09-Nov-2022 09:01:27

maple_area_test():
  MATLAB/Octave version 4.2.2
  maple_area() estimates the area of the maple leaf from its image.

  Polygonal boundary involves 1776 vertices.
  Graphics saved as "maple_leaf.png"

maple_area_estimate_grid_test():
  maple_area_estimate_grid() is given a polygon defining the
  boundary of the maple leaf, using a regular NxN grid of
  points to estimate the relative area.
  Hayes got a relative area of 0.4185 using a 1024x1024 grid.

   I     N       N^2  Estimated relative area

   0     1         1        1.000000
   1     2         4        0.000000
   2     4        16        0.500000
   3     8        64        0.406250
   4    16       256        0.406250
   5    32      1024        0.417969
   6    64      4096        0.417480
   7   128     16384        0.417664
   8   256     65536        0.417557
   9   512    262144        0.417191
  10  1024   1048576        0.417447

maple_area_estimate_mc_test():
  maple_area_estimate_mc() is given a polygon defining the
  boundary of the maple leaf, and uses SAMPLE_NUM Monte Carlo
  points to estimate the relative area.
  Each computation is done 10 times.
  Hayes got a relative area of 0.4185 using a 1024x1024 grid.

   I  SAMPLE_NUM        Estimate        Variance

   0           1        0.400000        0.240000
   1           4        0.475000        0.043125
   2          16        0.418750        0.023477
   3          64        0.432812        0.004104
   4         256        0.442969        0.001078
   5        1024        0.406152        0.000135
   6        4096        0.413306        0.000071
   7       16384        0.416144        0.000011
   8       65536        0.417165        0.000002
   9      262144        0.417577        0.000001

maple_area_estimate_qmc_test():
  maple_area_estimate_qmc() is given a polygon defining the
  boundary of the maple leaf, and uses SAMPLE_NUM Quasi Monte Carlo
  points to estimate the relative area.
  Hayes got a relative area of 0.4185 using a 1024x1024 grid.

   I  SAMPLE_NUM        Estimate

   0           1        0.000000
   1           4        0.500000
   2          16        0.250000
   3          64        0.390625
   4         256        0.406250
   5        1024        0.416016
   6        4096        0.418213
   7       16384        0.417908
   8       65536        0.417328
   9      262144        0.417412
  10     1048576        0.417396

maple_area_test():
  Normal end of execution.

09-Nov-2022 09:20:23