SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 1/0 1 1 -50/1 -50/1 1 6 -49/1 0 6 -48/1 -48/1 1 6 -47/1 0 6 -46/1 -46/1 1 6 -45/1 0 6 -44/1 -44/1 1 6 -43/1 0 6 -42/1 -42/1 1 6 -41/1 0 6 -40/1 -40/1 1 6 -39/1 0 6 -38/1 -38/1 1 6 -37/1 0 6 -36/1 -36/1 1 6 -35/1 0 6 -34/1 -34/1 1 6 -33/1 0 6 -32/1 -32/1 1 6 -31/1 0 6 -30/1 -30/1 1 6 -29/1 0 6 -28/1 -28/1 1 6 -27/1 0 6 -26/1 -26/1 1 6 -25/1 0 6 -24/1 -24/1 1 6 -23/1 0 6 -22/1 -22/1 1 6 -21/1 0 6 -20/1 -20/1 1 6 -19/1 0 6 -18/1 -18/1 1 6 -17/1 0 6 -16/1 -16/1 1 6 -15/1 0 6 -14/1 -14/1 1 6 -13/1 0 6 -12/1 -12/1 1 6 -11/1 0 6 -10/1 -10/1 1 6 -9/1 0 6 -8/1 -8/1 1 6 -7/1 0 6 -6/1 -6/1 1 6 -5/1 0 6 -4/1 -4/1 1 6 -3/1 0 6 -2/1 -2/1 1 6 -1/1 0 6 0/1 0/1 1 6 1/1 0 6 2/1 2/1 1 6 3/1 0 6 4/1 4/1 1 6 5/1 0 6 6/1 6/1 1 6 7/1 0 6 8/1 8/1 1 6 9/1 0 6 10/1 10/1 1 6 11/1 0 6 12/1 12/1 1 6 13/1 0 6 14/1 14/1 1 6 15/1 0 6 16/1 16/1 1 6 17/1 0 6 18/1 18/1 1 6 19/1 0 6 20/1 20/1 1 6 21/1 0 6 22/1 22/1 1 6 23/1 0 6 24/1 24/1 1 6 25/1 0 6 26/1 26/1 1 6 27/1 0 6 28/1 28/1 1 6 29/1 0 6 30/1 30/1 1 6 31/1 0 6 32/1 32/1 1 6 33/1 0 6 34/1 34/1 1 6 35/1 0 6 36/1 36/1 1 6 37/1 0 6 38/1 38/1 1 6 39/1 0 6 40/1 40/1 1 6 41/1 0 6 42/1 42/1 1 6 43/1 0 6 44/1 44/1 1 6 45/1 0 6 46/1 46/1 1 6 47/1 0 6 48/1 48/1 1 6 49/1 0 6 50/1 50/1 1 6 -49/2 1/0 1 3 0.040822 In 0.040341 0.041303 -47/2 1/0 1 3 0.042560 In 0.042037 0.043082 -45/2 1/0 1 3 0.044452 In 0.043881 0.045022 -43/2 1/0 1 3 0.046520 In 0.045895 0.047145 -41/2 1/0 1 3 0.048790 In 0.048103 0.049477 -39/2 1/0 1 3 0.051293 In 0.050534 0.052053 -37/2 1/0 1 3 0.054067 In 0.053224 0.054911 -35/2 1/0 1 3 0.057158 In 0.056216 0.058101 -33/2 1/0 1 3 0.060625 In 0.059564 0.061685 -31/2 1/0 1 3 0.064539 In 0.063337 0.065740 -29/2 1/0 1 3 0.068993 In 0.067619 0.070366 -27/2 1/0 1 3 0.074108 In 0.072523 0.075693 -25/2 1/0 1 3 0.080043 In 0.078194 0.081891 -23/2 1/0 1 3 0.087011 In 0.084827 0.089196 -21/2 1/0 1 3 0.095310 In 0.092690 0.097930 -19/2 1/0 1 3 0.105360 In 0.102159 0.108562 -17/2 1/0 1 3 0.117783 In 0.113783 0.121783 -15/2 1/0 1 3 0.133531 In 0.128392 0.138671 -13/2 1/0 1 3 0.154150 In 0.147304 0.160996 -11/2 1/0 1 3 0.182320 In 0.172751 0.191890 -9/2 1/0 1 3 0.223140 In 0.208826 0.237455 -7/2 1/0 1 3 