Calculating the sum of the lengths and plotting all curves on the same map
1
$begingroup$
I have a curve like below;
ParametricPlot[
FromPolarCoordinates[{Exp[(t + 0)*0.5], t}] // Evaluate, {t, 0,
Pi - 0}, PlotRange -> All]
This curve rotates around z axis. Therefore for a rotation of pi/2 gives something like this:
ParametricPlot[
FromPolarCoordinates[{Exp[(t + Pi/2)*0.5], t}] //
Evaluate, {t, -Pi/2, Pi - Pi/2}, PlotRange -> All]
What I want is to plot all the curves in a specified circle when it rotates with 3.6 degrees. And I want the sum of curves in the circle.
I tried this code but it didn't work:
ParametricPlot[Sum[HeavisideTheta[1 -
((Exp[(t + Pi*i/50)*0.5]*Cos[t] -
1)^2 + (Exp[(t + Pi*i/50)*0.5]*Sin[t])^2)]*
FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}] //
Evaluate, {t, -Pi*i/50, Pi - Pi*i/50}, PlotRange -> All]
I also tried this code:
ParametricPlot[ Evaluate@Sum[ HeavisideTheta[ 1 - ((Exp[(t + Pi*i/50)*0.5]Cos[t] - 1)^2 + (Exp[(t + Pii/50)*0.5]Sin[t])^2)] FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}], {t, -Pi, Pi}, PlotRange -> All]
But it gives something like below:
What I need is something like this:
And the sum of those curves in the circle area.
How should I write the code to achieve what I want?
plotting parametric-functions
asked 1 hour ago
Alper91Alper91
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 1 more comment
1
$begingroup$
I have a curve like below;
ParametricPlot[
FromPolarCoordinates[{Exp[(t + 0)*0.5], t}] // Evaluate, {t, 0,
Pi - 0}, PlotRange -> All]
This curve rotates around z axis. Therefore for a rotation of pi/2 gives something like this:
ParametricPlot[
FromPolarCoordinates[{Exp[(t + Pi/2)*0.5], t}] //
Evaluate, {t, -Pi/2, Pi - Pi/2}, PlotRange -> All]
What I want is to plot all the curves in a specified circle when it rotates with 3.6 degrees. And I want the sum of curves in the circle.
I tried this code but it didn't work:
ParametricPlot[Sum[HeavisideTheta[1 -
((Exp[(t + Pi*i/50)*0.5]*Cos[t] -
1)^2 + (Exp[(t + Pi*i/50)*0.5]*Sin[t])^2)]*
FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}] //
Evaluate, {t, -Pi*i/50, Pi - Pi*i/50}, PlotRange -> All]
I also tried this code:
ParametricPlot[ Evaluate@Sum[ HeavisideTheta[ 1 - ((Exp[(t + Pi*i/50)*0.5]Cos[t] - 1)^2 + (Exp[(t + Pii/50)*0.5]Sin[t])^2)] FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}], {t, -Pi, Pi}, PlotRange -> All]
But it gives something like below:
What I need is something like this:
And the sum of those curves in the circle area.
How should I write the code to achieve what I want?
plotting parametric-functions
asked 1 hour ago
Alper91Alper91
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Something like this:ParametricPlot[ Table[FromPolarCoordinates[{Exp[(t + 2 k Pi/100)*0.5], t}], {k, 1, 100, 5}], {t, -Pi, Pi}, PlotRange -> All, PlotStyle -> Red, RegionFunction -> Function[{x, y}, (x - 3)^2 + y^2 < 9]] // Show[#, ContourPlot[(x - 3)^2 + y^2 == 9, {x, 0, 6}, {y, -3, 3}, ContourStyle -> Blue]] &?
$endgroup$
– corey979
1 hour ago
$begingroup$
@kglr nope. I editted my answer and showed what your solution is like.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 Yes! Yes! Exactly like that one and the sum of the curves' length within the circle
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 However, your solution is not the rotation case. It is the case where radial growth of the spiral increases.
$endgroup$
– Alper91
1 hour ago
1
$begingroup$
So please provide relevant formulae. Reverse-engineering from code to what you are really after is cumbersome.
