streams - LibraryLink: What can we do with MInputStream and MOutputStream?

Version 9 introduced the WolframStreamsLibrary.h header for LibraryLink. It contains MInputStream and MOutputStream.

What can I do with this header? How can I use these functions? Are the documented anywhere?

Possibly related:

Update 2018 March: Partial spelunking results, someone else may want to pick up the trail.

Currently, my best guess is that this is for extending Mathematica with new streams. I believe it to be the analogue of DefineInputStreamMethod and DefineOutputStreamMethod. The struct MInputStream contains most of the functions that would be passed to DefineInputStreamMethod. The actual analogue is registerInputStreamMethod in WolframLibray.h, which I believe sets the equivalents of the ConstructorFunction and NameTestFunction. My (unverified!) guesses for the parameters of registerInputStreamMethod are:

const char *name, same as name in DefineInputStreamMethod

void (*ctor)(MInputStream, const char* msgHead, void* optionsIn), same as "ConstructorFunction". Should fill out the MInputStream struct passed to it. But in what format does it receive the options?

mbool (*handlerTest)(void*, char*), probably the same as "NameTestFunction". But what is the void * parameter for? The methodData?

void* methodData, possibly pointer to private data used by the stream implementation.

void (*destroyMethod)(void* methodData), possibly for freeing the methodData? This is not the "CloseFunction".

There are still many key questions remaining before one could actually implement everything that is needed.

What is the methodData? A state unique to each instance of the stream, or shared by all of them? (I assume this is shared, and the individual state is in the MInputStream struct.) What exactly should each of these functions do?

An example implementation is woefully needed. After some more spelunking, I found one in SystemFiles/Links/SocketLink/Source/C. This example may provide enough information for us to write our own implementation, but I have not yet had the time/motivation to do all this. I still wanted to share my findings with others who may be interested in continuing the spelunking.

Note that the SocketLink example won't answer all questions: it often passes NULL pointers or simply ignores arguments (e.g the options in the constructor).

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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 - 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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