Visualizing a complicated RegionVisualizing directoriesVisualizing a 2-dimensional PDFVisualizing Type System...

Does hiding behind 5-ft-wide cover give full cover?

Short story about people living in a different time streams

How to get SEEK accessing converted ID via view

Is there a QGIS plugin that reclassify raster symbology based on current extent?

Historically, were women trained for obligatory wars? Or did they serve some other military function?

How to implement float hashing with approximate equality

Airbnb - host wants to reduce rooms, can we get refund?

Why debootstrap can only run as root?

What are the spoon bit of a spoon and fork bit of a fork called?

How to reply this mail from potential PhD professor?

Pressure to defend the relevance of one's area of mathematics

A non-technological, repeating, visible object in the sky, holding its position in the sky for hours

What was the state of the German rail system in 1944?

Why do money exchangers give different rates to different bills

Entropy as a function of temperature: is temperature well defined?

Conflicting terms and the definition of a «child»

Can fracking help reduce CO2?

Why is Thanos so tough at the beginning of "Avengers: Endgame"?

Can I use 1000v rectifier diodes instead of 600v rectifier diodes?

How to efficiently calculate prefix sum of frequencies of characters in a string?

What is the most remote airport from the center of the city it supposedly serves?

If 1. e4 c6 is considered as a sound defense for black, why is 1. c3 so rare?

Visualizing a complicated Region

Survey Confirmation - Emphasize the question or the answer?



Visualizing a complicated Region


Visualizing directoriesVisualizing a 2-dimensional PDFVisualizing Type System OperationsRegion from pointsVisualizing Bendixson’s criterionVisualizing region unionsHalfplane region intersection anomalyVisualizing the complex logarithmParametric Region only showing half of regionVisualizing Trained Filters













3












$begingroup$


I was given the problem to find the area bounded by the polar curve



$$r=frac{1}{2}+frac{3}{2}cos(theta)$$



which looks like



                                      
enter image description here



To be clear, the region meant is the lighter of the two here



                                      
enter image description here



I know the integrals needed to actually find the area, and that really isn't the question anymore. Instead, visualization is. I believe that can define the region that I am interested in with the code block (a and b were defined for generality)



a=1/2;
b=3/2;
v={(a c+b c Cos[t])Cos[t],(a c+b c Cos[t])Sin[t]};
R1=ParametricRegion[v,{{c,0,1},{t,0,(2[Pi])/3}}];
R2=ParametricRegion[v,{{c,0,1},{t,2[Pi])/3,(4[Pi])/3}}];
R3=ParametricRegion[v,{{c,0,1},{t,(4[Pi])/3,2[Pi]}}];

R=RegionDifference[RegionUnion[R1,R3],R3];


I can look at these individually, but when I use Region to visualize the whole thing, it doesn't return even a picture, just some internal expression. How can I visualize just the region of interest?










share|improve this question









$endgroup$












  • $begingroup$
    Your code works for me, but very slowly. I obtained R1 in several minutes.
    $endgroup$
    – user64494
    4 hours ago
















3












$begingroup$


I was given the problem to find the area bounded by the polar curve



$$r=frac{1}{2}+frac{3}{2}cos(theta)$$



which looks like



                                      
enter image description here



To be clear, the region meant is the lighter of the two here



                                      
enter image description here



I know the integrals needed to actually find the area, and that really isn't the question anymore. Instead, visualization is. I believe that can define the region that I am interested in with the code block (a and b were defined for generality)



a=1/2;
b=3/2;
v={(a c+b c Cos[t])Cos[t],(a c+b c Cos[t])Sin[t]};
R1=ParametricRegion[v,{{c,0,1},{t,0,(2[Pi])/3}}];
R2=ParametricRegion[v,{{c,0,1},{t,2[Pi])/3,(4[Pi])/3}}];
R3=ParametricRegion[v,{{c,0,1},{t,(4[Pi])/3,2[Pi]}}];

R=RegionDifference[RegionUnion[R1,R3],R3];


I can look at these individually, but when I use Region to visualize the whole thing, it doesn't return even a picture, just some internal expression. How can I visualize just the region of interest?










share|improve this question









$endgroup$












  • $begingroup$
    Your code works for me, but very slowly. I obtained R1 in several minutes.
    $endgroup$
    – user64494
    4 hours ago














