Revisions to How to rescale the axis on a graph to make it more readable

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edited Jul 30, 2017 at 15:21

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Controlling tick marks

Here is a way to "manually" generate a specification for Ticks or FrameTicks.

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cp, Line[x_] :> x, -3];

log = logTheta[2] /@ pts;

ticks = {#, inverse[2][#]} & /@ FindDivisions[#, 11] & /@ CoordinateBounds[log];

ListLinePlot[log, Ticks -> ticks, AspectRatio -> 1]

And for the additional example:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

Table[
  log = logTheta[b] /@ pts2;
  ticks = {#, inverse[b][#]} & /@ FindDivisions[#, 11] & /@ CoordinateBounds[log];
  ListLinePlot[log, Ticks -> ticks, AspectRatio -> 1, ImageSize -> 200],
  {b, {2, 3, 4}}
] // Row

Controlling tick marks

Here is a way to "manually" generate a specification for Ticks or FrameTicks.

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cp, Line[x_] :> x, -3];

log = logTheta[2] /@ pts;

ticks = {#, inverse[2][#]} & /@ FindDivisions[#, 11] & /@ CoordinateBounds[log];

ListLinePlot[log, Ticks -> ticks, AspectRatio -> 1]

And for the additional example:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

Table[
  log = logTheta[b] /@ pts2;
  ticks = {#, inverse[b][#]} & /@ FindDivisions[#, 11] & /@ CoordinateBounds[log];
  ListLinePlot[log, Ticks -> ticks, AspectRatio -> 1, ImageSize -> 200],
  {b, {2, 3, 4}}
] // Row

deleted 363 characters in body

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edited Jul 30, 2017 at 5:33

Mr.Wizard

273.1k
34
595
1.4k

At least in v10.1 ContourPlot doesn't supportRevising this answer I propose extracting contours from ScalingFunctionsContourPlot, but ListLinePlot doesconverting to polar, unofficiallyscaling magnitude, then converting back and plotting. Therefore this might be of some I will use.

Using logscale code from ListLogLinearPlot for the whole real numbers :

logify[_][x_ /; x == 0] := 0
logify[off_][x_] := Sign[x] Max[0, (off + Re@Log@x)/off]

inverse[off_][x_] := Sign[x] Exp[(Abs[x] - 1) off]

logscale[n_] := {logify[n], inverse[n]}

And an auxiliary function:

logTheta[m_][pts_] :=
(* additional definitionFromPolarCoordinates *)/@ 
logscale[n_, m_] := logscale MapAt[logify[m], ToPolarCoordinates /@ pts, {nAll, m1}];

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cpCases[Normal @ cp, Line[x_] :> x, -3];

ListLinePlot[pts,ListLinePlot[logTheta[2] ScalingFunctions/@ ->pts
 logscale[2, 2], AspectRatioTicks -> 1]

You can change the numeric parameters in logscale to get different effects; see the linked post for further examples.

Working in polar coordinates makes things look nicer, but I lose automatic tick generation so I have to turn them off:

newpts = FromPolarCoordinatesCharting`ScaledTicks /@ logscale[2]
  MapAt[logify[2], ToPolarCoordinates /@ pts, {All, All, 1}];

ListLinePlot[newpts, Ticks -> None, AspectRatio -> 1]1
]

The ticks could be calculated with inverse[2] but I don't have timeAn additional example to complete that now.

Additional examples of each methodbetter illustrate variable "zoom" in the scaling:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

ListLinePlot[pts2, ScalingFunctionsListLinePlot[logTheta[#] ->/@ logscale[3,pts2
 3], AspectRatioTicks -> 1]

newpts2 = FromPolarCoordinatesCharting`ScaledTicks /@ logscale[#]
 , AspectRatio MapAt[logify[3],-> ToPolarCoordinates1
] & /@ pts2, {All2, All3, 14}];

ListLinePlot[newpts2, Ticks -> None, AspectRatio

Beware: if the "zoom" is not enough you'll create singularities in the polar/Cartesian conversion and get errors instead of a plot:

logTheta[1] ->/@ Automatic]pts2;

FromPolarCoordinates::bdpt: Evaluation point {0,1.92728} is not a valid set of polar or hyperspherical coordinates. >>

I expect this will be a problem if you have contours that cross the origin, but I will have to come back to that later.

