plotting - Conditional options in Plot

I was hoping to incorporate an If function into a Plot option, as in

Plot[Sin[t], {t, 0, 2 Pi}, Filling -> Axis, 
 FillingStyle -> If[Sin[t] > 0, LightGreen, LightRed]]

Plot[Sin[t], {t, 0, 2 Pi}, PlotStyle -> If[Sin[t] > 0, Dashed, Thick]]

to no avail. Is it possible to pass an If to the plot options?

I know that I can manually accomplish the effect via Piecewise, but I have more complicated applications in mind where I would not want to manually precompute the interval(s) on which my piecewise defined function would need to be defined.

Answer

Here is yet another crack at this problem.

ConditionalPlot[func_, condition_, varrange_, trueopts_, falseopts_] :=
  Module[{plottrue, plotfalse},
  plottrue = Plot[If[condition, func], varrange, trueopts];
  plotfalse = Plot[If[Not[condition], func], varrange, falseopts];
  Show[plottrue, plotfalse, PlotRange -> All]]

The first argument is the function or list of functions you want to plot. The second argument is the condition you want to apply. The third argument is the variable and range to plot in the form {x,xmin,xmax}. The third and fourth arguments are the options you apply when the condition is true or false, respectively.

For example, the plot you mentioned in your question can be had by

ConditionalPlot[Sin[x], 
 Sin[x] > 0, {x, 0, 2 Pi}, {Filling -> Axis, 
  FillingStyle -> LightGreen, PlotStyle -> Dashed}, {Filling -> Axis, 
  FillingStyle -> LightRed, PlotStyle -> Thick}]

enter image description here

This is versitile, you can give it a compound condition like

ConditionalPlot[Sin[x], 
 Sin[x] > .7 || Sin[x] < -.7, {x, 0, 2 Pi}, {Filling -> Axis, 
  FillingStyle -> LightGreen, PlotStyle -> Dashed}, {Filling -> Axis, 
  FillingStyle -> LightRed, PlotStyle -> Thick}]

enter image description here

You can give it multiple functions to plot

ConditionalPlot[{Sin[x], Cos[x]}, 
 Sin[x] > Cos[x], {x, 0, 4 Pi},
  {PlotStyle -> {Red, Thick}, Axes -> False, Frame -> True, BaseStyle -> 14}, 

      {PlotStyle -> {Black, Thick,Dashed}}]

enter image description here

Note that any global options you want to apply to the image in general should go in the trueopts as it is given to Show first.

Comments

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plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Adding a thick curve to a regionplot

Suppose we have the following simple RegionPlot: f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}] Now I'm trying to change the curve defined by $y=g[x]$ into a thick black curve, while leaving all other boundaries in the plot unchanged. I've tried adding the region $y=g[x]$ and playing with the plotstyle, which didn't work, and I've tried BoundaryStyle, which changed all the boundaries in the plot. Now I'm kinda out of ideas... Any help would be appreciated! Answer With f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 You can use Epilog to add the thick line: RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, Epilog -> (Plot[g[x], {x, 0, 2}, PlotStyle -> {Black, Thick}][[1]]), PlotStyle -> {Directive[Yellow, Opacity[0.4]], Directive[Pink, Opacity[0.4]],

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