Tue May 20 22:23:37 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
         3.44627
        0.733261
         2.96919
        0.631753
        0.134418
         2.55815

         2
               4
         1.92803
         2.10592
           1.793
          1.6511
         1.57711
         1.69683

         4
               4
        0.533295
         1.25617
        0.162319
       0.0574023
        0.693776
       0.0578148

         8
               4
        0.757376
          1.4847
        0.261917
        0.345459
        0.825306
        0.118925

        16
               4
          1.2511
         2.20797
        0.826602
         0.86879
         1.64841
        0.636602

        32
               4
         1.09201
        0.937238
        0.559479
          0.2412
        0.463564
        0.363904

        64
               4
         1.51128
         1.51796
        0.909922
        0.636685
          1.0299
        0.634983

       128
               4
         1.52089
         1.33885
        0.958077
        0.536446
        0.858612
        0.696327

       256
               4
         1.32801
         1.31393
         0.78685
        0.400116
        0.791055
        0.552732

       512
               4
          1.3394
         1.26214
         0.81803
        0.425105
        0.743687
        0.589995

      1024
               4
         1.25946
         1.36262
        0.747009
        0.431065
        0.809894
        0.530454

      2048
               4
         1.36577
         1.36424
        0.824554
        0.460815
        0.822339
         0.58833

      4096
               4
         1.32216
         1.31427
        0.794508
        0.435841
        0.779003
        0.568904

      8192
               4
         1.33206
         1.32973
        0.802367
        0.440347
        0.801549
        0.573611

     16384
               4
         1.31681
         1.33521
        0.790111
        0.443484
        0.799483
         0.56461

     32768
               4
         1.33263
         1.34036
        0.801762
        0.443872
        0.802968
         0.57368

     65536
               4
         1.33446
         1.33524
         0.79924
        0.446981
         0.80166
        0.569779

     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 :
     1.82104  
    0.522831  

      1 :
     1.61785  
    0.131905  

      2 :
    0.652112  
    0.425723  

      3 :
     1.38654  
    0.331994  

      4 :
    0.850585  
    0.510205  

      5 :
    0.956804  
     1.00754  

      6 :
     1.34748  
    0.544832  

      7 :
    0.477846  
    0.919631  

      8 :
    0.484308  
    0.191593  

      9 :
     1.87669  
    0.195659  

     10 :
     1.99878  
   0.0927686  

     11 :
     1.81376  
    0.384585  

     12 :
    0.560039  
    0.856172  

     13 :
    0.492912  
    0.749735  

     14 :
    0.978347  
     1.66708  

     15 :
    0.927472  
    0.586975  

     16 :
    0.431515  
    0.710474  

     17 :
    0.835149  
     1.77168  

     18 :
    0.239433  
    0.181136  

     19 :
    0.664188  
    0.828129  


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.
Tue May 20 22:23:38 2025