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Re: Re: Re: Visualization of a list of 3D points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89361] Re: [mg89327] Re: [mg89321] Re: Visualization of a list of 3D points
  • From: Syd Geraghty <sydgeraghty at mac.com>
  • Date: Sat, 7 Jun 2008 02:57:58 -0400 (EDT)
  • References: <g25nta$hu5$1@smc.vnet.net> <39600.1212644089509.JavaMail.root@m08>

Bobby & Jens,

Regarding:-

> Through is SO underutilised, don't you think? And why use Transpose  
> then
> Part, when Part does the job on its own?


I thought you might be interested (and perhaps surprised as I was) to  
see that using Through & Part was so much slower!

lst = Table[Table[RandomReal[{-5, 5}], {i, 3}], {x, 10^6}];

Timing[{ymin, ymax} = Through[{Min, Max}@lst[[All, 2]]]]

{0.186833, {-4.99997, 4.99999}}

Timing[{ymin, ymax} = {Min[#], Max[#]} &[Transpose[lst][[2]]]]

{0.059739, {-4.99997, 4.99999}}


Both are very elegant but Bobby's seems much more intuitive to me but  
it is slower on large data sets.

Cheers ... Syd


Syd Geraghty B.Sc, M.Sc.

sydgeraghty at mac.com

My System

Mathematica 6.0.2.1 for Mac OS X x86 (64 - bit) (March 13, 2008)
MacOS X V 10.5.2
MacBook Pro 2.33 Ghz Intel Core 2 Duo  2GB RAM






On Jun 6, 2008, at 6:45 AM, DrMajorBob wrote:

> Through is SO underutilised, don't you think? And why use Transpose  
> then
> Part, when Part does the job on its own?
>
> lst = {{3.30414, -2.86064, -2.54648}, {4.06572, 3.80403,
>     1.68897}, {-1.72822, -2.03097, -4.1024}};
> {ymin, ymax} = Through[{Min, Max}@lst[[All, 2]]]
>
> Graphics3D[{Hue[0.8*(#[[2]] - ymin)/(ymax - ymin)],
>     Sphere[#, 1/(2 + #[[2]] - ymin)]} & /@ lst]
>
> {-2.86064, 3.80403}
>
> Bobby
>
> On Wed, 04 Jun 2008 23:45:14 -0500, Jens-Peer Kuska
> <kuska at informatik.uni-leipzig.de> wrote:
>
>> Hi,
>>
>> lst = {{3.30414, -2.86064, -2.54648}, {4.06572, 3.80403,
>>    1.68897}, {-1.72822, -2.03097, -4.1024}};
>>
>> and
>> {ymin, ymax} = {Min[#], Max[#]} &[Transpose[lst][[2]]]
>> Graphics3D[
>>  {Hue[0.8*(#[[2]] - ymin)/(ymax - ymin)],
>>     Sphere[#, 1/(2 + #[[2]] - ymin)]} & /@ lst]
>>
>> Regards
>>   Jens
>>
>>
>> Alexei Boulbitch wrote:
>>> Dear MathGroup members,
>>>
>>> I have a list containing 3D coordinates of a number of points, like
>>> this one
>>> lst={{3.30414, -2.86064, -2.54648}, {4.06572, 3.80403,
>>>   1.68897}, {-1.72822, -2.03097, -4.1024}, ...}
>>>
>>> I would like to visualize them by plotting them. To plot them as a  
>>> set
>>> of points may be trivially done by say, ListPointPlot3D.  
>>> Alternatively,
>>> it may be visualized as a set of spheres with unit radius and  
>>> centered
>>> in the points specified by the list, e.g. in the point {3.30414,
>>> -2.86064, -2.54648}, in {4.06572, 3.80403, 1.68897} etc.
>>>
>>> Now comes the question. I would like to do it in such a way that the
>>> size (and may be the color) of each point or sphere would depend  
>>> upon
>>> one of the coordinates (say, y). In other words, the size and the  
>>> of the
>>> first point specified by lst with y=-2.86064 would be smaller than  
>>> that
>>> of the second point that has y=3.80403. The color or darkness may  
>>> also
>>> depend upon y. This would give a feeling of a perspective.
>>>
>>> Do you have an idea of how to do this?
>>>
>>> Best, Alexei
>>>
>>
>>
>
>
>
> -- 
>
> DrMajorBob at longhorns.com
>



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