Calculating list of areas between the curves in an intersection region












4












$begingroup$


I have 2 tables;



table 1:



ctr = {(Exp[Pi*0.5] + 1)/2, 0};
radius = (Exp[Pi*0.5] - 1)/2;
pp = PolarPlot[
Evaluate@Table[Exp[(t + 2*Pi*i/120)*0.5], {i, 1, 120}], {t, -Pi,
Pi}, RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
Total[ArcLength /@ Cases[pp, _Line, All]]


spiral



and table 2:



ctr = {(Exp[Pi*0.5] - 1)/2, 0};
radius = (Exp[Pi*0.5] - 1)/2;
pp2 = ParametricPlot[
Evaluate[Table[{t, t (Tan[2 j Pi / 120])}, {j, 1, 60}]], {t, -5, 5},
RegionFunction -> (Norm[{#, #2} - ctr] <= radius &),
PlotRange -> All]
Total[ArcLength /@ Cases[pp2, _Line, All]]


Line



I want to calculate each area between the curves and show them in histogram so I can evaluate maximum and minimum gaps between the tables. I illustrated what I want as below:



gradient



can you show me how?










share|improve this question









$endgroup$

















    4












    $begingroup$


    I have 2 tables;



    table 1:



    ctr = {(Exp[Pi*0.5] + 1)/2, 0};
    radius = (Exp[Pi*0.5] - 1)/2;
    pp = PolarPlot[
    Evaluate@Table[Exp[(t + 2*Pi*i/120)*0.5], {i, 1, 120}], {t, -Pi,
    Pi}, RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
    Total[ArcLength /@ Cases[pp, _Line, All]]


    spiral



    and table 2:



    ctr = {(Exp[Pi*0.5] - 1)/2, 0};
    radius = (Exp[Pi*0.5] - 1)/2;
    pp2 = ParametricPlot[
    Evaluate[Table[{t, t (Tan[2 j Pi / 120])}, {j, 1, 60}]], {t, -5, 5},
    RegionFunction -> (Norm[{#, #2} - ctr] <= radius &),
    PlotRange -> All]
    Total[ArcLength /@ Cases[pp2, _Line, All]]


    Line



    I want to calculate each area between the curves and show them in histogram so I can evaluate maximum and minimum gaps between the tables. I illustrated what I want as below:



    gradient



    can you show me how?










    share|improve this question









    $endgroup$















      4












      4








      4





      $begingroup$


      I have 2 tables;



      table 1:



      ctr = {(Exp[Pi*0.5] + 1)/2, 0};
      radius = (Exp[Pi*0.5] - 1)/2;
      pp = PolarPlot[
      Evaluate@Table[Exp[(t + 2*Pi*i/120)*0.5], {i, 1, 120}], {t, -Pi,
      Pi}, RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
      Total[ArcLength /@ Cases[pp, _Line, All]]


      spiral



      and table 2:



      ctr = {(Exp[Pi*0.5] - 1)/2, 0};
      radius = (Exp[Pi*0.5] - 1)/2;
      pp2 = ParametricPlot[
      Evaluate[Table[{t, t (Tan[2 j Pi / 120])}, {j, 1, 60}]], {t, -5, 5},
      RegionFunction -> (Norm[{#, #2} - ctr] <= radius &),
      PlotRange -> All]
      Total[ArcLength /@ Cases[pp2, _Line, All]]


      Line



      I want to calculate each area between the curves and show them in histogram so I can evaluate maximum and minimum gaps between the tables. I illustrated what I want as below:



      gradient



      can you show me how?










      share|improve this question









      $endgroup$




      I have 2 tables;



      table 1:



      ctr = {(Exp[Pi*0.5] + 1)/2, 0};
      radius = (Exp[Pi*0.5] - 1)/2;
      pp = PolarPlot[
      Evaluate@Table[Exp[(t + 2*Pi*i/120)*0.5], {i, 1, 120}], {t, -Pi,
      Pi}, RegionFunction -> (Norm[{#, #2} - ctr] <= radius &)]
      Total[ArcLength /@ Cases[pp, _Line, All]]


      spiral



      and table 2:



      ctr = {(Exp[Pi*0.5] - 1)/2, 0};
      radius = (Exp[Pi*0.5] - 1)/2;
      pp2 = ParametricPlot[
      Evaluate[Table[{t, t (Tan[2 j Pi / 120])}, {j, 1, 60}]], {t, -5, 5},
      RegionFunction -> (Norm[{#, #2} - ctr] <= radius &),
      PlotRange -> All]
      Total[ArcLength /@ Cases[pp2, _Line, All]]