0.287671 In 0.263945 0.311398 -5/2 1/0 1 3 0.405405 In 0.358593 0.452218 -3/2 1/0 1 3 0.692308 In 0.559073 0.825542 -1/2 1/0 1 3 3.000000 In 1.267949 4.732051 1/2 1/0 1 3 -3.000000 In -4.732051 -1.267949 3/2 1/0 1 3 -0.692308 In -0.825542 -0.559073 5/2 1/0 1 3 -0.405405 In -0.452218 -0.358593 7/2 1/0 1 3 -0.287671 In -0.311398 -0.263945 9/2 1/0 1 3 -0.223140 In -0.237455 -0.208826 11/2 1/0 1 3 -0.182320 In -0.191890 -0.172751 13/2 1/0 1 3 -0.154150 In -0.160996 -0.147304 15/2 1/0 1 3 -0.133531 In -0.138671 -0.128392 17/2 1/0 1 3 -0.117783 In -0.121783 -0.113783 19/2 1/0 1 3 -0.105360 In -0.108562 -0.102159 21/2 1/0 1 3 -0.095310 In -0.097930 -0.092690 23/2 1/0 1 3 -0.087011 In -0.089196 -0.084827 25/2 1/0 1 3 -0.080043 In -0.081891 -0.078194 27/2 1/0 1 3 -0.074108 In -0.075693 -0.072523 29/2 1/0 1 3 -0.068993 In -0.070366 -0.067619 31/2 1/0 1 3 -0.064539 In -0.065740 -0.063337 33/2 1/0 1 3 -0.060625 In -0.061685 -0.059564 35/2 1/0 1 3 -0.057158 In -0.058101 -0.056216 37/2 1/0 1 3 -0.054067 In -0.054911 -0.053224 39/2 1/0 1 3 -0.051293 In -0.052053 -0.050534 41/2 1/0 1 3 -0.048790 In -0.049477 -0.048103 43/2 1/0 1 3 -0.046520 In -0.047145 -0.045895 45/2 1/0 1 3 -0.044452 In -0.045022 -0.043881 47/2 1/0 1 3 -0.042560 In -0.043082 -0.042037 49/2 1/0 1 3 -0.040822 In -0.041303 -0.040341 -50/3 -16/1 1 2 0.059865 In 0.059269 0.060461 -49/3 0 2 -47/3 0 2 -46/3 -16/1 1 2 0.065392 In 0.064681 0.066104 -44/3 -14/1 1 2 0.068009 In 0.067239 0.068778 -43/3 0 2 -41/3 0 2 -40/3 -14/1 1 2 0.075233 In 0.074291 0.076175 -38/3 -12/1 1 2 0.078717 In 0.077686 0.079748 -37/3 0 2 -35/3 0 2 -34/3 -12/1 1 2 0.088561 In 0.087256 0.089866 -32/3 -10/1 1 2 0.093429 In 0.091977 0.094881 -31/3 0 2 -29/3 0 2 -28/3 -10/1 1 2 0.107629 In 0.105703 0.109556 -26/3 -8/1 1 2 0.114907 In 0.112711 0.117103 -25/3 0 2 -23/3 0 2 -22/3 -8/1 1 2 0.137168 In 0.134039 0.140297 -20/3 -6/1 1 2 0.149215 In 0.145513 0.152917 -19/3 0 2 -17/3 0 2 -16/3 -6/1 1 2 0.189076 In 0.183134 0.195018 -14/3 -4/1 1 2 0.212766 In 0.205244 0.220288 -13/3 0 2 -11/3 0 2 -10/3 -4/1 1 2 0.304348 In 0.288976 0.319720 -8/3 -2/1 1 2 0.370968 In 0.348158 0.393778 -7/3 0 2 -5/3 0 2 -4/3 -2/1 1 2 0.785714 In 0.684699 0.886730 -2/3 0/1 1 2 1.500000 