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Is it OK to use NestList in this situation?

Posted 8 years ago

Hello friends, I hope you are spending a few moments full of joy and fun, in my case I am having fun breaking my head with the problem that I will try to explain. I have the following function, which it does is cut a prism by the y-axis.

dtr[{{x_, y_, z_}, {x1_, y1_, z1_}}] := 
 Module[{yes, xs, zeta, inf, sup, val}, yes = (y1 - y)/2; 
  val = RandomChoice[{1, 3/2, 2, 5/2}]; xs = x1 - x; zeta = z1 - z; 
  inf = {{x, y, z} - {0, 0, val}, {x + xs, y + yes, zeta} - {0, 0, 
      val}}; sup = {{x, y + yes, z} + {0, 0, val}, {x + xs, y + 2 yes,
       zeta} + {0, 0, val}}; {inf, sup}]

Here is an example of what this function performs

dtr[{{0, 0, 0}, {32, 32, 8}}]
Graphics3D[Map[Cuboid, %]]

The problem arises, when you want to continue applying the function to the previous result on several occasions, I tried to use NestList, but without success, as shown in the following image.

Error obtained

This is something like what you expect to get after you have applied the function four times.

{{{0, 0, -6}, {32, 2, 23/2}}, {{0, 2, -3}, {32, 4, 29/2}}, {{0, 
   4, -3}, {32, 6, 23/2}}, {{0, 6, 0}, {32, 8, 29/2}}, {{0, 
   8, -(7/2)}, {32, 10, 19/2}}, {{0, 10, -(1/2)}, {32, 12, 25/
   2}}, {{0, 12, -(3/2)}, {32, 14, 19/2}}, {{0, 14, 3/2}, {32, 16, 25/
   2}}, {{0, 16, -4}, {32, 18, 11/2}}, {{0, 18, -2}, {32, 20, 15/
   2}}, {{0, 20, 1}, {32, 22, 11/2}}, {{0, 22, 3}, {32, 24, 15/
   2}}, {{0, 28, 9/2}, {32, 30, 1/2}}, {{0, 30, 13/2}, {32, 32, 5/
   2}}, {{0, 24, 2}, {32, 26, 0}}, {{0, 26, 5}, {32, 28, 3}}}

Could someone help me solve my problem?, Maybe the use of NestList is not correct in this case, any help is welcome. Thanks in advance

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POSTED BY: Luis Ledesma
4 Replies
Posted 8 years ago

A very interesting solution to analyze and test, thanks for sharing it. Greetings Luis

POSTED BY: Luis Ledesma

Hi Luis,

you do can use Nest in this case (an interesting problem by the way!):

r = v : {{x1_, y1_, z1_}, {x2_, y2_, z2_}} :> Sequence @@ dtr[v];
cuboids = Nest[# /. r &, {{{0, 0, 0}, {128, 128, 128}}}, 6];
Graphics3D[Cuboid /@ cuboids]

First I was playing around with SubstitutionSystem but I could not make that work ...

Regards -- Henrik

POSTED BY: Henrik Schachner
Posted 8 years ago

Hello l van Veen, thanks for your suggestions, I have solved it the following way as I put it in the following image and I share the code.

solved

But I have to tell you, the person who told me about the algorithm I'm trying to implement confused me, so I asked for some reference and gave me the following link Planar version, but I still do not finish to find out how the algorithm works, but I think Something will serve what I have done. I hope your comments on this, greetings

Luis Ledesma /...>

POSTED BY: Luis Ledesma

Hi Luis, it seems to me that dtr is not listable? So uno generates a list of two items. I would try to make dtr map over a list of results. your uno result does not match your pattern in dtr because of this.

POSTED BY: l van Veen
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