plotting - Ad hoc graphics primitives-like objects

Sphere is one of the three-dimensional graphics primitives available in Mathematica and can be easily used to created very useful images. For instance, in the figure below I created three images of an ellipsoidal object that is lit from a fixed direction and it is then just rotated around the z-axis.

GraphicsRow[
    Table[
        Graphics3D[
        Rotate[Scale[{GrayLevel[.7], Sphere[]}, {1, 1.5, 1}, {0, 0, 0}], 
        i Degree, {0, 0, 1}], PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}}, 
        AspectRatio -> 1, Background -> Black, Boxed -> False, 
        ViewPoint -> Front, SphericalRegion -> True, 
        Lighting -> {{"Directional", White, ImageScaled[{0, 0, 1}]}}
    ], {i, {0, 45, 90}}]]

ellipsoidalObject

Suppose that instead of using the ellipsoidal object I would like to use an object like this bump:

Plot3D[Exp[-(x^2 + y^2)], {x, -2, 2}, {y, -2, 2}]

bump

Is there a way to create a "graphics primitive" object of the bump, so as to just use it instead of Sphere in the above example?

I suppose there should be a way to extract all the polygons specifying the shape of the bump, but I couldn't find a way to do it. Any other approach is also more than welcome.

Answer

The result of Plot3D and related functions is something of the form Graphics3D[primitives, options], so to extract the graphics primitives you can simply take the first part of the plot. These can then be manipulated similar to Sphere[] in your example, e.g.

plot = Plot3D[Exp[-(x^2 + y^2)], {x, -2, 2}, {y, -2, 2}][[1]];


GraphicsRow[
 Table[Graphics3D[
   Rotate[Scale[{GrayLevel[.7], plot}, {1, 1.5, 1}, {0, 0, 0}], 
    i Degree, {0, 0, 1}], PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}}, 
   AspectRatio -> 1, Background -> Black, Boxed -> False, 
   ViewPoint -> Front, SphericalRegion -> True, 
   Lighting -> {{"Directional", White, 
      ImageScaled[{0, 0, 1}]}}], {i, {0, 45, 90}}]]

Mathematica graphics

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.

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