SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 0 4 -50/1 0 4 -49/1 0/1 1 4 0.020408 In 0.010204 0.030612 -48/1 0/1 2 4 0.020833 In 0.006102 0.035565 -47/1 0/1 1 4 0.021277 In 0.010638 0.031915 -46/1 0 4 -45/1 1/1 1 4 0.022348 In 0.010989 0.033708 -44/1 1/1 2 4 0.022991 In 0.006551 0.039432 -43/1 1/1 1 4 0.023394 In 0.011494 0.035294 -42/1 0 4 -41/1 0/1 1 4 0.024390 In 0.012195 0.036585 -40/1 0/1 2 4 0.025000 In 0.007322 0.042678 -39/1 0/1 1 4 0.025641 In 0.012821 0.038462 -38/1 0 4 -37/1 1/1 1 4 0.027215 In 0.013333 0.041096 -36/1 1/1 2 4 0.028174 In 0.007979 0.048370 -35/1 1/1 1 4 0.028781 In 0.014085 0.043478 -34/1 0 4 -33/1 0/1 1 4 0.030303 In 0.015152 0.045455 -32/1 0/1 2 4 0.031250 In 0.009153 0.053347 -31/1 0/1 1 4 0.032258 In 0.016129 0.048387 -30/1 0 4 -29/1 1/1 1 4 0.034790 In 0.016949 0.052632 -28/1 1/1 2 4 0.036375 In 0.010203 0.062548 -27/1 1/1 1 4 0.037393 In 0.018182 0.056604 -26/1 0 4 -25/1 0/1 1 4 0.040000 In 0.020000 0.060000 -24/1 0/1 2 4 0.041667 In 0.012204 0.071129 -23/1 0/1 1 4 0.043478 In 0.021739 0.065217 -22/1 0 4 -21/1 1/1 1 4 0.048213 In 0.023256 0.073171 -20/1 1/1 2 4 0.051314 In 0.014145 0.088484 -19/1 1/1 1 4 0.053361 In 0.025641 0.081081 -18/1 0 4 -17/1 0/1 1 4 0.058824 In 0.029412 0.088235 -16/1 0/1 2 4 0.062500 In 0.018306 0.106694 -15/1 0/1 1 4 0.066667 In 0.033333 0.100000 -14/1 0 4 -13/1 1/1 1 4 0.078519 In 0.037037 0.120000 -12/1 1/1 2 4 0.087108 In 0.023050 0.151166 -11/1 1/1 1 4 0.093168 In 0.043478 0.142857 -10/1 0 4 -9/1 0/1 1 4 0.111111 In 0.055556 0.166667 -8/1 0/1 2 4 0.125000 In 0.036612 0.213388 -7/1 0/1 1 4 0.142857 In 0.071429 0.214286 -6/1 0 4 -5/1 1/1 1 4 0.212121 In 0.090909 0.333333 -4/1 1/1 2 4 0.290323 In 0.062224 0.518422 -3/1 1/1 1 4 0.371429 In 0.142857 0.600000 -2/1 0 4 -1/1 0/1 1 4 1.000000 In 0.500000 1.500000 0/1 0/1 2 4 1/1 0/1 1 4 -1.000000 In -1.500000 -0.500000 2/1 0 4 3/1 1/1 1 4 -0.314286 In -0.428571 -0.200000 4/1 1/1 2 4 -0.225806 In -0.362666 -0.088947 5/1 1/1 1 4 -0.191919 In -0.272727 -0.111111 6/1 0 4 7/1 0/1 1 4 -0.142857 In -0.214286 -0.071429 8/1 0/1 2 4 -0.125000 In -0.213388 -0.036612 9/1 0/1 1 4 -0.111111 In -0.166667 -0.055556 10/1 0 4 11/1 1/1 1 4 -0.089027 In -0.130435 -0.047619 12/1 1/1 2 4 -0.080139 In -0.134343 -0.025936 13/1 1/1 1 4 -0.075556 In -0.111111 -0.040000 14/1 0 4 15/1 0/1 1 4 -0.066667 In -0.100000 -0.033333 16/1 0/1 2 4 -0.062500 In -0.106694 -0.018306 17/1 0/1 1 4 -0.058824 In -0.088235 -0.029412 18/1 0 4 19/1 1/1 1 4 -0.051975 In -0.076923 -0.027027 20/1 1/1 2 4 -0.048811 In -0.082441 -0.015181 21/1 1/1 1 4 -0.047079 In -0.069767 -0.024390 22/1 0 4 23/1 0/1 1 4 -0.043478 In -0.065217 -0.021739 24/1 0/1 2 4 -0.041667 In -0.071129 -0.012204 25/1 0/1 1 4 -0.040000 In -0.060000 -0.020000 26/1 0 4 27/1 1/1 1 4 -0.036707 In -0.054545 -0.018868 28/1 1/1 2 4 -0.035099 In -0.059466 -0.010731 29/1 1/1 1 4 -0.034196 In -0.050847 -0.017544 30/1 0 4 31/1 0/1 1 4 -0.032258 In -0.048387 -0.016129 32/1 0/1 2 4 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0.057178 In 0.055763 0.058593 -33/2 1/0 1 4 0.060620 In 0.059701 0.061538 -31/2 1/2 1 4 0.065053 In 0.031746 0.098361 -29/2 1/2 3 4 0.070812 In 0.008972 0.132653 -27/2 1/2 3 4 0.076210 In 0.009616 0.142805 -25/2 1/2 1 4 0.080832 In 0.039216 0.122449 -23/2 1/0 1 4 0.086998 In 0.085106 0.088889 -21/2 1/0 3 4 0.095400 In 0.091466 0.099335 -19/2 1/0 3 4 0.105482 In 0.100674 0.110290 -17/2 1/0 1 4 0.117749 In 0.114286 0.121212 -15/2 1/2 1 4 0.135706 In 0.064516 0.206897 -13/2 1/2 3 4 0.163447 In 0.019324 0.307570 -11/2 1/2 3 4 0.195426 In 0.022581 0.368271 -9/2 1/2 1 4 0.229102 In 0.105263 0.352941 -7/2 1/0 1 4 0.287179 In 0.266667 0.307692 -5/2 1/0 3 4 0.412371 In 0.340946 0.483796 -3/2 1/0 3 4 0.727273 In 0.517327 0.937218 -1/2 1/0 1 4 2.666667 In 1.333333 4.000000 1/2 1/2 1 4 3/2 1/2 3 4 -0.545455 In -0.965346 -0.125563 5/2 1/2 3 4 -0.350515 In -0.636215 -0.064816 7/2 1/2 1 4 -0.276923 In -0.400000 -0.153846 9/2 1/0 1 4 -0.222910 In -0.235294 -0.210526 11/2 1/0 3 4 -0.182952 In -0.197356 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1/3 2 4 0.068974 In 0.019654 0.118295 -43/3 1/1 1 4 0.069912 In 0.057471 0.082353 -41/3 0/1 1 4 0.073171 In 0.060976 0.085366 -40/3 2/3 2 4 0.076971 In 0.021217 0.132726 -38/3 0 4 -37/3 1/1 1 4 0.081279 In 0.066667 0.095890 -35/3 1/1 1 4 0.085936 In 0.070423 0.101449 -34/3 0 4 -32/3 2/1 2 4 0.094912 In 0.068620 0.121204 -31/3 0/1 1 4 0.096774 In 0.080645 0.112903 -29/3 1/1 1 4 0.103776 In 0.084746 0.122807 -28/3 -1/1 2 4 0.106573 In 0.084011 0.129136 -26/3 0 4 -25/3 0/1 1 4 0.120000 In 