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pgfplots: How to draw a tangent graph below two others?

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7

2

Assumed I want to draw three simple graphs based on the following illustration:

---

How can I plot those three graphs? I've tried to create something like this:

Minimum Working Example (MWE):

documentclassstandalone
usepackagepgfplots

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 endaxis
 endtikzpicture
enddocument

---

Screenshot of the current state:

---

Description of the issue:

However, I don't get the point on how to figure out the function of the third graph as well as how to clip the graphs in x and y direction to align them centered in the plot. It is not necessary to be completely precise, the accuracy of my upper template will be fine enough.

How to do that?

tikz-pgf pgfplots plot graphs polynomials

share|improve this question

edited 2 days ago

Dave

asked 2 days ago

DaveDave

1,185619

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  
  @close-voter: Please explain in a comment your reason for voting to close!
  
  – Kurt
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I accept the Kurt's comment.
  
  – Sebastiano
  2 days ago
  

  
  
  
  

add a comment | 

7

2

Assumed I want to draw three simple graphs based on the following illustration:

---

How can I plot those three graphs? I've tried to create something like this:

Minimum Working Example (MWE):

documentclassstandalone
usepackagepgfplots

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 endaxis
 endtikzpicture
enddocument

---

Screenshot of the current state:

---

Description of the issue:

However, I don't get the point on how to figure out the function of the third graph as well as how to clip the graphs in x and y direction to align them centered in the plot. It is not necessary to be completely precise, the accuracy of my upper template will be fine enough.

How to do that?

tikz-pgf pgfplots plot graphs polynomials

share|improve this question

edited 2 days ago

Dave

asked 2 days ago

DaveDave

1,185619

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  
  @close-voter: Please explain in a comment your reason for voting to close!
  
  – Kurt
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  I accept the Kurt's comment.
  
  – Sebastiano
  2 days ago
  

  
  
  
  

add a comment | 

Assumed I want to draw three simple graphs based on the following illustration:

---

How can I plot those three graphs? I've tried to create something like this:

Minimum Working Example (MWE):

documentclassstandalone
usepackagepgfplots

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 endaxis
 endtikzpicture
enddocument

---

Screenshot of the current state:

---

Description of the issue:

However, I don't get the point on how to figure out the function of the third graph as well as how to clip the graphs in x and y direction to align them centered in the plot. It is not necessary to be completely precise, the accuracy of my upper template will be fine enough.

How to do that?

tikz-pgf pgfplots plot graphs polynomials

share|improve this question

edited 2 days ago

Dave

asked 2 days ago

DaveDave

1,185619

documentclassstandalone
usepackagepgfplots

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 endaxis
 endtikzpicture
enddocument

share|improve this question

edited 2 days ago

Dave

asked 2 days ago

DaveDave

1,185619

share|improve this question

edited 2 days ago

Dave

asked 2 days ago

DaveDave

1,185619

asked 2 days ago

DaveDave

1,185619

asked 2 days ago

DaveDave

1,185619

2 Answers
2

active

oldest

votes

9

You can use the function f1*f2/(f1+f2) to get something like what you describe. To make the code a bit clearer I defined the functions f1 and f2.

documentclassstandalone
usepackagepgfplots
pgfplotsset%
 compat=1.12,
 /pgf/declare function=f1(x)=exp(3*x);,
 /pgf/declare function=f2(x)=-exp(3*x)+20;,

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] f1(x);
 addplot+[no marks, samples=100] f2(x);
 addplot+[no marks, samples=100] f1(x)*f2(x)/(f1(x)+f2(x));
 endaxis
 endtikzpicture
enddocument

If you want the function to follow more closely you can use sqrt(f1^2*f2^2/(f1^2+f2^2). Then replace the third plot with

addplot+[no marks, samples=100] sqrt(f1(x)*f1(x)*f2(x)*f2(x)/(f1(x)*f1(x)+f2(x)*f2(x)));

to get

Slightly more general, one can use the exponent a (does not have to be an integer):

 foreach a in 1,...,5
 addplot+[no marks, samples=100] (f1(x)^a*f2(x)^a/(f1(x)^a+f2(x)^a))^(1/a);
 

share|improve this answer

edited yesterday

answered 2 days ago

StefanHStefanH

10.9k1920

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  The lower one looks perfect, thank you very much!!
  
