ContourPlot — How do I color by contour curvature?Custom contour labels in ContourPlotListContourPlot is blocking my geometryHow to plot the contour of f[x,y]==0 if always f[x,y]>=0Contour coloring and (List)ContourPlot projectionMore stream lines in a ListStreamPlotContourPlot - unequal contour spacingContourPlot color problems3D Stack of Disks with dedicated height plotsHow to color Contours in ContourPlot with custom ColorFunctionChanging the color of a specific curve in ContourPlot
Pre-mixing cryogenic fuels and using only one fuel tank
Were Persian-Median kings illiterate?
Why Shazam when there is already Superman?
What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?
How to convince somebody that he is fit for something else, but not this job?
How to get directions in deep space?
A Trivial Diagnosis
Does "he squandered his car on drink" sound natural?
Why does AES have exactly 10 rounds for a 128-bit key, 12 for 192 bits and 14 for a 256-bit key size?
Which Article Helped Get Rid of Technobabble in RPGs?
Is this part of the description of the Archfey warlock's Misty Escape feature redundant?
Can I cause damage to electrical appliances by unplugging them when they are turned on?
Does the reader need to like the PoV character?
Is there a way to have vectors outlined in a Vector Plot?
What is Cash Advance APR?
I found an audio circuit and I built it just fine, but I find it a bit too quiet. How do I amplify the output so that it is a bit louder?
What (the heck) is a Super Worm Equinox Moon?
Why does this expression simplify as such?
Why is it that I can sometimes guess the next note?
C++ copy constructor called at return
How to explain what's wrong with this application of the chain rule?
Creating two special characters
How do you make your own symbol when Detexify fails?
What is going on with gets(stdin) on the site coderbyte?
ContourPlot — How do I color by contour curvature?
Custom contour labels in ContourPlotListContourPlot is blocking my geometryHow to plot the contour of f[x,y]==0 if always f[x,y]>=0Contour coloring and (List)ContourPlot projectionMore stream lines in a ListStreamPlotContourPlot - unequal contour spacingContourPlot color problems3D Stack of Disks with dedicated height plotsHow to color Contours in ContourPlot with custom ColorFunctionChanging the color of a specific curve in ContourPlot
$begingroup$
I'm plotting the stream lines of fluid flow past a cylinder, and I would like the colors to increase with contour curvature (i.e. increase as the velocity of the flow increases. Here's a MWE that seems to color it based on the the y-axis value:
ψ[r_, θ_] := U (r - a^2/r) Sin[θ]
r = Sqrt[x^2 + y^2];
θ = ArcSin[y/r];
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1,
x, -5,5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.025]
];
cyl = Graphics[Disk[0, 0, 1]];
Show[stream, cyl]
plotting color
edited yesterday
m_goldberg
87.7k872198
asked yesterday
dpholmesdpholmes
345111
$endgroup$
add a comment |
$begingroup$
I'm plotting the stream lines of fluid flow past a cylinder, and I would like the colors to increase with contour curvature (i.e. increase as the velocity of the flow increases. Here's a MWE that seems to color it based on the the y-axis value:
ψ[r_, θ_] := U (r - a^2/r) Sin[θ]
r = Sqrt[x^2 + y^2];
θ = ArcSin[y/r];
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1,
x, -5,5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.025]
];
cyl = Graphics[Disk[0, 0, 1]];
Show[stream, cyl]
plotting color
edited yesterday
m_goldberg
87.7k872198
asked yesterday
dpholmesdpholmes
345111
$endgroup$
add a comment |
$begingroup$
I'm plotting the stream lines of fluid flow past a cylinder, and I would like the colors to increase with contour curvature (i.e. increase as the velocity of the flow increases. Here's a MWE that seems to color it based on the the y-axis value:
ψ[r_, θ_] := U (r - a^2/r) Sin[θ]
r = Sqrt[x^2 + y^2];
θ = ArcSin[y/r];
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1,
x, -5,5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.025]
];
cyl = Graphics[Disk[0, 0, 1]];
Show[stream, cyl]
plotting color
edited yesterday
m_goldberg
87.7k872198
asked yesterday
dpholmesdpholmes
345111
$endgroup$
I'm plotting the stream lines of fluid flow past a cylinder, and I would like the colors to increase with contour curvature (i.e. increase as the velocity of the flow increases. Here's a MWE that seems to color it based on the the y-axis value:
ψ[r_, θ_] := U (r - a^2/r) Sin[θ]
r = Sqrt[x^2 + y^2];
θ = ArcSin[y/r];
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1,
x, -5,5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.025]
];
cyl = Graphics[Disk[0, 0, 1]];
Show[stream, cyl]
plotting color
plotting color
edited yesterday
m_goldberg
87.7k872198
asked yesterday
dpholmesdpholmes
345111
edited yesterday
m_goldberg
87.7k872198
asked yesterday
dpholmesdpholmes
345111
edited yesterday
m_goldberg
87.7k872198
edited yesterday