0.100000 0.140000 -23/3 0/1 1 4 0.130435 In 0.108696 0.152174 -22/3 0 4 -20/3 1/3 2 4 0.153942 In 0.042434 0.265451 -19/3 1/1 1 4 0.158697 In 0.128205 0.189189 -17/3 0/1 1 4 0.176471 In 0.147059 0.205882 -16/3 2/3 2 4 0.200787 In 0.050458 0.351117 -14/3 0 4 -13/3 1/1 1 4 0.232593 In 0.185185 0.280000 -11/3 1/1 1 4 0.275362 In 0.217391 0.333333 -10/3 0 4 -8/3 2/1 2 4 0.403226 In 0.243557 0.562895 -7/3 0/1 1 4 0.428571 In 0.357143 0.500000 -5/3 1/1 1 4 0.616162 In 0.454545 0.777778 -4/3 -1/1 2 4 0.741935 In 0.696316 0.787555 -2/3 0 4 -1/3 0/1 1 4 3.000000 In 2.500000 3.500000 1/3 0/1 1 4 -3.000000 In -3.500000 -2.500000 2/3 0 4 4/3 1/3 2 4 -0.677419 In -1.087997 -0.266841 5/3 1/1 1 4 -0.595960 In -0.636364 -0.555556 7/3 0/1 1 4 -0.428571 In -0.500000 -0.357143 8/3 2/3 2 4 -0.338710 In -0.543999 -0.133421 10/3 0 4 11/3 1/1 1 4 -0.271222 In -0.304348 -0.238095 13/3 1/1 1 4 -0.229630 In -0.259259 -0.200000 14/3 0 4 16/3 2/1 2 4 -0.185039 In -0.212878 -0.157201 17/3 0/1 1 4 -0.176471 In -0.205882 -0.147059 19/3 1/1 1 4 -0.157311 In -0.179487 -0.135135 20/3 -1/1 2 4 -0.151439 In -0.192149 -0.110730 22/3 0 4 23/3 0/1 1 4 -0.130435 In -0.152174 -0.108696 25/3 0/1 1 4 -0.120000 In -0.140000 -0.100000 26/3 0 4 28/3 1/3 2 4 -0.105297 In -0.178399 -0.032194 29/3 1/1 1 4 -0.103182 In -0.118644 -0.087719 31/3 0/1 1 4 -0.096774 In -0.112903 -0.080645 32/3 2/3 2 4 -0.090998 In -0.153268 -0.028728 34/3 0 4 35/3 1/1 1 4 -0.085528 In -0.098592 -0.072464 37/3 1/1 1 4 -0.080913 In -0.093333 -0.068493 38/3 0 4 40/3 2/1 2 4 -0.074468 In -0.089513 -0.059423 41/3 0/1 1 4 -0.073171 In -0.085366 -0.060976 43/3 1/1 1 4 -0.069642 In -0.080460 -0.058824 44/3 -1/1 2 4 -0.068458 In -0.085629 -0.051287 46/3 0 4 47/3 0/1 1 4 -0.063830 In -0.074468 -0.053191 49/3 0/1 1 4 -0.061224 In -0.071429 -0.051020 50/3 0 4 -49/4 0 4 -47/4 0 4 -45/4 0 4 -43/4 0 4 -41/4 0 4 -39/4 0 4 -37/4 0 4 -35/4 0 4 -33/4 0 4 -31/4 0 4 -29/4 0 4 -27/4 0 4 -25/4 0 4 -23/4 0 4 -21/4 0 4 -19/4 0 4 -17/4 0 4 -15/4 0 4 -13/4 0 4 -11/4 0 4 -9/4 0 4 -7/4 0 4 -5/4 0 4 -3/4 0 4 -1/4 0 4 1/4 0 4 3/4 0 4 5/4 0 4 7/4 0 4 9/4 0 4 11/4 0 4 13/4 0 4 15/4 0 4 17/4 0 4 19/4 0 4 21/4 0 4 23/4 0 4 25/4 0 4 27/4 0 4 29/4 0 4 31/4 0 4 33/4 0 4 35/4 0 4 37/4 0 4 39/4 0 4 41/4 0 4 43/4 0 4 45/4 0 4 47/4 0 4 49/4 0 4 -49/5 0/1 