  – Dave
  2 days ago
  

  
  
  
  

add a comment | 

5

Are you looking for the minimum? (I shifted the plot a bit but you can of course undo the shift.)

documentclass[border=3.14mm,tikz]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 addplot+[no marks, samples=6,smooth]
 min(exp(3*x),(-exp(3*x)+20))-pi/2;
 endaxis
 endtikzpicture
enddocument

share|improve this answer

answered 2 days ago

marmotmarmot

114k5145276

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you very much marmot! The user StefanH has also posted a great approach which looks very smooth - I hope you are not disappointed if I choose his option as an answer?
  
  – Dave
  2 days ago
  
  

  
  
  
  

add a comment | 

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9

You can use the function f1*f2/(f1+f2) to get something like what you describe. To make the code a bit clearer I defined the functions f1 and f2.

documentclassstandalone
usepackagepgfplots
pgfplotsset%
 compat=1.12,
 /pgf/declare function=f1(x)=exp(3*x);,
 /pgf/declare function=f2(x)=-exp(3*x)+20;,

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] f1(x);
 addplot+[no marks, samples=100] f2(x);
 addplot+[no marks, samples=100] f1(x)*f2(x)/(f1(x)+f2(x));
 endaxis
 endtikzpicture
enddocument

If you want the function to follow more closely you can use sqrt(f1^2*f2^2/(f1^2+f2^2). Then replace the third plot with

addplot+[no marks, samples=100] sqrt(f1(x)*f1(x)*f2(x)*f2(x)/(f1(x)*f1(x)+f2(x)*f2(x)));

to get

Slightly more general, one can use the exponent a (does not have to be an integer):

 foreach a in 1,...,5
 addplot+[no marks, samples=100] (f1(x)^a*f2(x)^a/(f1(x)^a+f2(x)^a))^(1/a);
 

share|improve this answer

edited yesterday

answered 2 days ago

StefanHStefanH

10.9k1920

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  The lower one looks perfect, thank you very much!!
  
  – Dave
  2 days ago
  

  
  
  
  

add a comment | 

9

You can use the function f1*f2/(f1+f2) to get something like what you describe. To make the code a bit clearer I defined the functions f1 and f2.

documentclassstandalone
usepackagepgfplots
pgfplotsset%
 compat=1.12,
 /pgf/declare function=f1(x)=exp(3*x);,
 /pgf/declare function=f2(x)=-exp(3*x)+20;,

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] f1(x);
 addplot+[no marks, samples=100] f2(x);
 addplot+[no marks, samples=100] f1(x)*f2(x)/(f1(x)+f2(x));
 endaxis
 endtikzpicture
enddocument

If you want the function to follow more closely you can use sqrt(f1^2*f2^2/(f1^2+f2^2). Then replace the third plot with

addplot+[no marks, samples=100] sqrt(f1(x)*f1(x)*f2(x)*f2(x)/(f1(x)*f1(x)+f2(x)*f2(x)));

to get

Slightly more general, one can use the exponent a (does not have to be an integer):

 foreach a in 1,...,5
 addplot+[no marks, samples=100] (f1(x)^a*f2(x)^a/(f1(x)^a+f2(x)^a))^(1/a);
 

share|improve this answer

edited yesterday

answered 2 days ago

StefanHStefanH

10.9k1920

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  The lower one looks perfect, thank you very much!!
  
