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 0 9 -46/1 0/1 1 9 0.021739 In 0.014493 0.028986 -45/1 1/1 1 9 0.022278 In 0.014706 0.029851 -44/1 0 9 -43/1 0 9 -42/1 0/1 1 9 0.023810 In 0.015873 0.031746 -41/1 0 9 -40/1 0/1 1 9 0.025000 In 0.016667 0.033333 -39/1 1/1 1 9 0.025716 In 0.016949 0.034483 -38/1 0 9 -37/1 0 9 -36/1 0/1 1 9 0.027778 In 0.018519 0.037037 -35/1 0 9 -34/1 0/1 1 9 0.029412 In 0.019608 0.039216 -33/1 1/1 1 9 0.030408 In 0.020000 0.040816 -32/1 0 9 -31/1 0 9 -30/1 0/1 1 9 0.033333 In 0.022222 0.044444 -29/1 0 9 -28/1 0/1 1 9 0.035714 In 0.023810 0.047619 -27/1 1/1 1 9 0.037195 In 0.024390 0.050000 -26/1 0 9 -25/1 0 9 -24/1 0/1 1 9 0.041667 In 0.027778 0.055556 -23/1 0 9 -22/1 0/1 1 9 0.045455 In 0.030303 0.060606 -21/1 1/1 1 9 0.047883 In 0.031250 0.064516 -20/1 0 9 -19/1 0 9 -18/1 0/1 1 9 0.055556 In 0.037037 0.074074 -17/1 0 9 -16/1 0/1 1 9 0.062500 In 0.041667 0.083333 -15/1 1/1 1 9 0.067194 In 0.043478 0.090909 -14/1 0 9 -13/1 0 9 -12/1 0/1 1 9 0.083333 In 0.055556 0.111111 -11/1 0 9 -10/1 0/1 1 9 0.100000 In 0.066667 0.133333 -9/1 1/1 1 9 0.112637 In 0.071429 0.153846 -8/1 0 9 -7/1 0 9 -6/1 0/1 1 9 0.166667 In 0.111111 0.222222 -5/1 0 9 -4/1 0/1 1 9 0.250000 In 0.166667 0.333333 -3/1 1/1 1 9 0.350000 In 0.200000 0.500000 -2/1 0 9 -1/1 0 9 0/1 0/1 1 9 1/1 0 9 2/1 0/1 1 9 -0.500000 In -0.666667 -0.333333 3/1 1/1 1 9 -0.325000 In -0.400000 -0.250000 4/1 0 9 5/1 0 9 6/1 0/1 1 9 -0.166667 In -0.222222 -0.111111 7/1 0 9 8/1 0/1 1 9 -0.125000 In -0.166667 -0.083333 9/1 1/1 1 9 -0.109890 In -0.142857 -0.076923 10/1 0 9 11/1 0 9 12/1 0/1 1 9 -0.083333 In -0.111111 -0.055556 13/1 0 9 14/1 0/1 1 9 -0.071429 In -0.095238 -0.047619 15/1 1/1 1 9 -0.066206 In -0.086957 -0.045455 16/1 0 9 17/1 0 9 18/1 0/1 1 9 -0.055556 In -0.074074 -0.037037 19/1 0 9 20/1 0/1 1 9 -0.050000 In -0.066667 -0.033333 21/1 1/1 1 9 -0.047379 In -0.062500 -0.032258 22/1 0 9 23/1 0 9 24/1 0/1 1 9 -0.041667 In -0.055556 -0.027778 25/1 0 9 26/1 0/1 1 9 -0.038462 In -0.051282 -0.025641 27/1 1/1 1 9 -0.036890 In -0.048780 -0.025000 28/1 0 9 29/1 0 9 30/1 0/1 1 9 -0.033333 In -0.044444 -0.022222 31/1 0 9 32/1 0/1 1 9 -0.031250 In -0.041667 -0.020833 33/1 1/1 1 9 -0.030204 In -0.040000 -0.020408 34/1 0 9 35/1 0 9 36/1 0/1 1 9 -0.027778 In -0.037037 -0.018519 37/1 0 9 38/1 0/1 1 9 -0.026316 In -0.035088 -0.017544 39/1 1/1 1 9 -0.025570 In -0.033898 -0.017241 40/1 0 9 41/1 0 9 42/1 0/1 1 9 -0.023810 In -0.031746 -0.015873 43/1 0 9 44/1 0/1 1 9 -0.022727 In -0.030303 -0.015152 45/1 1/1 1 9 -0.022169 In -0.029412 -0.014925 46/1 0 9 47/1 0 9 48/1 0/1 1 9 -0.020833 In -0.027778 -0.013889 49/1 0 9 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 1/1 1 9 0.042606 In 0.035211 0.050000 -45/2 0 9 -43/2 1/2 1 9 0.046635 In 0.030769 0.062500 -41/2 1/1 1 9 0.048850 In 0.040323 0.057377 -39/2 0 9 -37/2 1/0 1 9 0.054058 In 0.053571 0.054545 -35/2 1/1 1 9 0.057239 In 0.047170 0.067308 -33/2 0 9 -31/2 1/2 