A more detailed discussion of trs_apply

The trs_apply routine combines all of the low-level trs_ transformation routines to create a single script that uses one input parameter file tp perform an X,Y transformation.

  1. A simple run of trs_apply.
  2. The input parameter file.
  3. A collection of trs_apply sample runs.


A simple run of trs_apply.

Let's take our second exmaple of test data in our discussion of trs_make_xy_TestData and use trs_apply to transform those coordinates. We'll plot the original X,Y set, then the transformed set.

Here is a simple trs_apply example. We aim to take the point at X,Y=500,500 and translate (shift) it to the position X,Y=450,490. 

# We make the test data file (file1.xy):   
% cat t.1 
500 500
500 600
700 500
450 450
% trs_make_xy_TestData read  
% trs_plot.py Style.file 200 800 200 800 SHOW   (optional)  
% cp XY0.data file1.xy  
# Notice that point 1 is at X,Y=500,500.  

% cat TRS.1
 500.0  500.0   N      1.0   0.0    0.0 0.0

#   XoS    YoS   flip    scal  theta    XoF   YoF 
# So, you can guess that I am just doing a translation here!


# Transform the XY, write no header, write to standard out
% trs_apply file1.xy TRS.1 N
   0.000	  0.000
   0.000	  100.000
  200.000	  0.000
  -50.000	  -50.000

# Transform the XY, write a header, direct the data to a file (file2.xy)
% trs_apply file1.xy TRS.1 Y > file2.xy 
% cat file2.xy 
# data 
# data
  0.000	  0.000
  0.000	  100.000
  200.000	  0.000
  -50.000	  -50.000

# Plot the file1.xy and file2.xy data in one plot
% trs_2plot file1.xy file2.xy "My XY Transformation Example" 
% trs_plot.py Style.file 0 1000 0 1000 SHOW
Notice that we have indeed translated Point 1 (originally at X,Y=500,500) to the new position at X,Y=0.0.

Notice tat in the example above I used an specialized plotting tool named trs_2plot to build my input files for running trs_plot.py. Maybe a second example using a primitive (but pervasive in the codes!) tool would be useful. This tool, named "trs_build_plot_file" is easy to use. It will take as input the name of your XY data file (e.g. file1.xy). You'll also specify a few arguments that set the properties of the points (type, size, color) and a text string that describes this set. I direct this output to a file (e.g. XY2.plot) and I can add this file to the local "Style.file". When I run trs_plot.py this second (transformed) data set is included. The advantage here over trs_2plot is that we could build a plot with as many XY data files as we wish. In the figure below I give an example similar to the obe above, but I use this more general approach to making the plot.

Here is another simple trs_apply example. We aim to flip the points about the X axis. 

% ls 
file1.xy  PointNames

% cat TRS.2
 500.0  500.0   N      1.0   0.0    -450.0  -490.0

#   XoS    YoS   flip    scal  theta    XoF   YoF 
# So, you can guess that I am performing two translations here!


# Transform the XY, write a header, direct the data to a file (file2.xy)
% trs_apply file1.xy TRS.2 Y > file2.xy 
% cat file2.xy 
# data
  450.000	  490.000
  450.000	  590.000
  650.000	  490.000
  400.000	  440.000

# Build a plot file for the file1.xy data 
% trs_build_plot_file file1.xy r s 100 25 "Original set" > XY1.plot  
# Green (g) hexagon points (h) of size 140 with labels of size 25 
% cat XY1.plot 
point r s 100 25
Original set
  500	  500	1
  500	  600	2
  700	  500	3
  450	  450	4

# Build a plot file for the file2.xy data 
% trs_build_plot_file file2.xy g h 140 25 "Translated set" > XY2.plot  
# Green (g) hexagon points (h) of size 140 with labels of size 25 
% cat XY2.plot 
point g h 140 25
Reflected set
  450.000	  490.000	1
  450.000	  590.000	2
  650.000	  490.000	3
  400.000	  440.000	4

I edit or compose Style.file:
% cat Style.file  
Two translations
X axis 
Y axis 
XY1.plot
XY2.plot

% trs_plot.py Style.file -1000 1000 -1000 1000 SHOW 
Notice that I use a wider range of axis limits.
We sse that we have tranformed the Point 1 at X,Y=500,500 to be at X,Y=450,490. By changing the last two arguments in the TRS file we have applied a second translation that determined a new origin for our final transformed set (in file2.xy).



The input parameter file.

A way to produce a set of random X,Y data points is described here. 


To apply all of the coordinate transformation steps:
% trs_apply 
Usage: trs_apply file1.xy trs_terms Y 
arg1 - file with XY to be transformed  
arg2 - file with TRS terms 
arg3 - output header line (Y/N) 
Terms: XoS YoS Reflect(X,Y,N) scale theta XoF YoF 
XoS,YoS = X,Y to set origin in original system 
XoF,YoF = X,Y to set origin in final system 

An example of the "file with TRS terms":
% cat TRS.terms 
    0.0    0.0     Y      1.0   0.0     0.0  0.0
#   XoS    YoS    flip    scal  theta   XoF   YoF  

The tranformed X,Y are sent to standard out, but general redirected to some new file.

% trs_plot.py Style.file -30 30 -30 30 SHOW
Hence, the first pair of coordinates (XoS,YoS) establish the new origin for the initial (input) set of coordinates. After the reflection, scale, and rotation operations are performed, the second pair of coordinates (XoS,YoS) establish the origin in the final (output) set of coordinates.



A collection of trs_apply sample runs.

A set of trs_apply examples are given now to give us a sense of how each parameter in the TRS input file change the output X,Y values. I build a script named trs_apply_demoscript.

Example 1: Two transalations have been used to shift the transformed points (blue) to the left and down relative to the original (red) points. The full sequence of transformations performed by trs_apply (seen in trs_apply_ex.STEPS) is shown here: 
 
   Step1:   trs_translate.sh file1.xy 500.0 500.0
   Step2:   trs_reflect.sh xy.step1_translate N 
   Step3:   trs_scale.sh xy.step2_reflect 1.0 
   Step4:   trs_rotate.sh xy.step3_scale 0.0 
   Step5:   trs_translate.sh xy.step4_rotate -480 -490



Example 2: In addition to the translations of example 1 above, we have now reflected (flipped) the points about the Y axis (specified by argumen 3 in the TRS file). Note that the reflection was performed with: 

   trs_reflect.sh xy.step1_translate Y



Example 3: In addition to the translations of example 1, we have now applied a scale change of Sfactor=1.5. Note that the scale adjustment was performed with: 

   trs_scale.sh xy.step2_reflect 1.5



Example 4: Here we see an example of a rotation by 45 degress. To make the sense of thr rotation more evident I dispensed with the translation. Hence, the point of rotation (Point 1) remains fixed in the transformed set. A positive rotation angle in degree units (theta) produces a CLOCKWISE (CW) rotation by trs_apply. Note that the rotation was performed with: 

   trs_rotate.sh xy.step3_scale 45.0



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