, paramateric, closed curve defined in 2D, how can you close the top?
geometry differential-geometry manifolds parametric
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Assume I have a parametric curve $r(t) = <X(t),Y(t)>$ that defines a closed curve (like a circle or a closed B-spline) on a 2D plane.
The cylinder can be defined as:
$f(u,v) = <X(u), Y(u), v>$
For bounded values of $u$ and $v$.
This however gives us a sleeve (there's holes on the top and the bottom). If $r(t)$ is any arbitrary, paramateric, closed curve defined in 2D, how can you close the top?
geometry differential-geometry manifolds parametric
Assume I have a parametric curve $r(t) = <X(t),Y(t)>$ that defines a closed curve (like a circle or a closed B-spline) on a 2D plane.
The cylinder can be defined as:
$f(u,v) = <X(u), Y(u), v>$
For bounded values of $u$ and $v$.
This however gives us a sleeve (there's holes on the top and the bottom). If $r(t)$ is any arbitrary, paramateric, closed curve defined in 2D, how can you close the top?
geometry differential-geometry manifolds parametric
geometry differential-geometry manifolds parametric
asked yesterday


Makogan
726217
726217
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3007023%2fparametric-representation-of-a-closed-cylinder%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Ysn,O,dmQgJIcnOFpJP,st19BE x sW4E 26z4jtmzSEr F52Xhjfn,Nd1Q4YQ8 h3j9OPcpXHOBl9S,TI1nluS 9p,Z6D 5hdUiSSn6g