1 9 0.064755 In 0.042553 0.086957 -29/2 1/1 1 9 0.069107 In 0.056818 0.081395 -27/2 0 9 -25/2 1/0 1 9 0.080014 In 0.078947 0.081081 -23/2 1/1 1 9 0.087185 In 0.071429 0.102941 -21/2 0 9 -19/2 1/2 1 9 0.105911 In 0.068966 0.142857 -17/2 1/1 1 9 0.118077 In 0.096154 0.140000 -15/2 0 9 -13/2 1/0 1 9 0.153947 In 0.150000 0.157895 -11/2 1/1 1 9 0.182904 In 0.147059 0.218750 -9/2 0 9 -7/2 1/2 1 9 0.290909 In 0.181818 0.400000 -5/2 1/1 1 9 0.406250 In 0.312500 0.500000 -3/2 0 9 -1/2 1/0 1 9 2.250000 In 1.500000 3.000000 1/2 1/1 1 9 -2.125000 In -2.500000 -1.750000 3/2 0 9 5/2 1/2 1 9 -0.392857 In -0.500000 -0.285714 7/2 1/1 1 9 -0.284091 In -0.318182 -0.250000 9/2 0 9 11/2 1/0 1 9 -0.181985 In -0.187500 -0.176471 13/2 1/1 1 9 -0.153289 In -0.175000 -0.131579 15/2 0 9 17/2 1/2 1 9 -0.116923 In -0.153846 -0.080000 19/2 1/1 1 9 -0.104988 In -0.120690 -0.089286 21/2 0 9 23/2 1/0 1 9 -0.086975 In 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0.064516 0.129032 -29/3 0 3 -28/3 1/1 3 3 0.108557 In 0.068966 0.148148 -26/3 1/1 3 3 0.117037 In 0.074074 0.160000 -25/3 1/1 2 3 0.121196 In 0.084578 0.157814 -23/3 1/0 1 3 0.130517 In 0.127241 0.133793 -22/3 1/1 1 3 0.137147 In 0.107304 0.166989 -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 0/1 2 3 0.214286 In 0.155965 0.272607 -13/3 0/1 3 3 0.230769 In 0.153846 0.307692 -11/3 0 3 -10/3 1/1 3 3 0.313131 In 0.181818 0.444444 -8/3 1/1 3 3 0.396825 In 0.222222 0.571429 -7/3 1/1 2 3 0.448276 In 0.279346 0.617206 -5/3 1/0 1 3 0.608108 In 0.537890 0.678326 -4/3 1/1 1 3 0.787234 In 0.529269 1.045199 -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 0/1 2 3 -0.750000 In -0.954124 -0.545876 5/3 0/1 3 3 -0.600000 In -0.800000 -0.400000 7/3 0 3 8/3 1/1 3 3 -0.365079 In -0.444444 -0.285714 10/3 1/1 3 3 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3 -0.063547 In -0.079815 -0.047279 49/3 1/0 1 3 -0.061233 In -0.061954 -0.060512 50/3 1/1 1 3 -0.059875 In -0.070730 -0.049019 -49/4 1/1 1 9 0.081683 In 0.074324 0.089041 -47/4 1/2 1 9 0.085211 In 0.070423 0.100000 -45/4 0 9 -43/4 -1/1 1 9 0.092969 In 0.085938 0.100000 -41/4 1/2 1 9 0.097700 In 0.080645 0.114754 -39/4 0 9 -37/4 1/1 1 9 0.108198 In 0.098214 0.118182 -35/4 1/2 1 9 0.114478 In 0.094340 0.134615 -33/4 0 9 -31/4 1/1 1 9 0.129163 In 0.117021 0.141304 -29/4 1/0 1 9 0.137949 In 0.136364 0.139535 -27/4 0 9 -25/4 1/1 1 9 0.160206 In 0.144737 0.175676 -23/4 1/2 1 9 0.174370 In 0.142857 0.205882 -21/4 0 9 -19/4 -1/1 1 9 0.210283 In 0.196429 0.224138 -17/4 1/2 1 9 0.236154 In 0.192308 0.280000 -15/4 0 9 -13/4 1/1 1 9 0.308553 In 0.275000 0.342105 -11/4 1/2 1 9 0.365809 In 0.294118 0.437500 -9/4 0 9 -7/4 1/1 1 9 0.575000 In 0.500000 0.650000 -5/4 1/0 1 9 0.803571 In 0.750000 0.857143 -3/4 0 9 -1/4 1/1 1 9 4.625000 In 2.750000 6.500000 1/4 1/2 1 9 -4.250000 In -5.000000 -3.500000 3/4 0 9 5/4 -1/1 1 9 -0.808036 In -0.928571 -0.687500 7/4 1/2 1 9 -0.568182 In -0.636364 -0.500000 9/4 0 9 