  – Dave
  2 days ago
  

  
  
  
  

add a comment | 

You can use the function f1*f2/(f1+f2) to get something like what you describe. To make the code a bit clearer I defined the functions f1 and f2.

documentclassstandalone
usepackagepgfplots
pgfplotsset%
 compat=1.12,
 /pgf/declare function=f1(x)=exp(3*x);,
 /pgf/declare function=f2(x)=-exp(3*x)+20;,

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] f1(x);
 addplot+[no marks, samples=100] f2(x);
 addplot+[no marks, samples=100] f1(x)*f2(x)/(f1(x)+f2(x));
 endaxis
 endtikzpicture
enddocument

If you want the function to follow more closely you can use sqrt(f1^2*f2^2/(f1^2+f2^2). Then replace the third plot with

addplot+[no marks, samples=100] sqrt(f1(x)*f1(x)*f2(x)*f2(x)/(f1(x)*f1(x)+f2(x)*f2(x)));

to get

Slightly more general, one can use the exponent a (does not have to be an integer):

 foreach a in 1,...,5
 addplot+[no marks, samples=100] (f1(x)^a*f2(x)^a/(f1(x)^a+f2(x)^a))^(1/a);
 

share|improve this answer

edited yesterday

answered 2 days ago

StefanHStefanH

10.9k1920

documentclassstandalone
usepackagepgfplots
pgfplotsset%
 compat=1.12,
 /pgf/declare function=f1(x)=exp(3*x);,
 /pgf/declare function=f2(x)=-exp(3*x)+20;,

begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] f1(x);
 addplot+[no marks, samples=100] f2(x);
 addplot+[no marks, samples=100] f1(x)*f2(x)/(f1(x)+f2(x));
 endaxis
 endtikzpicture
enddocument

addplot+[no marks, samples=100] sqrt(f1(x)*f1(x)*f2(x)*f2(x)/(f1(x)*f1(x)+f2(x)*f2(x)));

 foreach a in 1,...,5
 addplot+[no marks, samples=100] (f1(x)^a*f2(x)^a/(f1(x)^a+f2(x)^a))^(1/a);
 

share|improve this answer

edited yesterday

answered 2 days ago

StefanHStefanH

10.9k1920

answered 2 days ago

StefanHStefanH

10.9k1920

answered 2 days ago

StefanHStefanH

10.9k1920

5

Are you looking for the minimum? (I shifted the plot a bit but you can of course undo the shift.)

documentclass[border=3.14mm,tikz]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 addplot+[no marks, samples=6,smooth]
 min(exp(3*x),(-exp(3*x)+20))-pi/2;
 endaxis
 endtikzpicture
enddocument

share|improve this answer

answered 2 days ago

marmotmarmot

114k5145276

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you very much marmot! The user StefanH has also posted a great approach which looks very smooth - I hope you are not disappointed if I choose his option as an answer?
  
  – Dave
  2 days ago
  
  

  
  
  
  

add a comment | 

5

Are you looking for the minimum? (I shifted the plot a bit but you can of course undo the shift.)

documentclass[border=3.14mm,tikz]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 addplot+[no marks, samples=6,smooth]
 min(exp(3*x),(-exp(3*x)+20))-pi/2;
 endaxis
 endtikzpicture
enddocument

share|improve this answer

answered 2 days ago

marmotmarmot

114k5145276

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you very much marmot! The user StefanH has also posted a great approach which looks very smooth - I hope you are not disappointed if I choose his option as an answer?
  
  – Dave
  2 days ago
  
  

  
  
  
  

add a comment | 

Are you looking for the minimum? (I shifted the plot a bit but you can of course undo the shift.)

documentclass[border=3.14mm,tikz]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 addplot+[no marks, samples=6,smooth]
 min(exp(3*x),(-exp(3*x)+20))-pi/2;
 endaxis
 endtikzpicture
enddocument

share|improve this answer

answered 2 days ago

marmotmarmot

114k5145276

documentclass[border=3.14mm,tikz]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
begindocument
 begintikzpicture
 beginaxis[domain=0:1]
 addplot+[no marks, samples=100] exp(3*x);
 addplot+[no marks, samples=100] (-exp(3*x)+20);
 addplot+[no marks, samples=6,smooth]
 min(exp(3*x),(-exp(3*x)+20))-pi/2;
 endaxis
 endtikzpicture
enddocument

share|improve this answer

answered 2 days ago

marmotmarmot

114k5145276

answered 2 days ago

marmotmarmot

114k5145276

answered 2 days ago

marmotmarmot

114k5145276