Skip to main content

plotting - 3D plot from lists


I'm trying to generate a 3D plot of some functions a,b,c, under certain inequality constraints. I have earlier defined the functions


a[x,y,z],b[x,y,z],c[x,y,z]

and


f[a[x,y,z],b[x,y,z],c[x,y,z]]

So far I have:


RegionPlot3D[
0 < f[a[x, y, z], b[x, y, z], c[x, y, z]] &&

0 < a[x, y, z] < 1 && 0 < b[x, y, z] < 1 && 0 < c[x, y, z] < 1,
{x, -Pi/2, Pi/2}, {y, 200, 2000}, {z, 100, 1000}]

This works great, and gives me a 3D plot showing the region in x, y, z space for which the constraint holds.




Now, I have lists of a,b,c from another calculation, i.e.,


mat=Table[{a[i],b[i],c[i]},{i,0,10}] 
alist=mat[[All,1]]

Essentially I want to use a similar RegionPlot3D code to plot the space in x, y, z for which the a,b,c values from the dataset fulfill the conditions (inequalities).



I'm struggling with:




  • Properly ordering/pairing my data sets, such as to thread each set of corresponding a, b and c values together




  • Calling values from the data table in the RegionPlot3D, i.e. running it for every data point in the table a, b, c




  • Plotting this on a 3D plot in terms of x,y,z. So essentially I have the functions a[x,y,z],b[x,y,z],c[x,y,z] and separately lists of a, b, c values.





Any help would be much appreciated!




Comments

Popular posts from this blog

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....