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MathGroup Archive 1998

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Re: set manipulation



hi,

try :

In[1]:=
data2D = {{4.4, 14}, {6.7, 15.25},
 {6.9, 12.8}, {2.1, 11.1}, {9.5, 14.9},
 {13.2, 11.9}, {10.3, 12.3}, {6.8, 9.5},
 {3.3, 7.7}, {0.6, 5.1}, {5.3, 2.4},
 {8.45, 4.7}, {11.5, 9.6}, {13.8, 7.3},
 {12.9, 3.1}, {11, 1.1}};
In[2]:=<<DiscreteMath`ComputationalGeometry` In[3]:=delval =
DelaunayTriangulation[data2D];

make lists {{z[1,2],z[1,5],...},,,} with a dummy function z:

In[9]:=o1=Apply[Thread[z[#1,#2]]&,delval,1];

now change indices to point coordinates : In[14]:=o2=o1/.z[u_ ,v_
]:>w[data2D[[u]],data2D[[v]] ];

now replace dummy fiunction w by your angle formula, either ArcTan[x/y]
...
In[15]:=o3=o2/.w[{x1_,y1_},{x2_,y2_}]:>ArcTan[(y2-y1)/(x2-x1)];

 ... or ArcTan[x,y] , check the help file!
In[16]:=o4=o2/.w[{x1_,y1_},{x2_,y2_}]:>ArcTan[(x2-x1),(y2-y1)];

if you want averages, add'm & count'm:
In[17]:=o5=((Plus@@#)/Length[#])&/@ o4;

finally, line'm up for presentation : In[18]:=o6 =
Transpose[{Range[Length[o5]],o5}] Out[18]=
{{1, -0.730339}, {2, -1.41916}, {3, 0.0795703}, 
  {4, -0.426948}, {5, -0.349634}, {6, 0.454106}, 
  {7, 0.221677}, {8, 0.190618}, {9, -0.345478}, 
  {10, 0.523639}, {11, 1.23956}, {12, 0.310264}, 
  {13, -0.621994}, {14, -0.103605}, {15, 0.608526}, 
  {16, 1.97183}}

have fun too !

wouter.





At 00:58 05.02.98 -0500, Nilay Saha wrote:
>Hello everyone,
>   I have a problem with data set manipulation. I have a data set;
>data2D={{1.3,2.4},{1.4,5.6},{ ,},{ ,}     }}
><<DiscreteMath`ComputationalGeometry` delval=DelaunayTriangulation.
>
>
>The set delval gives the nearest neighbour of each of the data2D
>points.Thus delval may look like:
>
>delval={{1,{2,5,6}},
>        {2,{3,6,4}},
>        {3,{2,4 1}},
>                     }}
>In the set delval 1=ist point in data2D (i.e in above eg. {1.3,2.4})
>                  2=2nd point
>                  3=3rd Point
>                      and so on.
>Thus 1st point has it's nearest neighbour as 2nd, 5th, 6th points.
>
>
>Now I have to calculate the angle of the lines joining point 1 with it's
>nearest neighbour, with the x-axis=>
>
>angle=TanInverse[y(2)-y(1)/(x(2)-x(1))], where for sake of explanation
>point1={x(1),y(1)}, point2={x(2),y(2)}  and so on for points 5,6.
>  This should be done for all the points of data2D. 
>
>
>Then I need to add the angles corresponding to each point and then find
>the average .
>  So If anyone who could give a slight hint of how this sort of data
>manipulation can be done , I would be extremely grateful , Thnking you,
>
>Yours Sincerely,
>Nilay Saha
>Kamerlingh Onnes Lab,
>2300RA Leiden
>Postbus: 9506,
>The Netherlands.
>Phone:
>(0031)71 5275476.
>
>

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