At least in v10.1 ContourPlot doesn't support ScalingFunctions, but ListLinePlot does, unofficially. Therefore this might be of some use.

Using logscale from ListLogLinearPlot for the whole real numbers :

logify[_][x_ /; x == 0] := 0
logify[off_][x_] := Sign[x] Max[0, (off + Re@Log@x)/off]

inverse[off_][x_] := Sign[x] Exp[(Abs[x] - 1) off]

logscale[n_] := {logify[n], inverse[n]}

(* additional definition *)
logscale[n_, m_] := logscale /@ {n, m}

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cp, Line[x_] :> x, -3];

ListLinePlot[pts, ScalingFunctions -> logscale[2, 2], AspectRatio -> 1]

You can change the numeric parameters in logscale to get different effects; see the linked post for further examples.

Working in polar coordinates makes things look nicer, but I lose automatic tick generation so I have to turn them off:

newpts = FromPolarCoordinates /@ 
  MapAt[logify[2], ToPolarCoordinates /@ pts, {All, All, 1}];

ListLinePlot[newpts, Ticks -> None, AspectRatio -> 1]

The ticks could be calculated with inverse[2] but I don't have time to complete that now.

Additional examples of each method:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

ListLinePlot[pts2, ScalingFunctions -> logscale[3, 3], AspectRatio -> 1]

newpts2 = FromPolarCoordinates /@ 
   MapAt[logify[3], ToPolarCoordinates /@ pts2, {All, All, 1}];

ListLinePlot[newpts2, Ticks -> None, AspectRatio -> Automatic]

Revising this answer I propose extracting contours from ContourPlot, converting to polar, scaling magnitude, then converting back and plotting. I will use code from ListLogLinearPlot for the whole real numbers:

logify[_][x_ /; x == 0] := 0
logify[off_][x_] := Sign[x] Max[0, (off + Re@Log@x)/off]

inverse[off_][x_] := Sign[x] Exp[(Abs[x] - 1) off]

logscale[n_] := {logify[n], inverse[n]}

And an auxiliary function:

logTheta[m_][pts_] :=
  FromPolarCoordinates /@ 
    MapAt[logify[m], ToPolarCoordinates /@ pts, {All, 1}];

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal @ cp, Line[x_] :> x, -3];

ListLinePlot[logTheta[2] /@ pts
  , Ticks -> Charting`ScaledTicks @ logscale[2]
  , AspectRatio -> 1
]

An additional example to better illustrate variable "zoom" in the scaling:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

ListLinePlot[logTheta[#] /@ pts2
 , Ticks -> Charting`ScaledTicks @ logscale[#]
 , AspectRatio -> 1
] & /@ {2, 3, 4}

Beware: if the "zoom" is not enough you'll create singularities in the polar/Cartesian conversion and get errors instead of a plot:

logTheta[1] /@ pts2;

FromPolarCoordinates::bdpt: Evaluation point {0,1.92728} is not a valid set of polar or hyperspherical coordinates. >>

I expect this will be a problem if you have contours that cross the origin, but I will have to come back to that later.

added 754 characters in body

Source Link

edited Jul 29, 2017 at 12:32

Mr.Wizard

273.1k
34
595
1.4k

At least in v10.1 ContourPlot doesn't support ScalingFunctions, but ListLinePlot does, unofficially. Therefore this might be of some use.

Using logscale from ListLogLinearPlot for the whole real numbers :

logify[_][x_ /; x == 0] := 0
logify[off_][x_] := Sign[x] Max[0, (off + Re@Log@x)/off]

inverse[off_][x_] := Sign[x] Exp[(Abs[x] - 1) off]

logscale[n_] := {logify[n], inverse[n]}

(* additional definition *)
logscale[n_, m_] := logscale /@ {n, m}

Now:

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cp, Line[x_] :> x, -3];

ListLinePlot[pts, ScalingFunctions -> logscale[2, 2], AspectRatio -> 1]

You can change the numeric parameters in logscale to get different effects; see the linked post for further examples.

