SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 0 3 -50/1 0 9 -49/1 0 9 -48/1 0/1 1 9 0.020833 In 0.013889 0.027778 -47/1 1/1 1 9 0.021328 In 0.014085 0.028571 -46/1 0/1 1 9 0.021739 In 0.014493 0.028986 -45/1 1/1 2 9 0.022334 In 0.011625 0.033044 -44/1 0 9 -43/1 0 9 -42/1 0/1 1 9 0.023810 In 0.015873 0.031746 -41/1 1/1 1 9 0.024458 In 0.016129 0.032787 -40/1 0/1 1 9 0.025000 In 0.016667 0.033333 -39/1 1/1 2 9 0.025791 In 0.013392 0.038190 -38/1 0 9 -37/1 0 9 -36/1 0/1 1 9 0.027778 In 0.018519 0.037037 -35/1 1/1 1 9 0.028665 In 0.018868 0.038462 -34/1 0/1 1 9 0.029412 In 0.019608 0.039216 -33/1 1/1 2 9 0.030513 In 0.015792 0.045234 -32/1 0 9 -31/1 0 9 -30/1 0/1 1 9 0.033333 In 0.022222 0.044444 -29/1 1/1 1 9 0.034619 In 0.022727 0.046512 -28/1 0/1 1 9 0.035714 In 0.023810 0.047619 -27/1 1/1 2 9 0.037353 In 0.019242 0.055465 -26/1 0 9 -25/1 0 9 -24/1 0/1 1 9 0.041667 In 0.027778 0.055556 -23/1 1/1 1 9 0.043697 In 0.028571 0.058824 -22/1 0/1 1 9 0.045455 In 0.030303 0.060606 -21/1 1/1 2 9 0.048147 In 0.024619 0.071676 -20/1 0 9 -19/1 0 9 -18/1 0/1 1 9 0.055556 In 0.037037 0.074074 -17/1 1/1 1 9 0.059231 In 0.038462 0.080000 -16/1 0/1 1 9 0.062500 In 0.041667 0.083333 -15/1 1/1 2 9 0.067721 In 0.034166 0.101276 -14/1 0 9 -13/1 0 9 -12/1 0/1 1 9 0.083333 In 0.055556 0.111111 -11/1 1/1 1 9 0.091912 In 0.058824 0.125000 -10/1 0/1 1 9 0.100000 In 0.066667 0.133333 -9/1 1/1 2 9 0.114168 In 0.055810 0.172526 -8/1 0 9 -7/1 0 9 -6/1 0/1 1 9 0.166667 In 0.111111 0.222222 -5/1 1/1 1 9 0.205357 In 0.125000 0.285714 -4/1 0/1 1 9 0.250000 In 0.166667 0.333333 -3/1 1/1 2 9 0.367089 In 0.152271 0.581906 -2/1 0 9 -1/1 0 9 0/1 0/1 1 9 1/1 1/1 1 9 2/1 0/1 1 9 -0.500000 In -0.666667 -0.333333 3/1 1/1 2 9 -0.316456 In -0.423864 -0.209047 4/1 0 9 5/1 0 9 6/1 0/1 1 9 -0.166667 In -0.222222 -0.111111 7/1 1/1 1 9 -0.140909 In -0.181818 -0.100000 8/1 0/1 1 9 -0.125000 In -0.166667 -0.083333 9/1 1/1 2 9 -0.108666 In -0.155352 -0.061979 10/1 0 9 11/1 0 9 12/1 0/1 1 9 -0.083333 In -0.111111 -0.055556 13/1 1/1 1 9 -0.076316 In -0.100000 -0.052632 14/1 0/1 1 9 -0.071429 In -0.095238 -0.047619 15/1 1/1 2 9 -0.065744 In -0.095105 -0.036383 16/1 0 9 17/1 0 9 18/1 0/1 1 9 -0.055556 In -0.074074 -0.037037 19/1 1/1 1 9 -0.052340 In -0.068966 -0.035714 20/1 0/1 1 9 -0.050000 In -0.066667 -0.033333 21/1 1/1 2 9 -0.047139 In -0.068529 -0.025749 22/1 0 9 23/1 0 9 24/1 0/1 1 9 -0.041667 In -0.055556 -0.027778 25/1 1/1 1 9 -0.039829 In -0.052632 -0.027027 26/1 0/1 1 9 -0.038462 In -0.051282 -0.025641 27/1 1/1 2 9 -0.036743 