SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 1/0 7 3 -50/1 0 9 -49/1 0 9 -48/1 -112/1 1 9 0.039062 In 0.015625 0.062500 -47/1 0 9 -46/1 0 9 -45/1 1/0 1 9 0.022223 In 0.022059 0.022388 -44/1 0 9 -43/1 0 9 -42/1 -98/1 1 9 0.044643 In 0.017857 0.071429 -41/1 0 9 -40/1 0 9 -39/1 1/0 1 9 0.025643 In 0.025424 0.025862 -38/1 0 9 -37/1 0 9 -36/1 -84/1 1 9 0.052083 In 0.020833 0.083333 -35/1 0 9 -34/1 0 9 -33/1 1/0 1 9 0.030306 In 0.030000 0.030612 -32/1 0 9 -31/1 0 9 -30/1 -70/1 1 9 0.062500 In 0.025000 0.100000 -29/1 0 9 -28/1 0 9 -27/1 1/0 1 9 0.037043 In 0.036585 0.037500 -26/1 0 9 -25/1 0 9 -24/1 -56/1 1 9 0.078125 In 0.031250 0.125000 -23/1 0 9 -22/1 0 9 -21/1 1/0 1 9 0.047631 In 0.046875 0.048387 -20/1 0 9 -19/1 0 9 -18/1 -42/1 1 9 0.104167 In 0.041667 0.166667 -17/1 0 9 -16/1 0 9 -15/1 1/0 1 9 0.066700 In 0.065217 0.068182 -14/1 0 9 -13/1 0 9 -12/1 -28/1 1 9 0.156250 In 0.062500 0.250000 -11/1 0 9 -10/1 0 9 -9/1 1/0 1 9 0.111264 In 0.107143 0.115385 -8/1 0 9 -7/1 0 9 -6/1 -14/1 1 9 0.312500 In 0.125000 0.500000 -5/1 0 9 -4/1 0 9 -3/1 1/0 1 9 0.337500 In 0.300000 0.375000 -2/1 0 9 -1/1 0 9 0/1 0/1 1 9 1/1 0 9 2/1 0 9 3/1 1/0 1 9 -0.337500 In -0.375000 -0.300000 4/1 0 9 5/1 0 9 6/1 14/1 1 9 -0.312500 In -0.500000 -0.125000 7/1 0 9 8/1 0 9 9/1 1/0 1 9 -0.111264 In -0.115385 -0.107143 10/1 0 9 11/1 0 9 12/1 28/1 1 9 -0.156250 In -0.250000 -0.062500 13/1 0 9 14/1 0 9 15/1 1/0 1 9 -0.066700 In -0.068182 -0.065217 16/1 0 9 17/1 0 9 18/1 42/1 1 9 -0.104167 In -0.166667 -0.041667 19/1 0 9 20/1 0 9 21/1 1/0 1 9 -0.047631 In -0.048387 -0.046875 22/1 0 9 23/1 0 9 24/1 56/1 1 9 -0.078125 In -0.125000 -0.031250 25/1 0 9 26/1 0 9 27/1 1/0 1 9 -0.037043 In -0.037500 -0.036585 28/1 0 9 29/1 0 9 30/1 70/1 1 9 -0.062500 In -0.100000 -0.025000 31/1 0 9 32/1 0 9 33/1 1/0 1 9 -0.030306 In -0.030612 -0.030000 34/1 0 9 35/1 0 9 36/1 84/1 1 9 -0.052083 In -0.083333 -0.020833 37/1 0 9 38/1 0 9 39/1 1/0 1 9 -0.025643 In -0.025862 -0.025424 40/1 0 9 41/1 0 9 42/1 98/1 1 9 -0.044643 In -0.071429 -0.017857 43/1 0 9 44/1 0 9 45/1 1/0 1 9 -0.022223 In -0.022388 -0.022059 46/1 0 9 47/1 0 9 48/1 112/1 1 9 -0.039062 In -0.062500 -0.015625 49/1 0 9 50/1 0 9 -49/2 0 9 -47/2 0 9 -45/2 -53/1 1 9 0.049105 In 0.037234 0.060976 -43/2 0 9 -41/2 0 9 -39/2 -45/1 1 9 0.056327 In 0.043210 0.069444 -37/2 0 9 -35/2 0 9 -33/2 -39/1 1 9 0.067029 In 0.050725 0.083333 -31/2 0 9 -29/2 0 9 -27/2 -31/1 1 9 0.081250 In 0.062500 0.100000 -25/2 0 9 -23/2 0 9 -21/2 -25/1 1 9 0.105562 In 0.079545 0.131579 -19/2 0 9 -17/2 0 9 -15/2 -17/1 1 9 0.145737 In 0.112903 0.178571 -13/2 0 9 -11/2 0 9 -9/2 -11/1 1 9 0.248355 In 0.184211 0.312500 -7/2 0 9 -5/2 0 9 -3/2 -3/1 1 9 0.708333 In 0.583333 0.833333 -1/2 0 9 1/2 0 9 3/2 3/1 1 9 -0.708333 In -0.833333 -0.583333 5/2 0 9 7/2 0 9 9/2 11/1 1 9 -0.248355 In -0.312500 -0.184211 11/2 0 9 13/2 0 9 15/2 17/1 1 9 -0.145737 In -0.178571 -0.112903 17/2 0 9 19/2 0 9 21/2 25/1 1 9 -0.105562 In -0.131579 -0.079545 