Testcase With Static Objects

As a first textcase we are using a testcase with the following signature: $ n_{obj}=3$, $ s$, $ n_{pos_obj}=4$, $ n_{pos_meas}=1$, Sequ. . This applies to a space of Y=5 ('rows') and X=7 (='columns') dimensions. In the used example these vectors will be 2-dimensional vectors from an 2-dimensional area describing positions in this area. The language data will be transmitted with additional data structures.

The area has three static objects whose vectors ('coordinates') are as follows:

   1.    2.  
    1.    3.  
    2.    2.  
    2.    3.  
    4.    4.  
    4.    5.  
    5.    4.  
    5.    5.  
    6.    1.  
    6.    2.  
    7.    1.  
    7.    2.

As later can be seen during the processing of the data it is helpful to normalize these data with regard to one length. This will be done using the 'longest' vector of the set as common measure. The computation will be done with the following user-defined scilab-function:

//************************************************************
// Normalize the input 2D-Input-Vektors with a UNIFORM norm
// Take INP as input and generate INP3 as output

function [INP3]=doNormU(INP)
  
  [r,c] = size(INP)
  Maxnorm=0
  INP3=[]
  printf('Length of Input Vector: %d\n',r)
  
  //Looping through the input to find maximal norm
  for i=1:r
  v=[INP(i,1) INP(i,2)]
  if norm(v) > Maxnorm then Maxnorm=norm(v)
  printf('NORM of vector: %f %f\n',norm(v), Maxnorm)
  end
end

  //Looping through the input to normalize uniformly
  for i=1:r
  v=[INP(i,1) INP(i,2)]
  printf('OLD coordinates: %d %d\n',v(1),v(2))
  v=v/Maxnorm
  printf('NEW coordinates: %f %f\n',v(1),v(2))

 //Store normalized values in new array
  INP3(i,1)=v(1)
  INP3(i,2)=v(2)
  end
  
endfunction 
//************************************************************

The uniformly normalized vectors are given as follows:

    0.1373606    0.2747211  
    0.1373606    0.4120817  
    0.2747211    0.2747211  
    0.2747211    0.4120817  
    0.5494423    0.5494423  
    0.5494423    0.6868028  
    0.6868028    0.5494423  
    0.6868028    0.6868028  
    0.8241634    0.1373606  
    0.8241634    0.2747211  
    0.9615239    0.1373606  
    0.9615239    0.2747211

Figure 8.2: Input data case 1 with static objects each having four positions
\includegraphics[width=4.0in]{case1_input_v3.eps}

To show these data points in a graph one can use in scilab the command:
plot2d(INP3(:,1), INP3(:,2), style=-3, rect=[-0.1,-0.1,1.1,1.1]) (cf. figure 8.2). One can detect three objects representing each a simple square given by four data points.



Subsections
Gerd Doeben-Henisch 2012-03-31