In 1.146447 1.853553 -1/3 0 2 1/3 0 2 2/3 0/1 1 2 -1.500000 In -1.853553 -1.146447 4/3 2/1 1 2 -0.785714 In -0.886730 -0.684699 5/3 0 2 7/3 0 2 8/3 2/1 1 2 -0.370968 In -0.393778 -0.348158 10/3 4/1 1 2 -0.304348 In -0.319720 -0.288976 11/3 0 2 13/3 0 2 14/3 4/1 1 2 -0.212766 In -0.220288 -0.205244 16/3 6/1 1 2 -0.189076 In -0.195018 -0.183134 17/3 0 2 19/3 0 2 20/3 6/1 1 2 -0.149215 In -0.152917 -0.145513 22/3 8/1 1 2 -0.137168 In -0.140297 -0.134039 23/3 0 2 25/3 0 2 26/3 8/1 1 2 -0.114907 In -0.117103 -0.112711 28/3 10/1 1 2 -0.107629 In -0.109556 -0.105703 29/3 0 2 31/3 0 2 32/3 10/1 1 2 -0.093429 In -0.094881 -0.091977 34/3 12/1 1 2 -0.088561 In -0.089866 -0.087256 35/3 0 2 37/3 0 2 38/3 12/1 1 2 -0.078717 In -0.079748 -0.077686 40/3 14/1 1 2 -0.075233 In -0.076175 -0.074291 41/3 0 2 43/3 0 2 44/3 14/1 1 2 -0.068009 In -0.068778 -0.067239 46/3 16/1 1 2 -0.065392 In -0.066104 -0.064681 47/3 0 2 49/3 0 2 50/3 16/1 1 2 -0.059865 In -0.060461 -0.059269 -49/4 -13/1 1 3 0.081746 In 0.081007 0.082485 -47/4 -11/1 1 3 0.084998 In 0.084200 0.085797 -45/4 -11/1 1 3 0.088848 In 0.088557 0.089139 -43/4 -11/1 1 3 0.093070 In 0.092751 0.093390 -41/4 -11/1 1 3 0.097725 In 0.096669 0.098780 -39/4 -9/1 1 3 0.102410 In 0.101250 0.103569 -37/4 -9/1 1 3 0.108048 In 0.107617 0.108478 -35/4 -9/1 1 3 0.114357 In 0.113875 0.114839 -33/4 -9/1 1 3 0.121469 In 0.119838 0.123100 -31/4 -7/1 1 3 0.128793 In 0.126960 0.130627 -29/4 -7/1 1 3 0.137833 In 0.137133 0.138534 -27/4 -7/1 1 3 0.148269 In 0.147459 0.149080 -25/4 -7/1 1 3 0.160460 In 0.157614 0.163306 -23/4 -5/1 1 3 0.173496 In 0.170169 0.176822 -21/4 -5/1 1 3 0.190293 In 0.188958 0.191627 -19/4 -5/1 1 3 0.210775 In 0.209138 0.212412 -17/4 -5/1 1 3 0.236342 In 0.230171 0.242513 -15/4 -3/1 1 3 0.265766 In 0.257964 0.273568 -13/4 -3/1 1 3 0.307229 In 0.303751 0.310707 -11/4 -3/1 1 3 0.364407 In 0.359514 0.369300 -9/4 -3/1 1 3 0.448718 In 0.426512 0.470924 -7/4 -1/1 1 3 0.568493 In 0.532903 0.604083 -5/4 -1/1 1 3 0.797297 In 0.773891 0.820703 -3/4 -1/1 1 3 1.346154 In 1.279537 1.412771 -1/4 -1/1 1 3 5.500000 In 2.901924 8.098076 1/4 1/1 1 3 -5.500000 In -8.098076 -2.901924 3/4 1/1 1 3 -1.346154 In -1.412771 -1.279537 5/4 1/1 1 3 -0.797297 In -0.820703 -0.773891 7/4 1/1 1 3 -0.568493 In -0.604083 -0.532903 9/4 3/1 1 3 -0.448718 In -0.470924 -0.426512 11/4 3/1 1 3 -0.364407 In -0.369300 -0.359514 13/4 3/1 1 3 -0.307229 In -0.310707 -0.303751 15/4 3/1 1 3 -0.265766 In -0.273568 -0.257964 17/4 5/1 1 3 -0.236342 In -0.242513 -0.230171 19/4 5/1 1 3 -0.210775 In 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6 -36/5 -8/1 1 6 0.139004 In 0.137734 0.140275 -34/5 -6/1 1 6 0.146957 In 0.145537 0.148377 -33/5 0 6 -32/5 -8/1 1 6 0.156579 In 0.153356 0.159802 -31/5 0 6 -29/5 0 6 -28/5 -4/1 1 6 0.178328 In 0.174148 0.182508 -27/5 0 6 -26/5 -6/1 1 6 0.192537 In 0.190100 0.194975 -24/5 -4/1 1 6 0.208140 In 0.205291 0.210988 -23/5 0 6 -22/5 -6/1 1 6 0.228033 In 0.221201 0.234866 -21/5 0 6 -19/5 0 6 -18/5 -2/1 1 6 0.277320 In 0.267219 0.287421 -17/5 0 6 -16/5 -4/1 1 6 0.313158 In 0.306712 0.319604 -14/5 -2/1 1 6 0.356655 In 0.348295 0.365015 -13/5 0 6 -12/5 -4/1 1 6 0.419811 In 0.396703 0.442920 -11/5 0 6 -9/5 0 6 -8/5 0/1 1 6 0.625000 In 0.573969 0.676031 -7/5 0 6 -6/5 -2/1 1 6 0.839623 In 0.793406 0.885839 -4/5 0/1 1 6 1.250000 In 1.147938 1.352062 -3/5 0 6 -2/5 -2/1 1 6 2.900000 In 1.920204 3.879796 -1/5 0 6 1/5 0 6 2/5 2/1 1 6 -2.900000 In -3.879796 -1.920204 3/5 0 6 4/5 0/1 1 6 -1.250000 In -1.352062 -1.147938 6/5 2/1 1 6 -0.839623 In -0.885839 -0.793406 7/5 0 6 8/5 0/1 1 6 -0.625000 In -0.676031 -0.573969 9/5 0 6 11/5 0 6 12/5 4/1 1 6 -0.419811 In -0.442920 -0.396703 13/5 0 6 14/5 2/1 1 6 -0.356655 In -0.365015 -0.348295 16/5 4/1 1 6 -0.313158 In -0.319604 -0.306712 17/5 0 6 18/5 2/1 1 6 -0.277320 In -0.287421 -0.267219 19/5 0 6 21/5 0 6 22/5 6/1 1 6 -0.228033 In -0.234866 -0.221201 23/5 0 6 24/5 4/1 1 6 -0.208140 In -0.210988 -0.205291 26/5 6/1 1 6 -0.192537 In -0.194975 -0.190100 27/5 0 6 28/5 4/1 1 6 -0.178328 In -0.182508 -0.174148 29/5 0 6 31/5 0 6 32/5 8/1 1 6 -0.156579 In -0.159802 -0.153356 33/5 0 6 34/5 6/1 1 6 -0.146957 In -0.148377 -0.145537 36/5 8/1 1 6 -0.139004 In -0.140275 -0.137734 37/5 0 6 38/5 6/1 1 6 -0.131433 In -0.133704 -0.129161 39/5 0 6 41/5 0 6 42/5 10/1 1 6 -0.119229 In -0.121098 -0.117360 43/5 0 6 44/5 8/1 1 6 -0.113573 In -0.114422 -0.112725 46/5 10/1 1 6 -0.108765 In -0.109543 -0.107987 