plotting - Tailoring RegionPlot3D with PlotPoints?

This seemingly tame solid gives Mathematica (v9) a bit of a workout if you want to generate a good picture:

rinner[y_] = Sqrt[y];

router[y_] = 1;
RegionPlot3D[rinner[y]^2 <= x^2 + z^2 <= router[y]^2, 
  {x, -1, 1}, {z, -1, 1}, {y, 0, 1}, AxesLabel -> {x, y, z}, PlotPoints -> 100, 
  PlotStyle -> Opacity[.75], MeshFunctions -> {#3 &}, Mesh -> 5]

Mathematica graphics

I kept increasing PlotPoints from 100 to 200 to 300 and things get pretty slow---without much of an improvement in the rendering of the choppy part of the region at the top. Bumping up MaxRecursion and PerformanceGoal->"Quality" didn't seem to help.

I tried playing with variations like PlotPoints->{100,100,300} to get better results faster, and this leads to my two questions.

What else should I try? (I experimented with RevolutionPlot3D, but I want solids.)

Is it possible to tailor the placement of PlotPoints to a subset of either

(a) an axis (say, 10x more points in the $z$ direction, but pack them into $0.9\le z\le 1$?, or

(b) a specific portion of the overall space (say, $x,y,z$ with $0.9^2\le x^2+y^2\le 1^2$ and $0.9\le z\le 1$, etc.)?

Thanks for any insight.

Answer

If you want to stick with RegionPlot3D but don't want the jagged edges, then you can smooth them by excluding the creased line from the plot region:

rinner[y_] = Sqrt[y];

router[y_] = 1;
ε = .05;
RegionPlot3D[(rinner[y])^2 <= x^2 + z^2 <= (router[y])^2 && 
  router[y] - rinner[y] > ε, {x, -1, 1}, {z, -1, 1}, {y, 0, 
  1}, AxesLabel -> {x, y, z}, PlotPoints -> 100, 
 PlotStyle -> Opacity[.75], MeshFunctions -> {#3 &}, Mesh -> 5]

rounded

Edges are always rounded in RegionPlot3D anyway, so rounding them by hand as I did here with the parameter ε may be acceptable.

The small parameter ε determines how close the inner and outer walls are allowed to come - thus preventing them from touching. The choice of PlotPoints will determine how small you can make ε.

Comments

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 - 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 - 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