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Calculating list of areas between the curves in an intersection region

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Calculating list of areas between the curves in an intersection region

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2

$begingroup$

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]]

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]]

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:

can you show me how?

regions intersection

share|improve this question

asked 2 hours ago

Alper91Alper91

1235

$endgroup$

add a comment | 

2

$begingroup$

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]]

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]]

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:

can you show me how?

regions intersection

share|improve this question

asked 2 hours ago

Alper91Alper91

1235

$endgroup$

add a comment | 

$begingroup$

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]]

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]]

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:

can you show me how?

regions intersection

share|improve this question

asked 2 hours ago

Alper91Alper91

1235

$endgroup$

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]]

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]]

share|improve this question

asked 2 hours ago

Alper91Alper91

1235

share|improve this question

asked 2 hours ago

Alper91Alper91

1235

asked 2 hours ago

Alper91Alper91

1235

asked 2 hours ago

Alper91Alper91

1235

1 Answer
1

active

oldest

votes

3

$begingroup$

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]

Area[DiscretizeRegion[reg10]]

(*0.0592725*)

share|improve this answer

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516

$endgroup$

add a comment | 

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3

$begingroup$

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]

Area[DiscretizeRegion[reg10]]

(*0.0592725*)

share|improve this answer

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516

$endgroup$

add a comment | 

3

$begingroup$

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]

Area[DiscretizeRegion[reg10]]

(*0.0592725*)

share|improve this answer

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516

$endgroup$

add a comment | 

$begingroup$

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]

Area[DiscretizeRegion[reg10]]

(*0.0592725*)

share|improve this answer

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516

$endgroup$

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]

Area[DiscretizeRegion[reg10]]

(*0.0592725*)

share|improve this answer

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516

answered 43 mins ago

Ulrich NeumannUlrich Neumann

8,956516