$endgroup$
– corey979
59 mins ago
|
show 1 more comment
1
1
1
$begingroup$
I have a curve like below;
ParametricPlot[
FromPolarCoordinates[{Exp[(t + 0)*0.5], t}] // Evaluate, {t, 0,
Pi - 0}, PlotRange -> All]
This curve rotates around z axis. Therefore for a rotation of pi/2 gives something like this:
ParametricPlot[
FromPolarCoordinates[{Exp[(t + Pi/2)*0.5], t}] //
Evaluate, {t, -Pi/2, Pi - Pi/2}, PlotRange -> All]
What I want is to plot all the curves in a specified circle when it rotates with 3.6 degrees. And I want the sum of curves in the circle.
I tried this code but it didn't work:
ParametricPlot[Sum[HeavisideTheta[1 -
((Exp[(t + Pi*i/50)*0.5]*Cos[t] -
1)^2 + (Exp[(t + Pi*i/50)*0.5]*Sin[t])^2)]*
FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}] //
Evaluate, {t, -Pi*i/50, Pi - Pi*i/50}, PlotRange -> All]
I also tried this code:
ParametricPlot[ Evaluate@Sum[ HeavisideTheta[ 1 - ((Exp[(t + Pi*i/50)*0.5]Cos[t] - 1)^2 + (Exp[(t + Pii/50)*0.5]Sin[t])^2)] FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}], {t, -Pi, Pi}, PlotRange -> All]
But it gives something like below:
What I need is something like this:
And the sum of those curves in the circle area.
How should I write the code to achieve what I want?
plotting parametric-functions
asked 1 hour ago
Alper91Alper91
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have a curve like below;
ParametricPlot[
FromPolarCoordinates[{Exp[(t + 0)*0.5], t}] // Evaluate, {t, 0,
Pi - 0}, PlotRange -> All]
This curve rotates around z axis. Therefore for a rotation of pi/2 gives something like this:
ParametricPlot[
FromPolarCoordinates[{Exp[(t + Pi/2)*0.5], t}] //
Evaluate, {t, -Pi/2, Pi - Pi/2}, PlotRange -> All]
What I want is to plot all the curves in a specified circle when it rotates with 3.6 degrees. And I want the sum of curves in the circle.
I tried this code but it didn't work:
ParametricPlot[Sum[HeavisideTheta[1 -
((Exp[(t + Pi*i/50)*0.5]*Cos[t] -
1)^2 + (Exp[(t + Pi*i/50)*0.5]*Sin[t])^2)]*
FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}] //
Evaluate, {t, -Pi*i/50, Pi - Pi*i/50}, PlotRange -> All]
I also tried this code:
ParametricPlot[ Evaluate@Sum[ HeavisideTheta[ 1 - ((Exp[(t + Pi*i/50)*0.5]Cos[t] - 1)^2 + (Exp[(t + Pii/50)*0.5]Sin[t])^2)] FromPolarCoordinates[{Exp[(t + Pi*i/50)*0.5], t}], {i, 1, 100}], {t, -Pi, Pi}, PlotRange -> All]
But it gives something like below:
What I need is something like this:
And the sum of those curves in the circle area.
How should I write the code to achieve what I want?
plotting parametric-functions
plotting parametric-functions
asked 1 hour ago
Alper91Alper91
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Alper91Alper91
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
Alper91
asked 1 hour ago
Alper91Alper91
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Alper91Alper91
1064
asked 1 hour ago
Alper91Alper91
1064
1064
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Alper91 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Something like this:ParametricPlot[ Table[FromPolarCoordinates[{Exp[(t + 2 k Pi/100)*0.5], t}], {k, 1, 100, 5}], {t, -Pi, Pi}, PlotRange -> All, PlotStyle -> Red, RegionFunction -> Function[{x, y}, (x - 3)^2 + y^2 < 9]] // Show[#, ContourPlot[(x - 3)^2 + y^2 == 9, {x, 0, 6}, {y, -3, 3}, ContourStyle -> Blue]] &?
$endgroup$
– corey979
1 hour ago
$begingroup$
@kglr nope. I editted my answer and showed what your solution is like.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 Yes! Yes! Exactly like that one and the sum of the curves' length within the circle
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 However, your solution is not the rotation case. It is the case where radial growth of the spiral increases.
$endgroup$
– Alper91
1 hour ago
1
$begingroup$
So please provide relevant formulae. Reverse-engineering from code to what you are really after is cumbersome.