An additional exampleWorking in polar coordinates makes things look nicer, but I lose automatic tick generation so I have to turn them off:

newpts = FromPolarCoordinates /@ 
  MapAt[logify[2], ToPolarCoordinates /@ pts, {All, All, 1}];

ListLinePlot[newpts, Ticks -> None, AspectRatio -> 1]

The ticks could be calculated with inverse[2] but I don't have time to complete that now.

Additional examples of each method:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

ListLinePlot[pts2, ScalingFunctions -> logscale[3, 3], AspectRatio -> 1]

newpts2 = FromPolarCoordinates /@ 
   MapAt[logify[3], ToPolarCoordinates /@ pts2, {All, All, 1}];

ListLinePlot[newpts2, Ticks -> None, AspectRatio -> Automatic]

At least in v10.1 ContourPlot doesn't support ScalingFunctions, but ListLinePlot does, unofficially. Therefore this might be of some use.

Using logscale from ListLogLinearPlot for the whole real numbers :

logify[_][x_ /; x == 0] := 0
logify[off_][x_] := Sign[x] Max[0, (off + Re@Log@x)/off]

inverse[off_][x_] := Sign[x] Exp[(Abs[x] - 1) off]

logscale[n_] := {logify[n], inverse[n]}

(* additional definition *)
logscale[n_, m_] := logscale /@ {n, m}

Now:

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cp, Line[x_] :> x, -3];

ListLinePlot[pts, ScalingFunctions -> logscale[2, 2], AspectRatio -> 1]

You can change the numeric parameters in logscale to get different effects; see the linked post for further examples.

An additional example:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

ListLinePlot[pts2, ScalingFunctions -> logscale[3, 3], AspectRatio -> 1]

At least in v10.1 ContourPlot doesn't support ScalingFunctions, but ListLinePlot does, unofficially. Therefore this might be of some use.

Using logscale from ListLogLinearPlot for the whole real numbers :

logify[_][x_ /; x == 0] := 0
logify[off_][x_] := Sign[x] Max[0, (off + Re@Log@x)/off]

inverse[off_][x_] := Sign[x] Exp[(Abs[x] - 1) off]

logscale[n_] := {logify[n], inverse[n]}

(* additional definition *)
logscale[n_, m_] := logscale /@ {n, m}

Now:

cp = ContourPlot[
   729 + x^4 + y^4 + 3 x^2 (-225 + y^2) == 730 y^2, {x, -32, 32}, {y, -34, 34}, 
   MaxRecursion -> 3];

pts = Cases[Normal@cp, Line[x_] :> x, -3];

ListLinePlot[pts, ScalingFunctions -> logscale[2, 2], AspectRatio -> 1]

You can change the numeric parameters in logscale to get different effects; see the linked post for further examples.

Working in polar coordinates makes things look nicer, but I lose automatic tick generation so I have to turn them off:

newpts = FromPolarCoordinates /@ 
  MapAt[logify[2], ToPolarCoordinates /@ pts, {All, All, 1}];

ListLinePlot[newpts, Ticks -> None, AspectRatio -> 1]

The ticks could be calculated with inverse[2] but I don't have time to complete that now.

Additional examples of each method:

cp2 = ContourPlot[
  Evaluate[x^2 + y^2 == # & /@ (3^Range[-3, 5])], {x, -16, 16}, {y, -16, 16}, 
  PlotPoints -> 50]

pts2 = Cases[Normal@cp2, Line[x_] :> x, -3];

ListLinePlot[pts2, ScalingFunctions -> logscale[3, 3], AspectRatio -> 1]

newpts2 = FromPolarCoordinates /@ 
   MapAt[logify[3], ToPolarCoordinates /@ pts2, {All, All, 1}];

ListLinePlot[newpts2, Ticks -> None, AspectRatio -> Automatic]

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edited Jul 29, 2017 at 12:16

Mr.Wizard

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595
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created Jul 29, 2017 at 12:01

Mr.Wizard

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Controlling tick marks

Controlling tick marks