Resource for a library of closed curves.Question about closed curves and surfacesCurves on $mathbbA^2$Product rule for curvespaths and curvesFormulas for space curvesCurves in 3D, cartesian coordinatesConvex curves with the axes for asymptotesBest spline method for closed curvesExercise on parametric curvesSpace filling curve's intersections with closed jordan curves
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Resource for a library of closed curves.
Question about closed curves and surfacesCurves on $mathbbA^2$Product rule for curvespaths and curvesFormulas for space curvesCurves in 3D, cartesian coordinatesConvex curves with the axes for asymptotesBest spline method for closed curvesExercise on parametric curvesSpace filling curve's intersections with closed jordan curves
$begingroup$
I am working on a computation project and I need a bunch of closed curves to test my programs on. Does anybody know of a resource or library of such curves somewhere preferably online. I would like to not have to come up with a bunch by hand especially since I want to avoid any bias that may appear in constructing them myself. Any help is greatly appreciated.
curves
asked Mar 13 at 19:06
WaltWalt
393115
$endgroup$
add a comment |
$begingroup$
I am working on a computation project and I need a bunch of closed curves to test my programs on. Does anybody know of a resource or library of such curves somewhere preferably online. I would like to not have to come up with a bunch by hand especially since I want to avoid any bias that may appear in constructing them myself. Any help is greatly appreciated.
curves
asked Mar 13 at 19:06
WaltWalt
393115
$endgroup$
add a comment |
$begingroup$
I am working on a computation project and I need a bunch of closed curves to test my programs on. Does anybody know of a resource or library of such curves somewhere preferably online. I would like to not have to come up with a bunch by hand especially since I want to avoid any bias that may appear in constructing them myself. Any help is greatly appreciated.
curves
asked Mar 13 at 19:06
WaltWalt
393115
$endgroup$
I am working on a computation project and I need a bunch of closed curves to test my programs on. Does anybody know of a resource or library of such curves somewhere preferably online. I would like to not have to come up with a bunch by hand especially since I want to avoid any bias that may appear in constructing them myself. Any help is greatly appreciated.
curves
curves
asked Mar 13 at 19:06
WaltWalt
393115
asked Mar 13 at 19:06
WaltWalt
393115
asked Mar 13 at 19:06
WaltWalt
393115
asked Mar 13 at 19:06
WaltWalt
393115
asked Mar 13 at 19:06
WaltWalt
393115
393115
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The following provides a way to get a somewhat unbiased set of many closed curves, but takes a bit of work by hand. Start from some table of integrals (say "Pierce's Short Table of Integrals"). Go to one of the chapters and for each formula that is not generic for unspecified $f(x)$, look at either the integrand or the result. Then plot that result as a polar plot, and observe when (if) the curve closes. There you have one sample curve.
For example, integral $3$ in chapter $1$ is $int fracdxx = log x$. Plotting
$r = log theta$ gives a curve that comes in from the left, crosses the origin from below, loops around and crosses itself at about $theta = 0.2913$. So take $r = log theta, theta in [0.2913, 0.2913+pi]$ as your first example closed curve.
In may cases the curve will not close; then just move on to the next one.
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
$endgroup$
add a comment |
$begingroup$
This is really a good site for what you are looking for.
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
$endgroup$
add a comment |
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2 Answers
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2 Answers
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active
oldest
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$begingroup$
The following provides a way to get a somewhat unbiased set of many closed curves, but takes a bit of work by hand. Start from some table of integrals (say "Pierce's Short Table of Integrals"). Go to one of the chapters and for each formula that is not generic for unspecified $f(x)$, look at either the integrand or the result. Then plot that result as a polar plot, and observe when (if) the curve closes. There you have one sample curve.
For example, integral $3$ in chapter $1$ is $int fracdxx = log x$. Plotting
$r = log theta$ gives a curve that comes in from the left, crosses the origin from below, loops around and crosses itself at about $theta = 0.2913$. So take $r = log theta, theta in [0.2913, 0.2913+pi]$ as your first example closed curve.
In may cases the curve will not close; then just move on to the next one.
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
$endgroup$
add a comment |
$begingroup$
The following provides a way to get a somewhat unbiased set of many closed curves, but takes a bit of work by hand. Start from some table of integrals (say "Pierce's Short Table of Integrals"). Go to one of the chapters and for each formula that is not generic for unspecified $f(x)$, look at either the integrand or the result. Then plot that result as a polar plot, and observe when (if) the curve closes. There you have one sample curve.
For example, integral $3$ in chapter $1$ is $int fracdxx = log x$. Plotting
$r = log theta$ gives a curve that comes in from the left, crosses the origin from below, loops around and crosses itself at about $theta = 0.2913$. So take $r = log theta, theta in [0.2913, 0.2913+pi]$ as your first example closed curve.
In may cases the curve will not close; then just move on to the next one.
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
$endgroup$
add a comment |
$begingroup$
The following provides a way to get a somewhat unbiased set of many closed curves, but takes a bit of work by hand. Start from some table of integrals (say "Pierce's Short Table of Integrals"). Go to one of the chapters and for each formula that is not generic for unspecified $f(x)$, look at either the integrand or the result. Then plot that result as a polar plot, and observe when (if) the curve closes. There you have one sample curve.
For example, integral $3$ in chapter $1$ is $int fracdxx = log x$. Plotting
$r = log theta$ gives a curve that comes in from the left, crosses the origin from below, loops around and crosses itself at about $theta = 0.2913$. So take $r = log theta, theta in [0.2913, 0.2913+pi]$ as your first example closed curve.
In may cases the curve will not close; then just move on to the next one.
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
$endgroup$
The following provides a way to get a somewhat unbiased set of many closed curves, but takes a bit of work by hand. Start from some table of integrals (say "Pierce's Short Table of Integrals"). Go to one of the chapters and for each formula that is not generic for unspecified $f(x)$, look at either the integrand or the result. Then plot that result as a polar plot, and observe when (if) the curve closes. There you have one sample curve.
For example, integral $3$ in chapter $1$ is $int fracdxx = log x$. Plotting
$r = log theta$ gives a curve that comes in from the left, crosses the origin from below, loops around and crosses itself at about $theta = 0.2913$. So take $r = log theta, theta in [0.2913, 0.2913+pi]$ as your first example closed curve.
In may cases the curve will not close; then just move on to the next one.
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
answered Mar 13 at 19:33
Mark FischlerMark Fischler
33.6k12552
33.6k12552
add a comment |
add a comment |
$begingroup$
This is really a good site for what you are looking for.
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
$endgroup$
add a comment |
$begingroup$
This is really a good site for what you are looking for.
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
$endgroup$
add a comment |
$begingroup$
This is really a good site for what you are looking for.
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
$endgroup$
This is really a good site for what you are looking for.
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
answered Mar 13 at 19:11
G CabG Cab
20.4k31341
20.4k31341
add a comment |
add a comment |
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