Wed Oct  8 08:46:30 2025

polygon_monte_carlo_tests():
  python version: 3.10.12
  numpy version:  1.26.4
  Test polygon_monte_carlo().

polygon_area_test():
  polygon_area() computes the area of a polygon.

  Number of polygonal vertices = 4

  The polygon vertices:

  Col: 
      0       
      1       

  Row
      0 :
           1  
           0  

      1 :
           2  
           1  

      2 :
           1  
           2  

      3 :
           0  
           1  


  Exact area is        2
  The computed area is 2

  Number of polygonal vertices = 8

  The polygon vertices:

  Col: 
      0       
      1       

  Row
      0 :
           0  
           0  

      1 :
           3  
           0  

      2 :
           3  
           3  

      3 :
           2  
           3  

      4 :
           2  
           1  

      5 :
           1  
           1  

      6 :
           1  
           2  

      7 :
           0  
           2  


  Exact area is        6
  The computed area is 6

polygon_monomial_integral_test():
  polygon_monomial_integral() evaluates the integral of a monomial
  x^p y^q over the interior of a polygon in 2D.

  Polygon vertices:

  Col: 
      0       
      1       

  Row
      0 :
           0  
           0  

      1 :
           1  
           0  

      2 :
           0  
           1  


   P   Q       Integral

   0   0             0.5
   0   1        0.166667
   1   0        0.166667
   0   2       0.0833333
   1   1       0.0416667
   2   0       0.0833333
   0   3            0.05
   1   2       0.0166667
   2   1       0.0166667
   3   0            0.05
   0   4       0.0333333
   1   3      0.00833333
   2   2      0.00555556
   3   1      0.00833333
   4   0       0.0333333

polygon_monte_carlo_test():
  polygon_sample() estimates integrals
  over the interior of a polygon in 2D.

         N
        1
              X^2 
             Y^2
             X^4
           X^2Y^2
             Y^4
           X^6

         1
               4
         1.43403
        0.298686
        0.514111
        0.107081
       0.0223033
        0.184313

         2
               4
         1.32745
         2.73369
        0.748704
         1.07194
         1.95632
        0.453009

         4
               4
        0.932989
         1.28544
        0.541734
        0.046211
        0.918929
        0.362874

         8
               4
        0.867506
         2.06281
        0.324141
        0.257254
         1.63643
        0.129426

        16
               4
         2.24854
        0.827632
         1.53649
        0.572241
        0.489459
         1.14503

        32
               4
         1.11794
         1.08233
        0.566388
        0.346816
        0.691187
        0.371323

        64
               4
         1.55951
         1.69789
        0.928857
        0.669912
         1.09027
        0.632112

       128
               4
         1.27795
          1.5043
        0.753899
        0.440824
         1.00134
        0.532669

       256
               4
         1.48542
         1.36897
         0.93521
        0.497543
        0.841705
        0.685499

       512
               4
         1.31225
          1.3232
        0.784496
        0.433859
        0.788242
        0.561162

      1024
               4
         1.35816
         1.36682
        0.821226
        0.443164
        0.829851
        0.587066

      2048
               4
         1.34468
         1.33614
        0.816258
        0.445085
        0.792714
        0.586191

      4096
               4
         1.31732
         1.31437
        0.795742
        0.431846
        0.782664
        0.572317

      8192
               4
         1.34801
         1.34118
        0.812915
        0.455819
        0.806244
        0.580579

     16384
               4
         1.32414
         1.33209
        0.792434
        0.440767
         0.79606
        0.564144

     32768
               4
         1.33691
         1.32835
        0.802074
        0.443761
        0.796871
        0.571677

     65536
               4
         1.33211
         1.33227
        0.798527
        0.440995
        0.796836
        0.570022

     Exact
               4
         1.33333
         1.33333
             0.8
        0.444444
             0.8
        0.571429


polygon_sample_test():
  polygon_sample() samples a polygon.

  Sample points:

  Col: 
      0       
      1       

  Row
      0 :
   0.0396002  
    0.574367  

      1 :
    0.266497  
    0.174618  

      2 :
     1.26365  
    0.331541  

      3 :
    0.643067  
     1.40394  

      4 :
    0.245491  
     0.44533  

      5 :
    0.146642  
     1.12678  

      6 :
     1.87894  
    0.456545  

      7 :
    0.951684  
     1.53528  

      8 :
    0.455012  
    0.277224  

      9 :
      1.9978  
    0.590049  

     10 :
     1.88362  
   0.0714635  

     11 :
    0.274638  
     1.09888  

     12 :
    0.443202  
     1.14536  

     13 :
    0.794091  
   0.0859335  

     14 :
     1.26605  
    0.940973  

     15 :
    0.500601  
    0.279066  

     16 :
    0.343784  
     1.19326  

     17 :
    0.600235  
   0.0693508  

     18 :
    0.781208  
     1.15776  

     19 :
     1.54951  
    0.343901  


triangle_area_test():
  triangle_area() computes the area of a triangle.

  (XA,YA) = (0,1)
  (XB,YB) = (0,0)
  (XC,YC) = (1,0)

  Triangle area is 0.5

polygon_monte_carlo_tests():
  Normal end of execution.
Wed Oct  8 08:46:31 2025