      Line



      I want to calculate each area between the curves and show them in histogram so I can evaluate maximum and minimum gaps between the tables. I illustrated what I want as below:



      gradient



      can you show me how?







      regions intersection






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Feb 23 at 12:09









      Alper91Alper91

      1356




      1356






















          1 Answer
          1






          active

          oldest

          votes


















          6












          $begingroup$

          You could define a ParametricRegion , examplary between curves #10 and #11



          reg10 = ParametricRegion[{{Cos[t], Sin[t]} Exp[(t + 2*Pi*ii/120)/2], (Sqrt[#.#] < radius) &[{Cos[t],Sin[t]} Exp[(t + 2*Pi*ii/120)/2] - ctr]}
          , {{t, -Pi, Pi}, {ii, 10, 11}}]
          DiscretizeRegion[reg10]


          enter image description here



          Area[DiscretizeRegion[reg10]]
          (*0.0592725*)


          addendum



          Knowing the plot pp a very fast straightforward solution is possible:
          First get the Line-objects from the plot



          linien = Cases[pp, _Line , Infinity];


          Two neighboring lines form a polygon from which the area can be calculated



          areas=Table[ Area@Polygon[Join[linien[[i]][[1]], Reverse[linien[[i + 1]][[1]]]]], {i,1, Length[linien] - 1}] 
          (*{0.0243947, 0.0281509, 0.0318023, 0.0353948, 0.039143, 0.0430014,
          0.0469289, 0.050997, 0.0551564, 0.0594015, 0.0639209, 0.0684968,
          0.0731468, 0.0780328, 0.0830698, 0.0882845, 0.0936695, 0.0992263,
          0.104955, 0.111007, 0.117283, 0.123424, 0.129694, 0.136315, 0.143126,
          0.150108, 0.157259, 0.164582, 0.172953, 0.1806, 0.187462, 0.195366,
          0.203387, 0.21151, 0.22005, 0.228322, 0.23627, 0.24457, 0.252866,
          0.261078, 0.269163, 0.27711, 0.284845, 0.292302, 0.299405, 0.306072,
          0.312203, 0.317686, 0.322383, 0.326143, 0.329235, 0.330515, 0.329747,
          0.327478, 0.322887, 0.315273, 0.304139, 0.288177, 0.265912, 0.234501,
          0.187173}*)


          That's it! Hope it helps.






          share|improve this answer











          $endgroup$













          • $begingroup$
            Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
            $endgroup$
            – Alper91
            Feb 23 at 15:30










          • $begingroup$
            Put it in a Table[...,{i,1,119}]
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 17:57










          • $begingroup$
            @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 19:44










          • $begingroup$
            Thanks. It worked easily.
            $endgroup$
            – Alper91
            Feb 24 at 7:29











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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          6












          $begingroup$

          You could define a ParametricRegion , examplary between curves #10 and #11



          reg10 = ParametricRegion[{{Cos[t], Sin[t]} Exp[(t + 2*Pi*ii/120)/2], (Sqrt[#.#] < radius) &[{Cos[t],Sin[t]} Exp[(t + 2*Pi*ii/120)/2] - ctr]}
          , {{t, -Pi, Pi}, {ii, 10, 11}}]
          DiscretizeRegion[reg10]


          enter image description here



          Area[DiscretizeRegion[reg10]]
          (*0.0592725*)


          addendum



          Knowing the plot pp a very fast straightforward solution is possible:
          First get the Line-objects from the plot



          linien = Cases[pp, _Line , Infinity];


          Two neighboring lines form a polygon from which the area can be calculated



          areas=Table[ Area@Polygon[Join[linien[[i]][[1]], Reverse[linien[[i + 1]][[1]]]]], {i,1, Length[linien] - 1}] 
          (*{0.0243947, 0.0281509, 0.0318023, 0.0353948, 0.039143, 0.0430014,
          0.0469289, 0.050997, 0.0551564, 0.0594015, 0.0639209, 0.0684968,
          0.0731468, 0.0780328, 0.0830698, 0.0882845, 0.0936695, 0.0992263,
          0.104955, 0.111007, 0.117283, 0.123424, 0.129694, 0.136315, 0.143126,
          0.150108, 0.157259, 0.164582, 0.172953, 0.1806, 0.187462, 0.195366,
          0.203387, 0.21151, 0.22005, 0.228322, 0.23627, 0.24457, 0.252866,
          0.261078, 0.269163, 0.27711, 0.284845, 0.292302, 0.299405, 0.306072,
          0.312203, 0.317686, 0.322383, 0.326143, 0.329235, 0.330515, 0.329747,
          0.327478, 0.322887, 0.315273, 0.304139, 0.288177, 0.265912, 0.234501,
          0.187173}*)