$endgroup$
– corey979
59 mins ago
|
show 1 more comment
1
$begingroup$
Something like this:ParametricPlot[ Table[FromPolarCoordinates[{Exp[(t + 2 k Pi/100)*0.5], t}], {k, 1, 100, 5}], {t, -Pi, Pi}, PlotRange -> All, PlotStyle -> Red, RegionFunction -> Function[{x, y}, (x - 3)^2 + y^2 < 9]] // Show[#, ContourPlot[(x - 3)^2 + y^2 == 9, {x, 0, 6}, {y, -3, 3}, ContourStyle -> Blue]] &?
$endgroup$
– corey979
1 hour ago
$begingroup$
@kglr nope. I editted my answer and showed what your solution is like.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 Yes! Yes! Exactly like that one and the sum of the curves' length within the circle
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 However, your solution is not the rotation case. It is the case where radial growth of the spiral increases.
$endgroup$
– Alper91
1 hour ago
1
$begingroup$
So please provide relevant formulae. Reverse-engineering from code to what you are really after is cumbersome.
$endgroup$
– corey979
59 mins ago
1
1
$begingroup$
Something like this:
ParametricPlot[ Table[FromPolarCoordinates[{Exp[(t + 2 k Pi/100)*0.5], t}], {k, 1, 100, 5}], {t, -Pi, Pi}, PlotRange -> All, PlotStyle -> Red, RegionFunction -> Function[{x, y}, (x - 3)^2 + y^2 < 9]] // Show[#, ContourPlot[(x - 3)^2 + y^2 == 9, {x, 0, 6}, {y, -3, 3}, ContourStyle -> Blue]] &?$endgroup$
– corey979
1 hour ago
$begingroup$
Something like this:
ParametricPlot[ Table[FromPolarCoordinates[{Exp[(t + 2 k Pi/100)*0.5], t}], {k, 1, 100, 5}], {t, -Pi, Pi}, PlotRange -> All, PlotStyle -> Red, RegionFunction -> Function[{x, y}, (x - 3)^2 + y^2 < 9]] // Show[#, ContourPlot[(x - 3)^2 + y^2 == 9, {x, 0, 6}, {y, -3, 3}, ContourStyle -> Blue]] &?$endgroup$
– corey979
1 hour ago
$begingroup$
@kglr nope. I editted my answer and showed what your solution is like.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@kglr nope. I editted my answer and showed what your solution is like.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 Yes! Yes! Exactly like that one and the sum of the curves' length within the circle
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 Yes! Yes! Exactly like that one and the sum of the curves' length within the circle
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 However, your solution is not the rotation case. It is the case where radial growth of the spiral increases.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 However, your solution is not the rotation case. It is the case where radial growth of the spiral increases.
$endgroup$
– Alper91
1 hour ago
1
1
$begingroup$
So please provide relevant formulae. Reverse-engineering from code to what you are really after is cumbersome.
$endgroup$
– corey979
59 mins ago
$begingroup$
So please provide relevant formulae. Reverse-engineering from code to what you are really after is cumbersome.
$endgroup$
– corey979
59 mins ago
|
show 1 more comment
1 Answer
1
active
oldest
votes
3
$begingroup$
ctr = {3, 0};
radius = 3;
pp = PolarPlot[Evaluate@Table[Exp[(t + Pi*i/50)*0.5], {i, 1, 100}], {t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
Total[ArcLength /@ Cases[pp, _Line, All]]
(* or Total[RegionMeasure /@ Cases[pp, _Line, All]] *)
314.511
If ypu have to use ParametricPlot, you can do
pp2 = ParametricPlot[Evaluate[Table[E^(((j*Pi)/50 + t)/2) { Cos[t], Sin[t]}, {j, 1, 100}]],
{t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &), PlotRange -> All]
Total[ArcLength /@ Cases[pp2, _Line, All]]
314.511
answered 42 mins ago
kglrkglr
184k10202419
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "387"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Alper91 is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
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%2fmathematica.stackexchange.com%2fquestions%2f191700%2fcalculating-the-sum-of-the-lengths-and-plotting-all-curves-on-the-same-map%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
3
$begingroup$
ctr = {3, 0};
radius = 3;