In -0.053561 -0.019925 28/1 0 9 29/1 0 9 30/1 0/1 1 9 -0.033333 In -0.044444 -0.022222 31/1 1/1 1 9 -0.032146 In -0.042553 -0.021739 32/1 0/1 1 9 -0.031250 In -0.041667 -0.020833 33/1 1/1 2 9 -0.030105 In -0.043960 -0.016250 34/1 0 9 35/1 0 9 36/1 0/1 1 9 -0.027778 In -0.037037 -0.018519 37/1 1/1 1 9 -0.026948 In -0.035714 -0.018182 38/1 0/1 1 9 -0.026316 In -0.035088 -0.017544 39/1 1/1 2 9 -0.025499 In -0.037278 -0.013720 40/1 0 9 41/1 0 9 42/1 0/1 1 9 -0.023810 In -0.031746 -0.015873 43/1 1/1 1 9 -0.023197 In -0.030769 -0.015625 44/1 0/1 1 9 -0.022727 In -0.030303 -0.015152 45/1 1/1 2 9 -0.022115 In -0.032359 -0.011871 46/1 0 9 47/1 0 9 48/1 0/1 1 9 -0.020833 In -0.027778 -0.013889 49/1 1/1 1 9 -0.020363 In -0.027027 -0.013699 50/1 0/1 1 9 -0.020000 In -0.026667 -0.013333 -49/2 1/0 1 9 0.040818 In 0.040541 0.041096 -47/2 0 9 -45/2 1/0 2 9 0.044449 In 0.043984 0.044915 -43/2 1/2 1 9 0.046635 In 0.030769 0.062500 -41/2 0 9 -39/2 1/0 2 9 0.051290 In 0.050670 0.051909 -37/2 1/0 1 9 0.054058 In 0.053571 0.054545 -35/2 0 9 -33/2 1/0 2 9 0.060618 In 0.059752 0.061484 -31/2 1/2 1 9 0.064755 In 0.042553 0.086957 -29/2 0 9 -27/2 1/0 2 9 0.074097 In 0.072803 0.075390 -25/2 1/0 1 9 0.080014 In 0.078947 0.081081 -23/2 0 9 -21/2 1/0 2 9 0.095286 In 0.093147 0.097425 -19/2 1/2 1 9 0.105911 In 0.068966 0.142857 -17/2 0 9 -15/2 1/0 2 9 0.133465 In 0.129271 0.137660 -13/2 1/0 1 9 0.153947 In 0.150000 0.157895 -11/2 0 9 -9/2 1/0 2 9 0.222834 In 0.211162 0.234505 -7/2 1/2 1 9 0.290909 In 0.181818 0.400000 -5/2 0 9 -3/2 1/0 2 9 0.683544 In 0.576136 0.790953 -1/2 1/0 1 9 2.250000 In 1.500000 3.000000 1/2 0 9 3/2 1/0 2 9 -0.683544 In -0.790953 -0.576136 5/2 1/2 1 9 -0.392857 In -0.500000 -0.285714 7/2 0 9 9/2 1/0 2 9 -0.222834 In -0.234505 -0.211162 11/2 1/0 1 9 -0.181985 In -0.187500 -0.176471 13/2 0 9 15/2 1/0 2 9 -0.133465 In -0.137660 -0.129271 17/2 1/2 1 9 -0.116923 In -0.153846 -0.080000 19/2 0 9 21/2 1/0 2 9 -0.095286 In -0.097425 -0.093147 23/2 1/0 1 9 -0.086975 In -0.088235 -0.085714 25/2 0 9 27/2 1/0 2 9 -0.074097 In -0.075390 -0.072803 29/2 1/2 1 9 -0.068710 In -0.090909 -0.046512 31/2 0 9 33/2 1/0 2 9 -0.060618 In -0.061484 -0.059752 35/2 1/0 1 9 -0.057148 In -0.057692 -0.056604 37/2 0 9 39/2 1/0 2 9 -0.051290 In -0.051909 -0.050670 41/2 1/2 1 9 -0.048652 In -0.064516 -0.032787 43/2 0 9 45/2 1/0 2 9 -0.044449 In -0.044915 -0.043984 47/2 1/0 1 9 -0.042555 In -0.042857 -0.042254 49/2 0 9 -50/3 1/1 1 3 0.060141 In 0.047900 0.072383 -49/3 0/1 1 3 0.061224 In 0.049442 0.073007 -47/3 0 3 -46/3 1/1 