11/4 1/1 1 9 -0.363051 In -0.382353 -0.343750 13/4 1/2 1 9 -0.306579 In -0.350000 -0.263158 15/4 0 9 17/4 1/1 1 9 -0.235000 In -0.250000 -0.220000 19/4 1/0 1 9 -0.210591 In -0.214286 -0.206897 21/4 0 9 23/4 1/1 1 9 -0.173739 In -0.185714 -0.161765 25/4 1/2 1 9 -0.159673 In -0.184211 -0.135135 27/4 0 9 29/4 -1/1 1 9 -0.138081 In -0.151163 -0.125000 31/4 1/2 1 9 -0.128816 In -0.148936 -0.108696 33/4 0 9 35/4 1/1 1 9 -0.114205 In -0.122642 -0.105769 37/4 1/2 1 9 -0.107955 In -0.125000 -0.090909 39/4 0 9 41/4 1/1 1 9 -0.097501 In -0.104839 -0.090164 43/4 1/0 1 9 -0.093029 In -0.093750 -0.092308 45/4 0 9 47/4 1/1 1 9 -0.085060 In -0.091549 -0.078571 49/4 1/2 1 9 -0.081544 In -0.094595 -0.068493 -49/5 0 9 -48/5 0/1 1 9 0.104167 In 0.097222 0.111111 -47/5 0 9 -46/5 0 9 -44/5 0/1 1 9 0.113636 In 0.106061 0.121212 -43/5 0 9 -42/5 0/1 1 9 0.119048 In 0.111111 0.126984 -41/5 0 9 -39/5 1/1 1 9 0.128288 In 0.118644 0.137931 -38/5 0/1 1 9 0.131579 In 0.122807 0.140351 -37/5 0 9 -36/5 0/1 1 9 0.138889 In 0.129630 0.148148 -34/5 0 9 -33/5 1/1 1 9 0.151633 In 0.140000 0.163265 -32/5 0/1 1 9 0.156250 In 0.145833 0.166667 -31/5 0 9 -29/5 0 9 -28/5 0 9 -27/5 1/1 1 9 0.185366 In 0.170732 0.200000 -26/5 0/1 1 9 0.192308 In 0.179487 0.205128 -24/5 0/1 1 9 0.208333 In 0.194444 0.222222 -23/5 0 9 -22/5 0 9 -21/5 1/1 1 9 0.238407 In 0.218750 0.258065 -19/5 0 9 -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 0 9 -12/5 0/1 1 9 0.416667 In 0.388889 0.444444 -11/5 0 9 -9/5 1/1 1 9 0.557692 In 0.500000 0.615385 -8/5 0/1 1 9 0.625000 In 0.583333 0.666667 -7/5 0 9 -6/5 0/1 1 9 0.833333 In 0.777778 0.888889 -4/5 0 9 -3/5 1/1 1 9 1.700000 In 1.400000 2.000000 -2/5 0/1 1 9 2.500000 In 2.333333 2.666667 -1/5 0 9 1/5 0 9 2/5 0 9 3/5 1/1 1 9 -1.675000 In -1.750000 -1.600000 4/5 0/1 1 9 -1.250000 In -1.333333 -1.166667 6/5 0/1 1 9 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0.127679 In 0.126110 0.129247 -43/6 1/1 1 3 0.139740 In 0.124437 0.155043 -41/6 1/0 2 3 0.146400 In 0.143484 0.149315 -37/6 0/1 3 3 0.162162 In 0.135135 0.189189 -35/6 0/1 3 3 0.171429 In 0.142857 0.200000 -31/6 1/1 2 3 0.194377 In 0.162919 0.225835 -29/6 1/0 1 3 0.206979 In 0.202858 0.211099 -25/6 1/1 1 3 0.240662 In 0.212010 0.269314 -23/6 1/2 2 3 0.263722 In 0.183361 0.344084 -19/6 0/1 3 3 0.315789 In 0.263158 0.368421 -17/6 0/1 3 3 0.352941 In 0.294118 0.411765 -13/6 1/1 2 3 0.467327 In 0.375168 0.559486 -11/6 1/0 1 3 0.546961 In 0.518253 0.575669 -7/6 1/1 1 3 0.869863 In 0.715639 1.024087 -5/6 1/0 2 3 1.232877 In 1.031549 1.434205 -1/6 0/1 3 3 6.000000 In 5.000000 7.000000 1/6 0/1 3 3 -6.000000 In -7.000000 -5.000000 5/6 1/1 2 3 -1.205479 In -1.239034 -1.171925 7/6 1/0 1 3 -0.863014 In -0.934194 -0.791834 11/6 1/1 1 3 -0.544199 In -0.568122 -0.520276 13/6 1/2 2 3 -0.455446 In -0.552455 -0.358436 17/6 0/1 3 3 -0.352941 In -0.411765 -0.294118 19/6 0/1 3 3 -0.315789 In -0.368421 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