1 4 0.102041 In 0.091837 0.112245 -48/5 2/1 2 4 0.104692 In 0.086876 0.122507 -47/5 -2/1 1 4 0.106205 In 0.097826 0.114583 -46/5 0 4 -44/5 1/1 2 4 0.113924 In 0.096023 0.131825 -43/5 1/1 1 4 0.116430 In 0.103448 0.129412 -42/5 0 4 -41/5 0/1 1 4 0.121951 In 0.109756 0.134146 -39/5 0/1 1 4 0.128205 In 0.115385 0.141026 -38/5 0 4 -37/5 1/1 1 4 0.135342 In 0.120000 0.150685 -36/5 1/1 2 4 0.139328 In 0.116950 0.161707 -34/5 0 4 -33/5 2/5 1 4 0.153952 In 0.073529 0.234375 -32/5 2/3 2 4 0.159491 In 0.086151 0.232831 -31/5 0/1 1 4 0.161290 In 0.145161 0.177419 -29/5 1/1 1 4 0.172762 In 0.152542 0.192982 -28/5 1/3 2 4 0.180600 In 0.100278 0.260922 -27/5 3/5 1 4 0.190918 In 0.087719 0.294118 -26/5 0 4 -24/5 0/1 2 4 0.208333 In 0.178871 0.237796 -23/5 0/1 1 4 0.217391 In 0.195652 0.239130 -22/5 0 4 -21/5 1/1 1 4 0.238798 In 0.209302 0.268293 -19/5 1/1 1 4 0.264033 In 0.230769 0.297297 -18/5 0 4 -17/5 0/1 1 4 0.294118 In 0.264706 0.323529 -16/5 0/1 2 4 0.312500 In 0.268306 0.356694 -14/5 0 4 -13/5 3/1 1 4 0.394303 In 0.310345 0.478261 -12/5 -1/1 2 4 0.414634 In 0.380141 0.449127 -11/5 1/1 1 4 0.457557 In 0.391304 0.523810 -9/5 0/1 1 4 0.555556 In 0.500000 0.611111 -8/5 2/1 2 4 0.661290 In 0.456001 0.866579 -7/5 -2/1 1 4 0.718750 In 0.687500 0.750000 -6/5 0 4 -4/5 1/1 2 4 1.322581 In 0.912003 1.733159 -3/5 1/1 1 4 1.742857 In 1.285714 2.200000 -2/5 0 4 -1/5 0/1 1 4 5.000000 In 4.500000 5.500000 1/5 0/1 1 4 -5.000000 In -5.500000 -4.500000 2/5 0 4 3/5 1/1 1 4 -1.685714 In -1.800000 -1.571429 4/5 1/1 2 4 -1.258065 In -1.303684 -1.212445 6/5 0 4 7/5 2/5 1 4 -0.677083 In -0.937500 -0.416667 8/5 2/3 2 4 -0.596774 In -0.756443 -0.437105 9/5 0/1 1 4 -0.555556 In -0.611111 -0.500000 11/5 1/1 1 4 -0.453416 In -0.478261 -0.428571 12/5 1/3 2 4 -0.407666 In -0.560420 -0.254911 13/5 3/5 1 4 -0.367316 In -0.517241 -0.217391 14/5 0 4 16/5 0/1 2 4 -0.312500 In -0.356694 -0.268306 17/5 0/1 1 4 -0.294118 In -0.323529 -0.264706 18/5 0 4 19/5 1/1 1 4 -0.262647 In -0.282051 -0.243243 21/5 1/1 1 4 -0.237663 In -0.255814 -0.219512 22/5 0 4 23/5 0/1 1 4 -0.217391 In -0.239130 -0.195652 24/5 0/1 2 4 -0.208333 In -0.237796 -0.178871 26/5 0 4 27/5 3/1 1 4 -0.184727 In -0.192982 -0.176471 28/5 -1/1 2 4 -0.179324 In -0.209106 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