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Use ContourPlot data in ParametricPlot

ContourPlot from Vector DataContourPlot with parameterUsing Show to place a ParametricPlot on a LogLog scaleScale coloring of ContourPlotContourPlot gives wrong outputLogLogPLot with two left&right axesHow to set the region of variable in the ParametricPlot?ParametricPlot not plotting resultsParametricPlot with more than two parametersParametricPlot table of complex functions in several graphs

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3

$begingroup$

Let me give an example,

probe1 = ContourPlot[10 == x + y, x, 0, 10, y, 0, 10, Frame -> True, FrameLabel -> "x", "y"]

This plots 10=f[x,y]=x+y, for a set of point (x,y) that solved the equality. Moreover,

probe2 = ParametricPlot[x y, x^2 + y^2, x, 0, 10, y, 0, 10]

where g=g[x,y]=xy and h=h[x,y]=x^2+y^2, plots h=h[g[x,y]]. What I want is to plot only the case in which x+y=10. What should I do?

plotting parametric-functions

share|improve this question

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  How about a parametric region Region[ParametricRegion[x y, x^2 + y^2, x + y == 10, x, 0, 10, y, 0, 10], Frame -> True]
  $endgroup$
  – Simon Woods
  7 hours ago
  

  
  
  
  

add a comment | 

3

$begingroup$

Let me give an example,

probe1 = ContourPlot[10 == x + y, x, 0, 10, y, 0, 10, Frame -> True, FrameLabel -> "x", "y"]

This plots 10=f[x,y]=x+y, for a set of point (x,y) that solved the equality. Moreover,

probe2 = ParametricPlot[x y, x^2 + y^2, x, 0, 10, y, 0, 10]

where g=g[x,y]=xy and h=h[x,y]=x^2+y^2, plots h=h[g[x,y]]. What I want is to plot only the case in which x+y=10. What should I do?

plotting parametric-functions

share|improve this question

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  How about a parametric region Region[ParametricRegion[x y, x^2 + y^2, x + y == 10, x, 0, 10, y, 0, 10], Frame -> True]
  $endgroup$
  – Simon Woods
  7 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Let me give an example,

probe1 = ContourPlot[10 == x + y, x, 0, 10, y, 0, 10, Frame -> True, FrameLabel -> "x", "y"]

This plots 10=f[x,y]=x+y, for a set of point (x,y) that solved the equality. Moreover,

probe2 = ParametricPlot[x y, x^2 + y^2, x, 0, 10, y, 0, 10]

where g=g[x,y]=xy and h=h[x,y]=x^2+y^2, plots h=h[g[x,y]]. What I want is to plot only the case in which x+y=10. What should I do?

plotting parametric-functions

share|improve this question

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

$endgroup$

probe1 = ContourPlot[10 == x + y, x, 0, 10, y, 0, 10, Frame -> True, FrameLabel -> "x", "y"]

probe2 = ParametricPlot[x y, x^2 + y^2, x, 0, 10, y, 0, 10]

share|improve this question

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

share|improve this question

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

asked 9 hours ago

Patrick El PolloPatrick El Pollo

1961010 bronze badges

2 Answers
2

active

oldest

votes

3

$begingroup$

You can use the argument of ContourPlot as the MeshFunctions option value in ParametricPlot as follows:

ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, 
 MeshFunctions -> Function[x, y, u, t, u + t - 10], 
 Mesh -> 0, 
 MeshStyle -> Directive[Red, Thick]]

share|improve this answer

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It worked. Thanks. Do you have a sugestion to include in the same ParametricPlot several cases of the condition, for example u+v-2 and u+v-5, etc? What should I change in your solution?
  $endgroup$
  – Patrick El Pollo
  16 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PatrickElPollo, try ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, MeshFunctions -> Function[x, y, u, t, u + t], Mesh -> 9, Directive[Red, Opacity[1], Thick], 10, Directive[Green, Opacity[1], Thick], 12, Directive[Black, Opacity[1], Thick]]
  $endgroup$
  – kglr
  3 mins ago
  

  
  
  
  

add a comment | 

1

$begingroup$

This may be what you want

Clear["Global`*"]

eqn = 10 == x + y;

ysol[x_] = y /. Solve[eqn, y][[1]]

(* 10 - x *)

Show[
 ParametricPlot[
 x y, x^2 + y^2,
 x, 0, 10, y, 0, 10],
 ParametricPlot[
 Evaluate[x y, x^2 + y^2 /. y -> ysol[x]],
 x, 0, 10,
 PlotStyle -> Red]]

share|improve this answer

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  it works, but what I want is a way to extract the pairs from ContourPlot when Solve does not work to use them as parameters in ParametricPlot.
  $endgroup$
  – Patrick El Pollo
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PatrickElPollo - have you tried using a numeric solver such as NSolve or FindRoot?
  $endgroup$
  – Bob Hanlon
  4 hours ago
  

  
  
  
  

add a comment | 

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3

$begingroup$

You can use the argument of ContourPlot as the MeshFunctions option value in ParametricPlot as follows:

ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, 
 MeshFunctions -> Function[x, y, u, t, u + t - 10], 
 Mesh -> 0, 
 MeshStyle -> Directive[Red, Thick]]

share|improve this answer

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It worked. Thanks. Do you have a sugestion to include in the same ParametricPlot several cases of the condition, for example u+v-2 and u+v-5, etc? What should I change in your solution?
  $endgroup$
  – Patrick El Pollo
  16 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PatrickElPollo, try ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, MeshFunctions -> Function[x, y, u, t, u + t], Mesh -> 9, Directive[Red, Opacity[1], Thick], 10, Directive[Green, Opacity[1], Thick], 12, Directive[Black, Opacity[1], Thick]]
  $endgroup$
  – kglr
  3 mins ago
  

  
  
  
  

add a comment | 

3

$begingroup$

You can use the argument of ContourPlot as the MeshFunctions option value in ParametricPlot as follows:

ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, 
 MeshFunctions -> Function[x, y, u, t, u + t - 10], 
 Mesh -> 0, 
 MeshStyle -> Directive[Red, Thick]]

share|improve this answer

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It worked. Thanks. Do you have a sugestion to include in the same ParametricPlot several cases of the condition, for example u+v-2 and u+v-5, etc? What should I change in your solution?
  $endgroup$
  – Patrick El Pollo
  16 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PatrickElPollo, try ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, MeshFunctions -> Function[x, y, u, t, u + t], Mesh -> 9, Directive[Red, Opacity[1], Thick], 10, Directive[Green, Opacity[1], Thick], 12, Directive[Black, Opacity[1], Thick]]
  $endgroup$
  – kglr
  3 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

You can use the argument of ContourPlot as the MeshFunctions option value in ParametricPlot as follows:

ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, 
 MeshFunctions -> Function[x, y, u, t, u + t - 10], 
 Mesh -> 0, 
 MeshStyle -> Directive[Red, Thick]]

share|improve this answer

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

$endgroup$

ParametricPlot[u t, u^2 + t^2, u, 0, 10, t, 0, 10, 
 MeshFunctions -> Function[x, y, u, t, u + t - 10], 
 Mesh -> 0, 
 MeshStyle -> Directive[Red, Thick]]

share|improve this answer

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

answered 3 hours ago

kglrkglr

203k1010 gold badges232232 silver badges462462 bronze badges

1

$begingroup$

This may be what you want

Clear["Global`*"]

eqn = 10 == x + y;

ysol[x_] = y /. Solve[eqn, y][[1]]

(* 10 - x *)

Show[
 ParametricPlot[
 x y, x^2 + y^2,
 x, 0, 10, y, 0, 10],
 ParametricPlot[
 Evaluate[x y, x^2 + y^2 /. y -> ysol[x]],
 x, 0, 10,
 PlotStyle -> Red]]

share|improve this answer

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  it works, but what I want is a way to extract the pairs from ContourPlot when Solve does not work to use them as parameters in ParametricPlot.
  $endgroup$
  – Patrick El Pollo
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PatrickElPollo - have you tried using a numeric solver such as NSolve or FindRoot?
  $endgroup$
  – Bob Hanlon
  4 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

This may be what you want

Clear["Global`*"]

eqn = 10 == x + y;

ysol[x_] = y /. Solve[eqn, y][[1]]

(* 10 - x *)

Show[
 ParametricPlot[
 x y, x^2 + y^2,
 x, 0, 10, y, 0, 10],
 ParametricPlot[
 Evaluate[x y, x^2 + y^2 /. y -> ysol[x]],
 x, 0, 10,
 PlotStyle -> Red]]

share|improve this answer

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  it works, but what I want is a way to extract the pairs from ContourPlot when Solve does not work to use them as parameters in ParametricPlot.
  $endgroup$
  – Patrick El Pollo
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PatrickElPollo - have you tried using a numeric solver such as NSolve or FindRoot?
  $endgroup$
  – Bob Hanlon
  4 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

This may be what you want

Clear["Global`*"]

eqn = 10 == x + y;

ysol[x_] = y /. Solve[eqn, y][[1]]

(* 10 - x *)

Show[
 ParametricPlot[
 x y, x^2 + y^2,
 x, 0, 10, y, 0, 10],
 ParametricPlot[
 Evaluate[x y, x^2 + y^2 /. y -> ysol[x]],
 x, 0, 10,
 PlotStyle -> Red]]

share|improve this answer

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges

$endgroup$

Clear["Global`*"]

eqn = 10 == x + y;

ysol[x_] = y /. Solve[eqn, y][[1]]

(* 10 - x *)

Show[
 ParametricPlot[
 x y, x^2 + y^2,
 x, 0, 10, y, 0, 10],
 ParametricPlot[
 Evaluate[x y, x^2 + y^2 /. y -> ysol[x]],
 x, 0, 10,
 PlotStyle -> Red]]

share|improve this answer

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges

answered 9 hours ago

Bob HanlonBob Hanlon

63.4k33 gold badges3636 silver badges9999 bronze badges