SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 0 8 -50/1 0 8 -49/1 0 4 -48/1 0 8 -47/1 1/0 1 2 0.021281 In 0.020961 0.021602 -46/1 0 8 -45/1 0 4 -44/1 0 8 -43/1 1/1 1 2 0.023533 In 0.006701 0.040364 -42/1 0 8 -41/1 0 4 -40/1 0 8 -39/1 1/1 1 2 0.025978 In 0.007376 0.044580 -38/1 0 8 -37/1 0 4 -36/1 0 8 -35/1 1/1 1 2 0.028991 In 0.008203 0.049780 -34/1 0 8 -33/1 0 4 -32/1 0 8 -31/1 1/0 1 2 0.032275 In 0.031539 0.033011 -30/1 0 8 -29/1 0 4 -28/1 0 8 -27/1 1/1 1 2 0.037749 In 0.010571 0.064927 -26/1 0 8 -25/1 0 4 -24/1 0 8 -23/1 1/1 1 2 0.044465 In 0.012355 0.076576 -22/1 0 8 -21/1 0 4 -20/1 0 8 -19/1 1/1 1 2 0.054092 In 0.014862 0.093321 -18/1 0 8 -17/1 0 4 -16/1 0 8 -15/1 1/0 1 2 0.066815 In 0.063665 0.069965 -14/1 0 8 -13/1 0 4 -12/1 0 8 -11/1 1/1 1 2 0.095436 In 0.025018 0.165853 -10/1 0 8 -9/1 0 4 -8/1 0 8 -7/1 1/1 1 2 0.154639 In 0.038003 0.271275 -6/1 0 8 -5/1 0 4 -4/1 0 8 -3/1 1/1 1 2 0.411765 In 0.079009 0.744521 -2/1 0 8 -1/1 0 4 0/1 0 8 1/1 1/0 1 2 -2.000000 In -3.414214 -0.585786 2/1 0 8 3/1 0 4 4/1 0 8 5/1 1/1 1 2 -0.183673 In -0.299119 -0.068227 6/1 0 8 7/1 0 4 8/1 0 8 9/1 1/1 1 2 -0.105590 In -0.175862 -0.035319 10/1 0 8 11/1 0 4 12/1 0 8 13/1 1/1 1 2 -0.074184 In -0.124542 -0.023826 14/1 0 8 15/1 0 4 16/1 0 8 17/1 1/0 1 2 -0.058925 In -0.061376 -0.056474 18/1 0 8 19/1 0 4 20/1 0 8 21/1 1/1 1 2 -0.046538 In -0.078643 -0.014433 22/1 0 8 23/1 0 4 24/1 0 8 25/1 1/1 1 2 -0.039231 In -0.066406 -0.012057 26/1 0 8 27/1 0 4 28/1 0 8 29/1 1/1 1 2 -0.033908 In -0.057465 -0.010352 30/1 0 8 31/1 0 4 32/1 0 8 33/1 1/0 1 2 -0.030317 In -0.030967 -0.029667 34/1 0 8 35/1 0 4 36/1 0 8 37/1 1/1 1 2 -0.026672 In -0.045273 -0.008070 38/1 0 8 39/1 0 4 40/1 0 8 41/1 1/1 1 2 -0.024100 In -0.040931 -0.007269 42/1 0 8 43/1 0 4 44/1 0 8 45/1 1/1 1 2 -0.021981 In -0.037349 -0.006613 46/1 0 8 47/1 0 4 48/1 0 8 49/1 1/0 1 2 -0.020412 In -0.020707 -0.020118 50/1 0 8 -49/2 2/1 1 8 0.040929 In 0.033123 0.048735 -47/2 0/1 1 8 0.042553 In 0.035031 0.050076 -45/2 2/1 1 8 0.044579 In 0.036022 0.053136 -43/2 0/1 1 8 0.046512 In 0.038289 0.054734 -41/2 2/1 1 8 0.048944 In 0.039476 0.058411 -39/2 0/1 1 8 0.051282 In 0.042217 0.060348 -37/2 2/1 1 8 0.054256 In 0.043664 0.064849 -35/2 2/1 1 