          That's it! Hope it helps.






          share|improve this answer











          $endgroup$













          • $begingroup$
            Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
            $endgroup$
            – Alper91
            Feb 23 at 15:30










          • $begingroup$
            Put it in a Table[...,{i,1,119}]
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 17:57










          • $begingroup$
            @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 19:44










          • $begingroup$
            Thanks. It worked easily.
            $endgroup$
            – Alper91
            Feb 24 at 7:29
















          6












          $begingroup$

          You could define a ParametricRegion , examplary between curves #10 and #11



          reg10 = ParametricRegion[{{Cos[t], Sin[t]} Exp[(t + 2*Pi*ii/120)/2], (Sqrt[#.#] < radius) &[{Cos[t],Sin[t]} Exp[(t + 2*Pi*ii/120)/2] - ctr]}
          , {{t, -Pi, Pi}, {ii, 10, 11}}]
          DiscretizeRegion[reg10]


          enter image description here



          Area[DiscretizeRegion[reg10]]
          (*0.0592725*)


          addendum



          Knowing the plot pp a very fast straightforward solution is possible:
          First get the Line-objects from the plot



          linien = Cases[pp, _Line , Infinity];


          Two neighboring lines form a polygon from which the area can be calculated



          areas=Table[ Area@Polygon[Join[linien[[i]][[1]], Reverse[linien[[i + 1]][[1]]]]], {i,1, Length[linien] - 1}] 
          (*{0.0243947, 0.0281509, 0.0318023, 0.0353948, 0.039143, 0.0430014,
          0.0469289, 0.050997, 0.0551564, 0.0594015, 0.0639209, 0.0684968,
          0.0731468, 0.0780328, 0.0830698, 0.0882845, 0.0936695, 0.0992263,
          0.104955, 0.111007, 0.117283, 0.123424, 0.129694, 0.136315, 0.143126,
          0.150108, 0.157259, 0.164582, 0.172953, 0.1806, 0.187462, 0.195366,
          0.203387, 0.21151, 0.22005, 0.228322, 0.23627, 0.24457, 0.252866,
          0.261078, 0.269163, 0.27711, 0.284845, 0.292302, 0.299405, 0.306072,
          0.312203, 0.317686, 0.322383, 0.326143, 0.329235, 0.330515, 0.329747,
          0.327478, 0.322887, 0.315273, 0.304139, 0.288177, 0.265912, 0.234501,
          0.187173}*)


          That's it! Hope it helps.






          share|improve this answer











          $endgroup$













          • $begingroup$
            Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
            $endgroup$
            – Alper91
            Feb 23 at 15:30










          • $begingroup$
            Put it in a Table[...,{i,1,119}]
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 17:57










          • $begingroup$
            @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 19:44










          • $begingroup$
            Thanks. It worked easily.
            $endgroup$
            – Alper91
            Feb 24 at 7:29














          6












          6








          6





          $begingroup$

          You could define a ParametricRegion , examplary between curves #10 and #11



          reg10 = ParametricRegion[{{Cos[t], Sin[t]} Exp[(t + 2*Pi*ii/120)/2], (Sqrt[#.#] < radius) &[{Cos[t],Sin[t]} Exp[(t + 2*Pi*ii/120)/2] - ctr]}
          , {{t, -Pi, Pi}, {ii, 10, 11}}]
          DiscretizeRegion[reg10]


          enter image description here



          Area[DiscretizeRegion[reg10]]
          (*0.0592725*)


          addendum



          Knowing the plot pp a very fast straightforward solution is possible:
          First get the Line-objects from the plot



          linien = Cases[pp, _Line , Infinity];


          Two neighboring lines form a polygon from which the area can be calculated



          areas=Table[ Area@Polygon[Join[linien[[i]][[1]], Reverse[linien[[i + 1]][[1]]]]], {i,1, Length[linien] - 1}] 
          (*{0.0243947, 0.0281509, 0.0318023, 0.0353948, 0.039143, 0.0430014,
          0.0469289, 0.050997, 0.0551564, 0.0594015, 0.0639209, 0.0684968,
          0.0731468, 0.0780328, 0.0830698, 0.0882845, 0.0936695, 0.0992263,
          0.104955, 0.111007, 0.117283, 0.123424, 0.129694, 0.136315, 0.143126,
          0.150108, 0.157259, 0.164582, 0.172953, 0.1806, 0.187462, 0.195366,
          0.203387, 0.21151, 0.22005, 0.228322, 0.23627, 0.24457, 0.252866,
          0.261078, 0.269163, 0.27711, 0.284845, 0.292302, 0.299405, 0.306072,
          0.312203, 0.317686, 0.322383, 0.326143, 0.329235, 0.330515, 0.329747,
          0.327478, 0.322887, 0.315273, 0.304139, 0.288177, 0.265912, 0.234501,
          0.187173}*)


