files and directories - What kind of check does DirectoryQ exactly perform?

I'm using Mathematica 9.0.1 on Windows XP and my drive letters are assigned as follows: C: and D: are hard local disks, while E: is assigned to some removable media. Now, the situation is as follows

DirectoryQ[# <> ":\\"] & /@ {"c", "d", "e"}

returns {True,True,True}, even when an optical disk isn't in the drive.

To outflank the problem I use a directoryQ function, defined in the code below.

However, it obviously fails against a full hard disk or when I don't have write access. Therefore, I' m wondering about the kind of check DirectoryQ basically performs. Is there a better solution to fix the problem?

   directoryQ[unit_]:=Module[
       {root,file,ret},
       ret=False;
       root=unit<>":\\";
       file = FileNameJoin[{root, "testFile.txt"}];
       If[
         DirectoryQ[root],

         Quiet[Export[file,"test","Text"]];
         If[
           FileExistsQ[file],
           DeleteFile[file];
           ret=True
         ];
       ];
       Return[ret];
];


directoryQ["c"]
directoryQ["e"]

Answer

Since Mathematica is written in the C programming language, it is likely that any file-system status operation is doing nothing more than calling C's built-in functions. In this case, that would be stat.

So let's test what stat does on Windows. According to the C language documentation, stat is given the name of something in the file system, and returns a C structure whose fields describe the properties of that thing. In particular, the st_mode field seems relevant:

st_mode: Bit mask for file-mode information. The _S_IFDIR bit is set if path specifies a directory; the _S_IFREG bit is set if path specifies an ordinary file or a device. User read/write bits are set according to the file's permission mode; user execute bits are set according to the filename extension.

I wrote a simple test program in Microsoft Visual C that tests the stat function. Drive C: is my Windows system drive; drive E: is my DVD drive, which currently doesn't have anything in it. Here's what I found:

stat("C:\\WINDOWS") returns success and sets _S_IFDIR

stat("C:\\WINDOWS\\SYSTEM32\\NOTEPAD.EXE") returns success and does not set _S_IFDIR
stat("C:\\") returns success and sets _S_IFDIR
stat("E:\\") returns success and sets _S_IFDIR
stat("W:\\") returns failure

So we can conclude from this that Windows, or at least the stat function on Windows, considers empty DVD drives to be "there." I also have a flash memory stick that I can plug into a USB slot, which I have mapped to drive W, but that "isn't there" when it's unplugged.

This is consistent with what Windows Explorer shows me when I click on "My Computer". I see drive C: with a name, and I see drive E:, even though I get an error message when I double-click on it. I don't see drive W: (my flash memory stick) after I pulled it out of the socket. So Windows does consider an empty DVD drive to be present, which is probably why stat says it's a valid directory.

I have no idea how to find out whether a DVD drive is full or empty in C, much less in Mathematica. But at least we can see the core of the problem.

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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