8 0.057370 In 0.046110 0.068631 -33/2 2/1 1 8 0.060864 In 0.048846 0.072881 -31/2 2/1 1 8 0.064810 In 0.051927 0.077693 -29/2 0/1 1 8 0.068966 In 0.056774 0.081157 -27/2 0/1 1 8 0.074074 In 0.060980 0.087169 -25/2 0/1 1 8 0.080000 In 0.065858 0.094142 -23/2 0/1 1 8 0.086957 In 0.071585 0.102328 -21/2 2/1 1 8 0.095914 In 0.075848 0.115979 -19/2 0/1 1 8 0.105263 In 0.086655 0.123871 -17/2 2/1 1 8 0.118718 In 0.092982 0.144453 -15/2 0/1 1 8 0.133333 In 0.109763 0.156904 -13/2 2/1 1 8 0.155786 In 0.120116 0.191456 -11/2 0/1 1 8 0.181818 In 0.149677 0.213959 -9/2 2/1 1 8 0.226708 In 0.169612 0.283804 -7/2 0/1 1 8 0.285714 In 0.235207 0.336222 -5/2 2/1 1 8 0.418367 In 0.288491 0.548244 -3/2 2/1 1 8 0.735294 In 0.444133 1.026456 -1/2 2/1 1 8 4.500000 In 0.964466 8.035534 1/2 2/1 1 8 -3.500000 In -5.621320 -1.378680 3/2 0/1 1 8 -0.666667 In -0.784518 -0.548816 5/2 0/1 1 8 -0.400000 In -0.470711 -0.329289 7/2 0/1 1 8 -0.285714 In -0.336222 -0.235207 9/2 0/1 1 8 -0.222222 In -0.261506 -0.182939 11/2 2/1 1 8 -0.180498 In -0.201036 -0.159960 13/2 0/1 1 8 -0.153846 In -0.181043 -0.126650 15/2 2/1 1 8 -0.132517 In -0.149840 -0.115193 17/2 0/1 1 8 -0.117647 In -0.138444 -0.096850 19/2 2/1 1 8 -0.104716 In -0.119427 -0.090005 21/2 0/1 1 8 -0.095238 In -0.112074 -0.078402 23/2 2/1 1 8 -0.086566 In -0.099276 -0.073855 25/2 0/1 1 8 -0.080000 In -0.094142 -0.065858 27/2 2/1 1 8 -0.073782 In -0.084944 -0.062619 29/2 2/1 1 8 -0.068709 In -0.079225 -0.058193 31/2 2/1 1 8 -0.064289 In -0.074228 -0.054351 33/2 2/1 1 8 -0.060404 In -0.069824 -0.050985 35/2 0/1 1 8 -0.057143 In -0.067244 -0.047041 37/2 0/1 1 8 -0.054054 In -0.063610 -0.044499 39/2 0/1 1 8 -0.051282 In -0.060348 -0.042217 41/2 0/1 1 8 -0.048780 In -0.057404 -0.040157 43/2 2/1 1 8 -0.046389 In -0.053848 -0.038930 45/2 0/1 1 8 -0.044444 In -0.052301 -0.036588 47/2 2/1 1 8 -0.042450 In -0.049333 -0.035566 49/2 0/1 1 8 -0.040816 In -0.048032 -0.033601 -50/3 0 8 -49/3 1/0 2 2 0.061250 In 0.060000 0.062500 -47/3 0 4 -46/3 0 8 -44/3 0 8 -43/3 0 4 -41/3 1/0 2 2 0.073214 In 0.071429 0.075000 -40/3 0 8 -38/3 0 8 -37/3 1/1 1 2 0.081476 In 0.060808 0.102144 -35/3 0 4 -34/3 0 8 -32/3 0 8 -31/3 0 4 -29/3 1/0 3 2 0.103633 In 0.099256 0.108010 -28/3 