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Picking out pieces of a list
*To*: mathgroup at smc.vnet.net
*Subject*: [mg75910] Picking out pieces of a list
*From*: Hatto von Aquitanien <abbot at AugiaDives.hre>
*Date*: Sun, 13 May 2007 05:45:51 -0400 (EDT)
Here's the motivation. I want to draw slice out of a cone. (I don't know
the proper mathematical term for this, but my meaning should be clear from
the code.) Note: See Feynman, Vol II, Page 1-8.
(*A function that generates coordinates:*)
R3[\[Theta]_, r_: 1.0, p_: {0, 0, 0}] :=
r {0, Cos@\[Theta], Sin@\[Theta]} + p
(*Some "constant" values:*)
r1 = 1.0;
r2 = 0.8;
\[CapitalDelta]x = 0.5;
(*Points representing the centers of the circular faces:*)
p1 = {\[CapitalDelta]x, 0, 0};
p2 = {0, 0, 0};
(*A list of point pairs:*)
pts = {R3[#, r1, p1], R3[#, r2, p2]} & /@Range[-\[Pi], \[Pi], \[Pi]/20];
(*Draw the circular faces, and the reference curve:*)
Graphics3D[{
Opacity[.3]
, EdgeForm[]
, {Line[#], Polygon[#]} &@pts[[All, 1]]
, Polygon[#] &@pts[[All, 2]]
}]
Now, I know I can use table, or some kind of brute force manipulation with
(...)&/Range[Length@pts] to extract the points in the correct order to draw
the polygons for the sides. What I want to know is whether there is a way
to use Part[] to get the four points in one statement.
Here's a little scratch-pad code I created to explore the problem.
c = CharacterRange["1", "9"]
(lst = Table[
DisplayForm[
SubscriptBox["P", c[[i]] <> c[[j]] <> c[[k]]]]
, {i, 1, Length@c}
, {j, 1, 2}
, {k, 1, 2}]) // MatrixForm
(*Get the points of the first ring*)
lst[[All, 1]] // MatrixForm
(*Get the points of the second ring*)
lst[[All, 2]] // MatrixForm
(*Here is /a/ solution to the problem:*)
m[n_, lst_] := lst[[Mod[n + 1, Length@lst, 1]]]
Join[lst[[#]][[{1, 2}]], m[#, lst][[{2, 1}]]] & /@ Range@len // MatrixForm
Is there a "tighter" way to accomplish the same thing?
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