          That's it! Hope it helps.






          share|improve this answer











          $endgroup$



          You could define a ParametricRegion , examplary between curves #10 and #11



          reg10 = ParametricRegion[{{Cos[t], Sin[t]} Exp[(t + 2*Pi*ii/120)/2], (Sqrt[#.#] < radius) &[{Cos[t],Sin[t]} Exp[(t + 2*Pi*ii/120)/2] - ctr]}
          , {{t, -Pi, Pi}, {ii, 10, 11}}]
          DiscretizeRegion[reg10]


          enter image description here



          Area[DiscretizeRegion[reg10]]
          (*0.0592725*)


          addendum



          Knowing the plot pp a very fast straightforward solution is possible:
          First get the Line-objects from the plot



          linien = Cases[pp, _Line , Infinity];


          Two neighboring lines form a polygon from which the area can be calculated



          areas=Table[ Area@Polygon[Join[linien[[i]][[1]], Reverse[linien[[i + 1]][[1]]]]], {i,1, Length[linien] - 1}] 
          (*{0.0243947, 0.0281509, 0.0318023, 0.0353948, 0.039143, 0.0430014,
          0.0469289, 0.050997, 0.0551564, 0.0594015, 0.0639209, 0.0684968,
          0.0731468, 0.0780328, 0.0830698, 0.0882845, 0.0936695, 0.0992263,
          0.104955, 0.111007, 0.117283, 0.123424, 0.129694, 0.136315, 0.143126,
          0.150108, 0.157259, 0.164582, 0.172953, 0.1806, 0.187462, 0.195366,
          0.203387, 0.21151, 0.22005, 0.228322, 0.23627, 0.24457, 0.252866,
          0.261078, 0.269163, 0.27711, 0.284845, 0.292302, 0.299405, 0.306072,
          0.312203, 0.317686, 0.322383, 0.326143, 0.329235, 0.330515, 0.329747,
          0.327478, 0.322887, 0.315273, 0.304139, 0.288177, 0.265912, 0.234501,
          0.187173}*)


          That's it! Hope it helps.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Feb 23 at 19:42

























          answered Feb 23 at 14:21









          Ulrich NeumannUlrich Neumann

          9,613617




          9,613617












          • $begingroup$
            Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
            $endgroup$
            – Alper91
            Feb 23 at 15:30










          • $begingroup$
            Put it in a Table[...,{i,1,119}]
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 17:57










          • $begingroup$
            @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 19:44










          • $begingroup$
            Thanks. It worked easily.
            $endgroup$
            – Alper91
            Feb 24 at 7:29


















          • $begingroup$
            Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
            $endgroup$
            – Alper91
            Feb 23 at 15:30










          • $begingroup$
            Put it in a Table[...,{i,1,119}]
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 17:57










          • $begingroup$
            @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
            $endgroup$
            – Ulrich Neumann
            Feb 23 at 19:44










          • $begingroup$
            Thanks. It worked easily.
            $endgroup$
            – Alper91
            Feb 24 at 7:29
















          $begingroup$
          Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
          $endgroup$
          – Alper91
          Feb 23 at 15:30




          $begingroup$
          Thank you very much! However, how could I store each of the ares into a table so I can show the histogram could you help me with that as well?
          $endgroup$
          – Alper91
          Feb 23 at 15:30












          $begingroup$
          Put it in a Table[...,{i,1,119}]
          $endgroup$
          – Ulrich Neumann
          Feb 23 at 17:57




          $begingroup$
          Put it in a Table[...,{i,1,119}]
          $endgroup$
          – Ulrich Neumann
          Feb 23 at 17:57












          $begingroup$
          @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
          $endgroup$
          – Ulrich Neumann
          Feb 23 at 19:44




          $begingroup$
          @ Alper91 Look at the edit of my answer, I added a solution which only needs to know pp
          $endgroup$
          – Ulrich Neumann
          Feb 23 at 19:44












          $begingroup$
          Thanks. It worked easily.
          $endgroup$
          – Alper91
          Feb 24 at 7:29




          $begingroup$
          Thanks. It worked easily.
          $endgroup$
          – Alper91
          Feb 24 at 7:29


















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