parametric representation of a closed “Cylinder”
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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
asked yesterday
Makogan
726217
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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
asked yesterday
Makogan
726217
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
asked yesterday
Makogan
726217
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
asked yesterday
Makogan
726217
asked yesterday
Makogan
726217
asked yesterday
Makogan
726217
asked yesterday
Makogan
726217
726217
add a comment |
add a comment |
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