m_goldberg
87.7k872198
edited yesterday
m_goldberg
87.7k872198
87.7k872198
asked yesterday
dpholmesdpholmes
345111
asked yesterday
dpholmesdpholmes
345111
asked yesterday
dpholmesdpholmes
345111
345111
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
f = ψ[r, θ] /. U -> 10, a -> 1;
gradf = D[f, x, y, 1];
Hessf = D[f, x, y, 2];
normal = gradf[[1]]/Sqrt[gradf[[1]].gradf[[1]]] // Simplify;
secondfundamentalform = -PseudoInverse[gradf].Hessf // ComplexExpand // Simplify;
tangent = RotationMatrix[Pi/2].normal;
curvaturevector = (secondfundamentalform.tangent).tangent // Simplify;
signedcurvature = curvaturevector.normal // Simplify;
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1, x, -5, 5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.2],
ContourShading -> None
];
curvatureplot = DensityPlot[signedcurvature, x, -5, 5, y, -5, 5,
ColorFunction -> "RedGreenSplit",
ClippingStyle -> Automatic,
PlotPoints -> 100,
PlotRange -> -1, 1
];
Show[
curvatureplot,
stream,
cyl
]
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
$endgroup$
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
);
);
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%2f193665%2fcontourplot-how-do-i-color-by-contour-curvature%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
$begingroup$
f = ψ[r, θ] /. U -> 10, a -> 1;
gradf = D[f, x, y, 1];
Hessf = D[f, x, y, 2];
normal = gradf[[1]]/Sqrt[gradf[[1]].gradf[[1]]] // Simplify;
secondfundamentalform = -PseudoInverse[gradf].Hessf // ComplexExpand // Simplify;
tangent = RotationMatrix[Pi/2].normal;
curvaturevector = (secondfundamentalform.tangent).tangent // Simplify;
signedcurvature = curvaturevector.normal // Simplify;
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1, x, -5, 5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.2],
ContourShading -> None
];
curvatureplot = DensityPlot[signedcurvature, x, -5, 5, y, -5, 5,
ColorFunction -> "RedGreenSplit",
ClippingStyle -> Automatic,
PlotPoints -> 100,
PlotRange -> -1, 1
];
Show[
curvatureplot,
stream,
cyl
]
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
$endgroup$
add a comment |
$begingroup$
f = ψ[r, θ] /. U -> 10, a -> 1;
gradf = D[f, x, y, 1];
Hessf = D[f, x, y, 2];
normal = gradf[[1]]/Sqrt[gradf[[1]].gradf[[1]]] // Simplify;
secondfundamentalform = -PseudoInverse[gradf].Hessf // ComplexExpand // Simplify;
tangent = RotationMatrix[Pi/2].normal;
curvaturevector = (secondfundamentalform.tangent).tangent // Simplify;
signedcurvature = curvaturevector.normal // Simplify;
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1, x, -5, 5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.2],
ContourShading -> None
];
curvatureplot = DensityPlot[signedcurvature, x, -5, 5, y, -5, 5,
ColorFunction -> "RedGreenSplit",
ClippingStyle -> Automatic,
PlotPoints -> 100,
PlotRange -> -1, 1
];
Show[
curvatureplot,
stream,
cyl
]
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
$endgroup$
add a comment |
$begingroup$
f = ψ[r, θ] /. U -> 10, a -> 1;
gradf = D[f, x, y, 1];
Hessf = D[f, x, y, 2];
normal = gradf[[1]]/Sqrt[gradf[[1]].gradf[[1]]] // Simplify;
secondfundamentalform = -PseudoInverse[gradf].Hessf // ComplexExpand // Simplify;
tangent = RotationMatrix[Pi/2].normal;
curvaturevector = (secondfundamentalform.tangent).tangent // Simplify;
signedcurvature = curvaturevector.normal // Simplify;
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1, x, -5, 5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.2],
ContourShading -> None
];
curvatureplot = DensityPlot[signedcurvature, x, -5, 5, y, -5, 5,
ColorFunction -> "RedGreenSplit",
ClippingStyle -> Automatic,
PlotPoints -> 100,
PlotRange -> -1, 1
];
Show[
curvatureplot,
stream,
cyl
]
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
$endgroup$
f = ψ[r, θ] /. U -> 10, a -> 1;
gradf = D[f, x, y, 1];
Hessf = D[f, x, y, 2];
normal = gradf[[1]]/Sqrt[gradf[[1]].gradf[[1]]] // Simplify;
secondfundamentalform = -PseudoInverse[gradf].Hessf // ComplexExpand // Simplify;
tangent = RotationMatrix[Pi/2].normal;
curvaturevector = (secondfundamentalform.tangent).tangent // Simplify;
signedcurvature = curvaturevector.normal // Simplify;
stream = ContourPlot[
ψ[r, θ] /. U -> 10, a -> 1, x, -5, 5, y, -5, 5,
Contours -> 10 Table[i, i, -10, 10, 0.2],
ContourShading -> None
];
curvatureplot = DensityPlot[signedcurvature, x, -5, 5, y, -5, 5,
ColorFunction -> "RedGreenSplit",
ClippingStyle -> Automatic,
PlotPoints -> 100,
PlotRange -> -1, 1
];
Show[
curvatureplot,
stream,
cyl
]
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
edited 20 hours ago
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
answered yesterday
Henrik SchumacherHenrik Schumacher
57.4k578158
57.4k578158
add a comment |
add a comment |
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.
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%2f193665%2fcontourplot-how-do-i-color-by-contour-curvature%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
