# Tag Info

15

Edit I had some time so I've added full surface torus. Old code in edit history. DynamicModule[{x = 2., l = 100., x2 = 2., l2 = 100., grid, fast, slow}, Grid[{{ Graphics3D[{ Dynamic[Map[{Blue, Polygon[#[[{1, 2, 4, 3}]]]} &, Join @@@ (Join @@ Partition[#, {2, 2}, 1]) ]&[ ...

5

There are two ways: Calculate the density analytically. For the distribution you use this is difficult but since this for producing something pretty, and not for accuracy, you can consider using a different distribution. Approximate the distribution numerically. I'm going to do no. 2. below. I don't have version 7, so it is just a guess that these ...

3

Folding or mapping? Mapping is simple. Say you have a rectangular piece of paper of width $a$ and height $b$, so that any point $P$ on the paper has the coordinates $(x,y)$ with $0\leq x\leq a$ and $0\leq y\leq b$ then you can simply use the same coordinates on the torus and identify $x=0$ with $x=a$ (and $y=0$ with $y=b$), respectively. If you are ...

3

I don't think kuba answer, although correct, really addresses the texture issue. ViewVertical is essential, but ViewAngle is not needed. Also, SphericalRegion helps. Manipulate[ SphericalPlot3D[1 , {u, 0, 180 °}, {v, 0, 360 °}, Mesh -> None, TextureCoordinateFunction -> ({#5 - 1/2, 1 - #4} &), PlotStyle -> ...

3

Here is a brute force approach, approximating the density by simply counting near neighbors: all = Ball[10000]; blz = {Count[ all, p_ /; (Norm[p - #] < .5)], #} & /@ all ; ..Go get lunch.. Then directly color each point.. Graphics3D[{AbsolutePointSize[3], {Hue[N[(2/3) Log[#[[1]]]/7]], Point[#[[2]]]} & /@ blz}, Boxed -> True, ...

2

Here is a work around, in case you need to work with the flat (unordered) data: interp = Interpolation[{#[[;; 3]], #[[4]]} & /@ gauss]; ContourPlot3D[interp[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2},Contours -> {.5}] worth pointing out this seems to work fine for completely unordered data: gauss = Table[ Join[#, {Exp[-#[[1]]^2 - ...

1

As suggested by Szabolcs ViewAngle and ViewVertical is the answer. SphericalRegion is, in fact, redundant so I don't have to explain it (I can't ;P). Manipulate[Graphics3D[Cone[{{0, 0, -1}, {0, 0, 1}}, 1], ViewVector -> {2*{Cos[t], 0, Sin[t]}, {0, 0, 0}}, ViewAngle -> Pi/2, ...

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