07-Jan-2022 22:55:41 maple_area_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 maple_area() estimates the area of the maple leaf from its image. Polygonal boundary involves 1776 vertices. 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 0.200000 0.160000 1 4 0.450000 0.035000 2 16 0.450000 0.020156 3 64 0.442188 0.002249 4 256 0.432031 0.000620 5 1024 0.420605 0.000147 6 4096 0.418042 0.000041 7 16384 0.419397 0.000012 8 65536 0.417180 0.000002 9 262144 0.416997 0.000000 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. 07-Jan-2022 23:00:19