0 8 -26/3 0 8 -25/3 1/0 2 2 0.120192 In 0.115385 0.125000 -23/3 0 4 -22/3 0 8 -20/3 0 8 -19/3 0 4 -17/3 1/0 2 2 0.177083 In 0.166667 0.187500 -16/3 0 8 -14/3 0 8 -13/3 1/0 3 2 0.232836 In 0.210900 0.254772 -11/3 0 4 -10/3 0 8 -8/3 0 8 -7/3 0 4 -5/3 1/1 1 2 0.632653 In 0.401761 0.863545 -4/3 0 8 -2/3 0 8 -1/3 1/0 2 2 1.500000 Right 1/3 0 4 2/3 0 8 4/3 0 8 5/3 0 4 7/3 1/0 2 2 -0.437500 In -0.500000 -0.375000 8/3 0 8 10/3 0 8 11/3 1/1 1 2 -0.269710 In -0.316654 -0.222765 13/3 0 4 14/3 0 8 16/3 0 8 17/3 0 4 19/3 1/0 3 2 -0.158554 In -0.168774 -0.148333 20/3 0 8 22/3 0 8 23/3 1/0 2 2 -0.130682 In -0.136364 -0.125000 25/3 0 4 26/3 0 8 28/3 0 8 29/3 0 4 31/3 1/0 2 2 -0.096875 In -0.100000 -0.093750 32/3 0 8 34/3 0 8 35/3 1/0 3 2 -0.085819 In -0.088822 -0.082816 37/3 0 4 38/3 0 8 40/3 0 8 41/3 0 4 43/3 1/1 1 2 -0.069516 In -0.084817 -0.054215 44/3 0 8 46/3 0 8 47/3 1/0 2 2 -0.063859 In -0.065217 -0.062500 49/3 0 4 50/3 0 8 -49/4 0 8 -47/4 0 8 -45/4 0 8 -43/4 0 8 -41/4 0 8 -39/4 0 8 -37/4 0 8 -35/4 0 8 -33/4 0 8 -31/4 0 8 -29/4 0 8 -27/4 0 8 -25/4 0 8 -23/4 0 8 -21/4 0 8 -19/4 0 8 -17/4 0 8 -15/4 0 8 -13/4 0 8 -11/4 0 8 -9/4 0 8 -7/4 0 8 -5/4 0 8 -3/4 0 8 -1/4 0 8 1/4 0 8 3/4 0 8 5/4 0 8 7/4 0 8 9/4 0 8 11/4 0 8 13/4 0 8 15/4 0 8 17/4 0 8 19/4 0 8 21/4 0 8 23/4 0 8 25/4 0 8 27/4 0 8 29/4 0 8 31/4 0 8 33/4 0 8 35/4 0 8 37/4 0 8 39/4 0 8 41/4 0 8 43/4 0 8 45/4 0 8 47/4 0 8 49/4 0 8 -49/5 0 4 -48/5 0 8 -47/5 1/1 1 2 0.106633 In 0.089984 0.123283 -46/5 0 8 -44/5 0 8 -43/5 1/1 4 2 0.117488 In 0.080735 0.154241 -42/5 0 8 -41/5 0 4 -39/5 1/1 1 2 0.128576 In 0.108114 0.149038 -38/5 0 8 -37/5 0 4 -36/5 0 8 -34/5 0 8 -33/5 0 4 -32/5 0 8 -31/5 1/1 1 2 0.161895 In 0.135392 0.188398 -29/5 0 4 -28/5 0 8 -27/5 1/1 4 2 0.188446 In 0.126197 0.250694 -26/5 0 8 -24/5 0 8 -23/5 1/1 1 2 0.218543 In 0.181080 0.256006 -22/5 0 8 -21/5 0 4 -19/5 0/1 1 2 0.263158 In 0.225942 0.300374 -18/5 0 8 -17/5 0 4 -16/5 0 8 -14/5 0 8 -13/5 0 4 -12/5 0 8 -11/5 1/1 4 2 0.478992 In 0.288845 0.669138 -9/5 0 4 -8/5 0 8 -7/5 1/1 1 2 0.731959 In 0.557005 0.906913 -6/5 0 8 -4/5 0 8 -3/5 2/1 1 2 2.285714 In 0.972516 3.598913 -2/5 0 8 -1/5 0 4 1/5 1/1 1 2 -9.000000 In -14.656854 -3.343146 2/5 0 8 3/5 0 4 4/5 0 8 6/5 0 8 7/5 