3 3 0.065721 In 0.042553 0.088889 -44/3 1/1 5 3 0.069102 In 0.037734 0.100470 -43/3 1/1 3 3 0.070346 In 0.045455 0.095238 -41/3 1/0 3 3 0.073214 In 0.071429 0.075000 -40/3 1/0 2 3 0.075031 In 0.073500 0.076563 -38/3 0/1 1 3 0.078947 In 0.063754 0.094141 -37/3 0/1 2 3 0.081081 In 0.059014 0.103149 -35/3 0 3 -34/3 1/1 2 3 0.088863 In 0.062715 0.115012 -32/3 1/1 1 3 0.094106 In 0.074366 0.113846 -31/3 0/1 1 3 0.096774 In 0.078150 0.115398 -29/3 0 3 -28/3 1/1 3 3 0.108557 In 0.068966 0.148148 -26/3 1/1 5 3 0.118141 In 0.062622 0.173661 -25/3 1/1 3 3 0.121795 In 0.076923 0.166667 -23/3 1/0 3 3 0.130682 In 0.125000 0.136364 -22/3 1/0 2 3 0.136552 In 0.131484 0.141620 -20/3 0/1 1 3 0.150000 In 0.121132 0.178868 -19/3 0/1 2 3 0.157895 In 0.114921 0.200868 -17/3 0 3 -16/3 1/1 2 3 0.190601 In 0.129843 0.251358 -14/3 1/1 1 3 0.216354 In 0.166193 0.266516 -13/3 0/1 1 3 0.230769 In 0.186358 0.275181 -11/3 0 3 -10/3 1/1 3 3 0.313131 In 0.181818 0.444444 -8/3 1/1 5 3 0.411765 In 0.183942 0.639587 -7/3 1/1 3 3 0.458333 In 0.250000 0.666667 -5/3 1/0 3 3 0.625000 In 0.500000 0.750000 -4/3 1/0 2 3 0.782609 In 0.622859 0.942358 -2/3 0/1 1 3 1.500000 In 1.211325 1.788675 -1/3 0/1 2 3 3.000000 In 2.183503 3.816497 1/3 0 3 2/3 1/1 2 3 -1.600000 In -1.844949 -1.355051 4/3 1/1 1 3 -0.744681 In -0.781533 -0.707829 5/3 0/1 1 3 -0.600000 In -0.715470 -0.484530 7/3 0 3 8/3 1/1 3 3 -0.365079 In -0.444444 -0.285714 10/3 1/1 5 3 -0.288136 In -0.380037 -0.196234 11/3 1/1 3 3 -0.266667 In -0.333333 -0.200000 13/3 1/0 3 3 -0.232143 In -0.250000 -0.214286 14/3 1/0 2 3 -0.215017 In -0.227557 -0.202477 16/3 0/1 1 3 -0.187500 In -0.223584 -0.151416 17/3 0/1 2 3 -0.176471 In -0.224500 -0.128441 19/3 0 3 20/3 1/1 2 3 -0.148581 In -0.183340 -0.113822 22/3 1/1 1 3 -0.135768 In -0.158449 -0.113088 23/3 0/1 1 3 -0.130435 In -0.155537 -0.105333 25/3 0 3 26/3 1/1 3 3 -0.114074 In -0.148148 -0.080000 28/3 1/1 5 3 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-27/4 1/0 2 9 0.148193 In 0.145606 0.150781 -25/4 0 9 -23/4 1/2 1 9 0.174370 In 0.142857 0.205882 -21/4 1/0 2 9 0.190572 In 0.186294 0.194850 -19/4 0 9 -17/4 1/0 1 9 0.235385 In 0.230769 0.240000 -15/4 1/2 2 9 0.268908 In 0.197603 0.340212 -13/4 0 9 -11/4 1/2 1 9 0.365809 In 0.294118 0.437500 -9/4 3/2 2 9 0.472574 In 0.293559 0.651588 -7/4 0 9 -5/4 1/0 1 9 0.803571 In 0.750000 0.857143 -3/4 1/0 2 9 1.367089 In 1.152271 1.581906 -1/4 0 9 1/4 1/2 1 9 -4.250000 In -5.000000 -3.500000 3/4 1/0 2 9 -1.367089 In -1.581906 -1.152271 5/4 0 9 7/4 1/0 1 9 -0.572727 In -0.600000 -0.545455 9/4 1/2 2 9 -0.440165 In -0.521867 -0.358464 11/4 0 9 13/4 1/2 1 9 -0.306579 In -0.350000 -0.263158 15/4 3/2 2 9 -0.263079 In -0.301130 -0.225029 17/4 0 9 19/4 1/0 1 9 -0.210591 In -0.214286 -0.206897 21/4 1/0 2 9 -0.190572 In -0.194850 -0.186294 23/4 0 9 25/4 1/2 1 9 -0.159673 In -0.184211 -0.135135 27/4 1/0 2 9 -0.148193 In -0.150781 -0.145606 29/4 0 9 31/4 1/0 1 9 -0.129047 In -0.130435 -0.127660 33/4 1/2 2 9 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0.222222 -23/5 0 9 -22/5 0 9 -21/5 1/1 2 9 0.238719 In 0.210913 0.266526 -19/5 1/1 1 9 0.263547 In 0.241379 0.285714 -18/5 0/1 1 9 0.277778 In 0.259259 0.296296 -17/5 0 9 -16/5 0 9 -14/5 0/1 1 9 0.357143 In 0.333333 0.380952 -13/5 1/1 1 9 0.385526 In 0.350000 0.421053 -12/5 0/1 1 9 0.416667 In 0.388889 0.444444 -11/5 0 9 -9/5 1/1 2 9 0.559835 In 0.478133 0.641536 -8/5 0/1 1 9 0.625000 In 0.583333 0.666667 -7/5 1/1 1 9 0.718182 In 0.636364 0.800000 -6/5 0/1 1 9 0.833333 In 0.777778 0.888889 -4/5 0 9 -3/5 1/1 2 9 1.734177 In 1.304543 2.163812 -2/5 0/1 1 9 2.500000 In 2.333333 2.666667 -1/5 1/1 1 9 5.750000 In 3.500000 8.000000 1/5 0 9 2/5 0 9 3/5 1/1 2 9 -1.683544 In -1.790953 -1.576136 4/5 0/1 1 9 -1.250000 In -1.333333 -1.166667 6/5 0/1 1 9 -0.833333 In -0.888889 -0.777778 7/5 0 9 8/5 0 9 9/5 1/1 2 9 -0.554333 In -0.577676 -0.530990 11/5 1/1 1 9 -0.454044 In -0.470588 -0.437500 12/5 0/1 1 9 -0.416667 In -0.444444 -0.388889 13/5 0 9 14/5 0 9 16/5 0/1 1 9 -0.312500 In -0.333333 -0.291667 17/5 1/1 1 9 -0.293846 In -0.307692 -0.280000 18/5 0/1 1 9 -0.277778 In -0.296296 -0.259259 19/5 0 9 21/5 1/1 2 9 -0.237711 In -0.254823 -0.220599 22/5 0/1 1 9 -0.227273 In -0.242424 -0.212121 23/5 1/1 1 9 -0.217227 In -0.228571 -0.205882 24/5 0/1 1 9 -0.208333 In -0.222222 -0.194444 26/5 0 9 27/5 1/1 2 9 -0.184937 In -0.199167 -0.170706 28/5 0/1 1 9 -0.178571 In -0.190476 -0.166667 29/5 1/1 1 9 -0.172304 In -0.181818 -0.162791 31/5 0 9 32/5 0 9 33/5 1/1 2 9 -0.151342 In -0.163465 -0.139219 34/5 0/1 1 9 -0.147059 In -0.156863 -0.137255 36/5 0/1 1 9 -0.138889 In -0.148148 -0.129630 37/5 0 9 38/5 0 9 39/5 1/1 2 9 -0.128078 In -0.138617 -0.117539 41/5 1/1 1 9 -0.121893 In -0.129032 -0.114754 42/5 0/1 1 9 -0.119048 In -0.126984 -0.111111 43/5 0 9 44/5 0 9 46/5 0/1 1 9 -0.108696 In -0.115942 -0.101449 47/5 1/1 1 9 -0.106338 In -0.112676 -0.100000 48/5 0/1 1 9 -0.104167 In -0.111111 -0.097222 49/5 0 9 -49/6 0 3 -47/6 1/0 3 3 0.127717 In 0.125000 0.130435 -43/6 1/0 2 3 0.139585 In 0.136935 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