3












3








3





$begingroup$


I was given the problem to find the area bounded by the polar curve



$$r=frac{1}{2}+frac{3}{2}cos(theta)$$



which looks like



                                      
enter image description here



To be clear, the region meant is the lighter of the two here



                                      
enter image description here



I know the integrals needed to actually find the area, and that really isn't the question anymore. Instead, visualization is. I believe that can define the region that I am interested in with the code block (a and b were defined for generality)



a=1/2;
b=3/2;
v={(a c+b c Cos[t])Cos[t],(a c+b c Cos[t])Sin[t]};
R1=ParametricRegion[v,{{c,0,1},{t,0,(2[Pi])/3}}];
R2=ParametricRegion[v,{{c,0,1},{t,2[Pi])/3,(4[Pi])/3}}];
R3=ParametricRegion[v,{{c,0,1},{t,(4[Pi])/3,2[Pi]}}];

R=RegionDifference[RegionUnion[R1,R3],R3];


I can look at these individually, but when I use Region to visualize the whole thing, it doesn't return even a picture, just some internal expression. How can I visualize just the region of interest?










share|improve this question









$endgroup$




I was given the problem to find the area bounded by the polar curve



$$r=frac{1}{2}+frac{3}{2}cos(theta)$$



which looks like



                                      
enter image description here



To be clear, the region meant is the lighter of the two here



                                      
enter image description here



I know the integrals needed to actually find the area, and that really isn't the question anymore. Instead, visualization is. I believe that can define the region that I am interested in with the code block (a and b were defined for generality)



a=1/2;
b=3/2;
v={(a c+b c Cos[t])Cos[t],(a c+b c Cos[t])Sin[t]};
R1=ParametricRegion[v,{{c,0,1},{t,0,(2[Pi])/3}}];
R2=ParametricRegion[v,{{c,0,1},{t,2[Pi])/3,(4[Pi])/3}}];
R3=ParametricRegion[v,{{c,0,1},{t,(4[Pi])/3,2[Pi]}}];

R=RegionDifference[RegionUnion[R1,R3],R3];


I can look at these individually, but when I use Region to visualize the whole thing, it doesn't return even a picture, just some internal expression. How can I visualize just the region of interest?







regions visualization






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 6 hours ago









Brandon MyersBrandon Myers

1305




1305












  • $begingroup$
    Your code works for me, but very slowly. I obtained R1 in several minutes.
    $endgroup$
    – user64494
    4 hours ago


















  • $begingroup$
    Your code works for me, but very slowly. I obtained R1 in several minutes.
    $endgroup$
    – user64494
    4 hours ago
















$begingroup$
Your code works for me, but very slowly. I obtained R1 in several minutes.
$endgroup$
– user64494
4 hours ago




$begingroup$
Your code works for me, but very slowly. I obtained R1 in several minutes.
$endgroup$
– user64494
4 hours ago










2 Answers
2






active

oldest

votes


















4












$begingroup$

We can construct such a region with CrossingPolygon and in this instance Polygon will work too.



c = 1;
pts = Table[v, {t, Subdivide[0., 2π, 200]}];
pts[[-1]] = pts[[1]];

Graphics[{EdgeForm[ColorData[97][1]], Opacity[.3], ColorData[97][2], Polygon[pts]}]




CrossingCount[Polygon[pts], {0.5, 0}]



2






share|improve this answer









$endgroup$





















    2












    $begingroup$

    I think your plot is not quite correct, as the region should only extend to $x=2$ on the horizontal axis.



    Here's how to plot it using RegionPlot:



    RegionPlot[-1/2 + 3/2 x/Sqrt[x^2 + y^2] < Sqrt[x^2 + y^2] < 1/2 + 3/2 x/Sqrt[x^2 + y^2],
    {x, -1/2, 2}, {y, -5/4, 5/4}, PlotPoints -> 100]


    enter image description here



    The trick is to use $r=sqrt{x^2+y^2}$ and $cos(theta)=x/r$.






    share|improve this answer











    $endgroup$














      Your Answer








      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
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f197308%2fvisualizing-a-complicated-region%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      4












      $begingroup$

      We can construct such a region with CrossingPolygon and in this instance Polygon will work too.



      c = 1;
      pts = Table[v, {t, Subdivide[0., 2π, 200]}];
      pts[[-1]] = pts[[1]];

      Graphics[{EdgeForm[ColorData[97][1]], Opacity[.3], ColorData[97][2], Polygon[pts]}]




      CrossingCount[Polygon[pts], {0.5, 0}]