pp = PolarPlot[Evaluate@Table[Exp[(t + Pi*i/50)*0.5], {i, 1, 100}], {t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
Total[ArcLength /@ Cases[pp, _Line, All]]
(* or Total[RegionMeasure /@ Cases[pp, _Line, All]] *)
314.511
If ypu have to use ParametricPlot, you can do
pp2 = ParametricPlot[Evaluate[Table[E^(((j*Pi)/50 + t)/2) { Cos[t], Sin[t]}, {j, 1, 100}]],
{t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &), PlotRange -> All]
Total[ArcLength /@ Cases[pp2, _Line, All]]
314.511
answered 42 mins ago
kglrkglr
184k10202419
$endgroup$
add a comment |
3
$begingroup$
ctr = {3, 0};
radius = 3;
pp = PolarPlot[Evaluate@Table[Exp[(t + Pi*i/50)*0.5], {i, 1, 100}], {t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
Total[ArcLength /@ Cases[pp, _Line, All]]
(* or Total[RegionMeasure /@ Cases[pp, _Line, All]] *)
314.511
If ypu have to use ParametricPlot, you can do
pp2 = ParametricPlot[Evaluate[Table[E^(((j*Pi)/50 + t)/2) { Cos[t], Sin[t]}, {j, 1, 100}]],
{t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &), PlotRange -> All]
Total[ArcLength /@ Cases[pp2, _Line, All]]
314.511
answered 42 mins ago
kglrkglr
184k10202419
$endgroup$
add a comment |
3
3
3
$begingroup$
ctr = {3, 0};
radius = 3;
pp = PolarPlot[Evaluate@Table[Exp[(t + Pi*i/50)*0.5], {i, 1, 100}], {t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
Total[ArcLength /@ Cases[pp, _Line, All]]
(* or Total[RegionMeasure /@ Cases[pp, _Line, All]] *)
314.511
If ypu have to use ParametricPlot, you can do
pp2 = ParametricPlot[Evaluate[Table[E^(((j*Pi)/50 + t)/2) { Cos[t], Sin[t]}, {j, 1, 100}]],
{t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &), PlotRange -> All]
Total[ArcLength /@ Cases[pp2, _Line, All]]
314.511
answered 42 mins ago
kglrkglr
184k10202419
$endgroup$
ctr = {3, 0};
radius = 3;
pp = PolarPlot[Evaluate@Table[Exp[(t + Pi*i/50)*0.5], {i, 1, 100}], {t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
Total[ArcLength /@ Cases[pp, _Line, All]]
(* or Total[RegionMeasure /@ Cases[pp, _Line, All]] *)
314.511
If ypu have to use ParametricPlot, you can do
pp2 = ParametricPlot[Evaluate[Table[E^(((j*Pi)/50 + t)/2) { Cos[t], Sin[t]}, {j, 1, 100}]],
{t, -Pi, Pi},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &), PlotRange -> All]
Total[ArcLength /@ Cases[pp2, _Line, All]]
314.511
answered 42 mins ago
kglrkglr
184k10202419
edited 35 mins ago
answered 42 mins ago
kglrkglr
184k10202419
answered 42 mins ago
kglrkglr
184k10202419
answered 42 mins ago
kglrkglr
184k10202419
184k10202419
add a comment |
add a comment |
Alper91 is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
Alper91 is a new contributor. Be nice, and check out our Code of Conduct.
Alper91 is a new contributor. Be nice, and check out our Code of Conduct.
Alper91 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
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%2fmathematica.stackexchange.com%2fquestions%2f191700%2fcalculating-the-sum-of-the-lengths-and-plotting-all-curves-on-the-same-map%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
1
$begingroup$
Something like this:
ParametricPlot[ Table[FromPolarCoordinates[{Exp[(t + 2 k Pi/100)*0.5], t}], {k, 1, 100, 5}], {t, -Pi, Pi}, PlotRange -> All, PlotStyle -> Red, RegionFunction -> Function[{x, y}, (x - 3)^2 + y^2 < 9]] // Show[#, ContourPlot[(x - 3)^2 + y^2 == 9, {x, 0, 6}, {y, -3, 3}, ContourStyle -> Blue]] &?$endgroup$
– corey979
1 hour ago
$begingroup$
@kglr nope. I editted my answer and showed what your solution is like.
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 Yes! Yes! Exactly like that one and the sum of the curves' length within the circle
$endgroup$
– Alper91
1 hour ago
$begingroup$
@corey979 However, your solution is not the rotation case. It is the case where radial growth of the spiral increases.
$endgroup$
– Alper91
1 hour ago
1
$begingroup$
So please provide relevant formulae. Reverse-engineering from code to what you are really after is cumbersome.
$endgroup$
– corey979
59 mins ago