plotting - RevolutionPlot3D: but NOT revolving about the z axis

I want to demonstrate generating a solid of revolution by revolving a planar region about, say, a horizontal axis. However, RevolutionPlot3D doesn't seem to have an option for revolving a curve about something other than the $z$ axis. I'm curious how you all would handle this.

Here's a simple example:

theta0 = Pi;
Manipulate[

  GraphicsRow[{
    Plot[x^2, {x, 0, 1}, PlotStyle -> {Thick, Black}, Filling -> Axis],
    Rotate[RevolutionPlot3D[Sqrt[x], {x, 0, 1}, {t, theta0 - .001, T},
    PlotRange -> {{-1, 1}, {-1, 1}, {0, 1}}, BoxRatios -> 1, 
    Boxed -> False, Axes -> False, ViewPoint -> {0, -2, 1}], -Pi/2]
  }],
{T, theta0, theta0 + 2 Pi}]

enter image description here

My questions:

Is there a "better" way to showcase revolving about a horizontal axis of revolution than what I've done with Rotate?

Is it possible to generate the higher quality, finished surface of revolution while the slider bar is moving instead of only when the slider is released?

How do I prevent the vertical tick labels on the far left edge as well as the graphic on the far right edge from being clipped? (I tried Spacings and ImagePadding.)

How do I vertically align the horizontal axis of revolution of the right graphic with the horizontal axis of the left graphic?

Edit: I had a follow up question but I will spin that off as a separate question.

Answer

Answers:

RevolutionAxis, set to either "X" or {1,0,0}. (This also required adjustments to the PlotRange and ViewPoint options.)

PerformanceGoal -> "Quality"

I switched from GraphicsRow to Row, which I like much better. (I then also set ImageSize -> Small to make the plots a bit bigger than they'd naturally be in Row.)

I was able to align the plots pretty well by setting BaselinePosition for each of the plots.

I also turned off the Mesh since I felt it was distracting, especially at the beginning of the sequence.

theta0 = Pi;
Manipulate[Row[{
   Plot[x^2, {x, 0, 1}, PlotStyle -> {Thick, Black}, 
       Filling -> Axis, BaselinePosition -> Axis, ImageSize -> Small], 
   RevolutionPlot3D[x^2, {x, 0, 1}, {t, theta0 - .001, T}, 
       PlotRange -> {{0, 1}, {-1, 1}, {-1, 1}}, BoxRatios -> 1, 

       Boxed -> False, Axes -> False, ViewPoint -> {1, -2, 0}, 
       Mesh -> None, RevolutionAxis -> "X", PerformanceGoal -> "Quality",
       BaselinePosition -> Center, ImageSize -> Small]
   }], {T, theta0, theta0 + 2 Pi}]

enter image description here

Comments

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 - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

Blog

Search This Blog