      2






      share|improve this answer









      $endgroup$


















        4












        $begingroup$

        We can construct such a region with CrossingPolygon and in this instance Polygon will work too.



        c = 1;
        pts = Table[v, {t, Subdivide[0., 2π, 200]}];
        pts[[-1]] = pts[[1]];

        Graphics[{EdgeForm[ColorData[97][1]], Opacity[.3], ColorData[97][2], Polygon[pts]}]




        CrossingCount[Polygon[pts], {0.5, 0}]



        2






        share|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          We can construct such a region with CrossingPolygon and in this instance Polygon will work too.



          c = 1;
          pts = Table[v, {t, Subdivide[0., 2π, 200]}];
          pts[[-1]] = pts[[1]];

          Graphics[{EdgeForm[ColorData[97][1]], Opacity[.3], ColorData[97][2], Polygon[pts]}]




          CrossingCount[Polygon[pts], {0.5, 0}]



          2






          share|improve this answer









          $endgroup$



          We can construct such a region with CrossingPolygon and in this instance Polygon will work too.



          c = 1;
          pts = Table[v, {t, Subdivide[0., 2π, 200]}];
          pts[[-1]] = pts[[1]];

          Graphics[{EdgeForm[ColorData[97][1]], Opacity[.3], ColorData[97][2], Polygon[pts]}]




          CrossingCount[Polygon[pts], {0.5, 0}]



          2







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 4 hours ago









          Chip HurstChip Hurst

          23.9k15995




          23.9k15995























              2












              $begingroup$

              I think your plot is not quite correct, as the region should only extend to $x=2$ on the horizontal axis.



              Here's how to plot it using RegionPlot:



              RegionPlot[-1/2 + 3/2 x/Sqrt[x^2 + y^2] < Sqrt[x^2 + y^2] < 1/2 + 3/2 x/Sqrt[x^2 + y^2],
              {x, -1/2, 2}, {y, -5/4, 5/4}, PlotPoints -> 100]


              enter image description here



              The trick is to use $r=sqrt{x^2+y^2}$ and $cos(theta)=x/r$.






              share|improve this answer











              $endgroup$


















                2












                $begingroup$

                I think your plot is not quite correct, as the region should only extend to $x=2$ on the horizontal axis.



                Here's how to plot it using RegionPlot:



                RegionPlot[-1/2 + 3/2 x/Sqrt[x^2 + y^2] < Sqrt[x^2 + y^2] < 1/2 + 3/2 x/Sqrt[x^2 + y^2],
                {x, -1/2, 2}, {y, -5/4, 5/4}, PlotPoints -> 100]


                enter image description here



                The trick is to use $r=sqrt{x^2+y^2}$ and $cos(theta)=x/r$.






                share|improve this answer











                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  I think your plot is not quite correct, as the region should only extend to $x=2$ on the horizontal axis.



                  Here's how to plot it using RegionPlot:



                  RegionPlot[-1/2 + 3/2 x/Sqrt[x^2 + y^2] < Sqrt[x^2 + y^2] < 1/2 + 3/2 x/Sqrt[x^2 + y^2],
                  {x, -1/2, 2}, {y, -5/4, 5/4}, PlotPoints -> 100]


                  enter image description here



                  The trick is to use $r=sqrt{x^2+y^2}$ and $cos(theta)=x/r$.






                  share|improve this answer











                  $endgroup$



                  I think your plot is not quite correct, as the region should only extend to $x=2$ on the horizontal axis.



                  Here's how to plot it using RegionPlot:



                  RegionPlot[-1/2 + 3/2 x/Sqrt[x^2 + y^2] < Sqrt[x^2 + y^2] < 1/2 + 3/2 x/Sqrt[x^2 + y^2],
                  {x, -1/2, 2}, {y, -5/4, 5/4}, PlotPoints -> 100]


                  enter image description here



                  The trick is to use $r=sqrt{x^2+y^2}$ and $cos(theta)=x/r$.







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 6 hours ago

























                  answered 6 hours ago









                  RomanRoman

                  6,58111134




                  6,58111134






























                      draft saved

                      draft discarded




















































                      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














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f197308%2fvisualizing-a-complicated-region%23new-answer', 'question_page');
                      }
                      );

                      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







                      Popular posts from this blog

                      El tren de la libertad Índice Antecedentes "Porque yo decido" Desarrollo de la...

                      Castillo d'Acher Características Menú de navegación

                      Connecting two nodes from the same mother node horizontallyTikZ: What EXACTLY does the the |- notation for...