0 4 8/5 0 8 9/5 1/1 1 2 -0.552795 In -0.587931 -0.517659 11/5 0 4 12/5 0 8 13/5 0/1 1 2 -0.384615 In -0.439008 -0.330223 14/5 0 8 16/5 0 8 17/5 1/1 1 2 -0.292894 In -0.322306 -0.263483 18/5 0 8 19/5 0 4 21/5 1/1 4 2 -0.234624 In -0.286167 -0.183081 22/5 0 8 23/5 0 4 24/5 0 8 26/5 0 8 27/5 0 4 28/5 0 8 29/5 2/1 1 2 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1.234694 In 0.989371 1.480017 -1/6 2/1 1 8 12.500000 In 3.307612 21.692388 1/6 0/1 1 8 -6.000000 In -6.353553 -5.646447 5/6 4/1 1 8 -1.282609 In -1.574675 -0.990543 7/6 -2/1 1 8 -0.871134 In -1.009639 -0.732629 11/6 2/1 1 8 -0.545643 In -0.548577 -0.542709 13/6 0/1 1 8 -0.461538 In -0.488735 -0.434342 17/6 0/1 1 8 -0.352941 In -0.373738 -0.332144 19/6 0/1 1 8 -0.315789 In -0.334398 -0.297181 23/6 0/1 1 8 -0.260870 In -0.276241 -0.245498 25/6 2/3 1 8 -0.238991 In -0.274658 -0.203324 29/6 2/3 1 8 -0.206127 In -0.237676 -0.174579 31/6 4/3 1 8 -0.192388 In -0.217826 -0.166950 35/6 2/1 1 8 -0.171294 In -0.177935 -0.164654 37/6 2/1 1 8 -0.162039 In -0.168498 -0.155580 41/6 2/1 1 8 -0.146236 In -0.152337 -0.140135 43/6 0/1 1 8 -0.139535 In -0.147757 -0.131313 47/6 0/1 1 8 -0.127660 In -0.135182 -0.120137 49/6 0/1 1 8 -0.122449 In -0.129664 -0.115234 -50/7 0 8 -48/7 0 8 -47/7 0 4 -46/7 0 8 -45/7 2/1 1 2 0.156204 In 0.135581 0.176826 -44/7 0 8 -43/7 0 4 -41/7 2/1 3 2 0.173134 In 0.132919 0.213350 -40/7 0 8 -39/7 0 4 -38/7 0 8 -37/7 2/1 1 2 0.190198 In 0.163817 0.216578 -36/7 0 8 -34/7 0 8 -33/7 1/0 2 2 0.212316 In 0.205882 0.218750 -32/7 0 8 -31/7 0 4 -30/7 0 8 -29/7 0/1 1 2 0.241379 In 0.216996 0.265762 -27/7 0 4 -26/7 0 8 -25/7 0/1 3 2 0.280000 In 0.231010 0.328990 -24/7 0 8 -23/7 0 4 -22/7 0 8 -20/7 0 8 -19/7 0 4 -18/7 0 8 -17/7 1/0 2 2 0.413194 In 0.388889 0.437500 -16/7 0 8 -15/7 0 4 -13/7 2/1 1 2 0.550898 In 0.436576 0.665221 -12/7 0 8 -11/7 0 4 -10/7 0 8 -9/7 2/1 3 2 0.880000 In 0.504412 1.255588 -8/7 0 8 -6/7 0 8 -5/7 2/1 1 2 1.565217 In 0.981086 2.149349 -4/7 0 8 -3/7 0 4 -2/7 0 8 -1/7 1/0 2 2 3.500000 Right 1/7 0 4 2/7 0 8 3/7 2/1 1 2 -2.857143 In -3.968311 -1.745975 4/7 0 8 5/7 0 4 6/7 0 8 8/7 0 8 9/7 0 4 10/7 0 8 11/7 0/1 1 2 -0.636364 In -0.700646 -0.572081 12/7 0 8 13/7 0 4 15/7 1/0 2 2 -0.468750 In -0.500000 -0.437500 16/7 0 8 17/7 0 4 18/7 0 8 19/7 0/1 1 2 -0.368421 In -0.405637 -0.331205 20/7 0 8 22/7 0 8 23/7 0/1 3 2 -0.304348 In -0.357598 -0.251098 24/7 0 8 25/7 0 4 26/7 0 8 27/7 0/1 1 2 -0.259259 In -0.285448 -0.233070 29/7 0 4 30/7 0 8 31/7 1/0 2 2 -0.226042 In -0.233333 -0.218750 32/7 0 8 33/7 0 4 34/7 0 8 36/7 0 8 37/7 0 4 38/7 0 8 39/7 2/1 3 2 -0.178218 In -0.198428 -0.158008 40/7 0 8 41/7 0 4 43/7 2/1 1 2 -0.162426 In -0.173528 -0.151323 44/7 0 8 45/7 0 4 46/7 0 8 47/7 1/0 2 2 -0.149004 In -0.152174 -0.145833 48/7 0 8 50/7 0 8 -49/8 0 8 -47/8 0 8 -45/8 0 8 -43/8 0 8 -41/8 0 8 -39/8 0 8 -37/8 0 8 -35/8 0 8 -33/8 0 8 -31/8 0 8 -29/8 0 8 -27/8 0 8 -25/8 0 8 -23/8 0 8 -21/8 0 8 -19/8 0 8 -17/8 0 8 -15/8 0 8 -13/8 0 8 -11/8 0 8 -9/8 0 8 -7/8 0 8 -5/8 0 8 -3/8 0 8 -1/8 0 8 1/8 0 8 3/8 0 8 5/8 0 8 7/8 0 8 9/8 0 8 11/8 0 8 13/8 0 8 15/8 0 8 17/8 0 8 19/8 0 8 21/8 0 8 23/8 0 8 25/8 0 8 27/8 0 8 29/8 0 8 31/8 0 8 33/8 0 8 35/8 0 8 37/8 0 8 39/8 0 8 41/8 0 8 43/8 0 8 45/8 0 8 47/8 0 8 49/8 0 8 -50/9 0 8 -49/9 0 4 -47/9 1/0 2 2 0.191576 In 0.187500 0.195652 -46/9 0 8 -44/9 0 8 -43/9 2/1 1 2 0.210070 In 0.186717 0.233424 -41/9 0 4 -40/9 0 8 -38/9 0 8 -37/9 0 4 -35/9 0/1 1 2 0.257143 In 0.236940 0.277346 -34/9 0 8 -32/9 0 8 -31/9 1/2 2 2 0.292708 In 0.218750 0.366667 -29/9 0 4 -28/9 0 8 -26/9 0 8 -25/9 0 4 -23/9 2/1 3 2 0.401530 In 0.305517 0.497542 -22/9 0 8 -20/9 0 8 -19/9 2/1 1 2 0.479109 In 0.406231 0.551986 -17/9 0 4 -16/9 0 8 -14/9 0 8 -13/9 0 4 -11/9 2/1 1 2 0.840336 In 0.668016 1.012656 -10/9 0 8 -8/9 0 8 -7/9 2/1 3 2 1.534884 In 0.822823 2.246945 -5/9 0 4 -4/9 0 8 -2/9 0 8 -1/9 0 4 1/9 1/0 2 2 -4.500000 Left 2/9 0 8 4/9 0 8 5/9 2/1 1 2 -1.913043 In -2.312713 -1.513374 7/9 0 4 8/9 0 8 10/9 0 8 11/9 0 4 13/9 0/1 1 2 -0.692308 In -0.746701 -0.637915 14/9 0 8 16/9 0 8 17/9 1/0 2 2 -0.531250 In -0.562500 -0.500000 19/9 0 4 20/9 0 8 22/9 0 8 23/9 0 4 25/9 0/1 3 2 -0.360000 In -0.408990 -0.311010 26/9 0 8 28/9 0 8 29/9 0/1 1 2 -0.310345 In -0.334728 -0.285962 31/9 0 4 32/9 0 8 34/9 0 8 35/9 0 4 37/9 0/1 1 2 -0.243243 In -0.262354 -0.224132 38/9 0 8 40/9 0 8 41/9 0/1 3 2 -0.219512 In -0.249384 -0.189640 43/9 0 4 44/9 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