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Re: Visualization of a list of 3D points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89389] Re: Visualization of a list of 3D points
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sun, 8 Jun 2008 02:31:20 -0400 (EDT)
  • References: <g25nta$hu5$1@smc.vnet.net> <39600.1212644089509.JavaMail.root@m08> <g2dbkt$9me$1@smc.vnet.net>

Hi,

I had a reason why I don't use Through[] !

Regards
   Jens

Syd Geraghty wrote:
> 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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