47/5 0 6 48/5 8/1 1 6 -0.104070 In -0.105494 -0.102646 49/5 0 6 -49/6 -9/1 1 1 0.122845 In 0.120690 0.125000 -47/6 -7/1 1 1 0.127315 In 0.125000 0.129630 -43/6 -7/1 1 1 0.139444 In 0.138889 0.140000 -41/6 -7/1 1 1 0.146446 In 0.145833 0.147059 -37/6 -7/1 1 1 0.162879 In 0.159091 0.166667 -35/6 -5/1 1 1 0.170833 In 0.166667 0.175000 -31/6 -5/1 1 1 0.193376 In 0.192308 0.194444 -29/6 -5/1 1 1 0.207108 In 0.205882 0.208333 -25/6 -5/1 1 1 0.241667 In 0.233333 0.250000 -23/6 -3/1 1 1 0.259615 In 0.250000 0.269231 -19/6 -3/1 1 1 0.315341 In 0.312500 0.318182 -17/6 -3/1 1 1 0.353571 In 0.350000 0.357143 -13/6 -3/1 1 1 0.468750 In 0.437500 0.500000 -11/6 -1/1 1 1 0.541667 In 0.500000 0.583333 -7/6 -1/1 1 1 0.854167 In 0.833333 0.875000 -5/6 -1/1 1 1 1.208333 In 1.166667 1.250000 -1/6 -1/1 1 1 3.500000 Right 1/6 1/1 1 1 -3.500000 Left 5/6 1/1 1 1 -1.208333 In -1.250000 -1.166667 7/6 1/1 1 1 -0.854167 In -0.875000 -0.833333 11/6 1/1 1 1 -0.541667 In -0.583333 -0.500000 13/6 3/1 1 1 -0.468750 In -0.500000 -0.437500 17/6 3/1 1 1 -0.353571 In -0.357143 -0.350000 19/6 3/1 1 1 -0.315341 In -0.318182 -0.312500 23/6 3/1 1 1 -0.259615 In -0.269231 -0.250000 25/6 5/1 1 1 -0.241667 In -0.250000 -0.233333 29/6 5/1 1 1 -0.207108 In -0.208333 -0.205882 31/6 5/1 1 1 -0.193376 In -0.194444 -0.192308 35/6 5/1 1 1 -0.170833 In -0.175000 -0.166667 37/6 7/1 1 1 -0.162879 In -0.166667 -0.159091 41/6 7/1 1 1 -0.146446 In -0.147059 -0.145833 43/6 7/1 1 1 -0.139444 In -0.140000 -0.138889 47/6 7/1 1 1 -0.127315 In -0.129630 -0.125000 49/6 9/1 1 1 -0.122845 In -0.125000 -0.120690 -50/7 -6/1 1 6 0.139936 In 0.138626 0.141245 -48/7 -8/1 1 6 0.145930 In 0.144506 0.147354 -47/7 0 6 -46/7 -6/1 1 6 0.152133 In 0.151359 0.152907 -45/7 0 6 -44/7 -8/1 1 6 0.159280 In 0.156735 0.161824 -43/7 0 6 -41/7 0 6 -40/7 -4/1 1 6 0.174875 In 0.171808 0.177942 -39/7 0 6 -38/7 -6/1 1 6 0.184284 In 0.183148 0.185419 -37/7 0 6 -36/7 -4/1 1 6 0.194330 In 0.191805 0.196855 -34/7 -6/1 1 6 0.206087 In 0.203247 0.208927 -33/7 0 6 -32/7 -4/1 1 6 0.218668 In 0.217070 0.220267 -31/7 0 6 -30/7 -6/1 1 6 0.233781 In 0.228301 0.239261 -29/7 0 6 -27/7 0 6 -26/7 -2/1 1 6 0.269003 In 0.261749 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