23/2 0 9 25/2 0 9 27/2 31/1 1 9 -0.081250 In -0.100000 -0.062500 29/2 0 9 31/2 0 9 33/2 39/1 1 9 -0.067029 In -0.083333 -0.050725 35/2 0 9 37/2 0 9 39/2 45/1 1 9 -0.056327 In -0.069444 -0.043210 41/2 0 9 43/2 0 9 45/2 53/1 1 9 -0.049105 In -0.060976 -0.037234 47/2 0 9 49/2 0 9 -50/3 0 3 -49/3 -38/1 2 3 0.084589 In 0.047690 0.121487 -47/3 1/0 2 3 0.063849 In 0.062740 0.064958 -46/3 -36/1 1 3 0.074822 In 0.053565 0.096078 -44/3 -34/1 1 3 0.077816 In 0.056221 0.099411 -43/3 1/0 2 3 0.069793 In 0.068467 0.071118 -41/3 -32/1 2 3 0.101836 In 0.056854 0.146819 -40/3 0 3 -38/3 0 3 -37/3 1/0 3 3 0.081140 In 0.078947 0.083333 -35/3 1/0 3 3 0.085784 In 0.083333 0.088235 -34/3 0 3 -32/3 0 3 -31/3 -24/1 2 3 0.133449 In 0.075431 0.191467 -29/3 1/0 2 3 0.103530 In 0.100615 0.106445 -28/3 -22/1 1 3 0.123126 In 0.087892 0.158361 -26/3 -20/1 1 3 0.131450 In 0.095277 0.167623 -25/3 1/0 2 3 0.120128 In 0.116205 0.124052 -23/3 -18/1 2 3 0.182109 In 0.101242 0.262976 -22/3 0 3 -20/3 0 3 -19/3 1/0 3 3 0.158333 In 0.150000 0.166667 -17/3 1/0 3 3 0.177083 In 0.166667 0.187500 -16/3 0 3 -14/3 0 3 -13/3 -10/1 2 3 0.315961 In 0.180321 0.451600 -11/3 1/0 2 3 0.274238 In 0.253882 0.294594 -10/3 -8/1 1 3 0.347458 In 0.244709 0.450206 -8/3 -6/1 1 3 0.423077 In 0.312048 0.534106 -7/3 1/0 2 3 0.434483 In 0.383804 0.485162 -5/3 -4/1 2 3 0.860465 In 0.461711 1.259219 -4/3 0 3 -2/3 0 3 -1/3 1/0 3 3 1.500000 Right 1/3 1/0 3 3 -1.500000 Left 2/3 0 3 4/3 0 3 5/3 4/1 2 3 -0.860465 In -1.259219 -0.461711 7/3 1/0 2 3 -0.434483 In -0.485162 -0.383804 8/3 6/1 1 3 -0.423077 In -0.534106 -0.312048 10/3 8/1 1 3 -0.347458 In -0.450206 -0.244709 11/3 1/0 2 3 -0.274238 In -0.294594 -0.253882 13/3 10/1 2 3 -0.315961 In -0.451600 -0.180321 14/3 0 3 16/3 0 3 17/3 1/0 3 3 -0.177083 In -0.187500 -0.166667 19/3 1/0 3 3 -0.158333 In -0.166667 -0.150000 20/3 0 3 22/3 0 3 23/3 18/1 2 3 -0.182109 In -0.262976 -0.101242 25/3 1/0 2 3 -0.120128 In -0.124052 -0.116205 26/3 20/1 1 3 -0.131450 In -0.167623 -0.095277 28/3 22/1 1 3 -0.123126 In -0.158361 -0.087892 29/3 1/0 2 3 -0.103530 In -0.106445 -0.100615 31/3 24/1 2 3 -0.133449 In -0.191467 -0.075431 32/3 0 3 34/3 0 3 35/3 1/0 3 3 -0.085784 In -0.088235 -0.083333 37/3 1/0 3 3 -0.081140 In -0.083333 -0.078947 38/3 0 3 40/3 0 3 41/3 32/1 2 3 -0.101836 In -0.146819 -0.056854 43/3 1/0 2 3 -0.069793 In -0.071118 -0.068467 44/3 34/1 1 3 -0.077816 In -0.099411 -0.056221 46/3 36/1 1 3 -0.074822 In -0.096078 -0.053565 47/3 1/0 2 3 -0.063849 In -0.064958 -0.062740 49/3 38/1 2 3 -0.084589 In -0.121487 -0.047690 50/3 0 3 -49/4 0 9 -47/4 0 9 -45/4 -27/1 1 9 0.091049 In 0.080247 0.101852 -43/4 0 9 -41/4 0 9 -39/4 -21/1 1 9 0.104393 In 0.094203 0.114583 -37/4 0 9 -35/4 0 9 -33/4 -21/1 1 9 0.124679 In 0.108333 0.141026 -31/4 0 9 -29/4 0 9 -27/4 -15/1 1 9 0.151042 In 0.135417 0.166667 -25/4 0 9 -23/4 0 9 -21/4 -13/1 1 9 0.195526 In 0.171053 0.220000 -19/4 0 9 -17/4 0 9 -15/4 -7/1 1 9 0.269737 In 0.250000 0.289474 -13/4 0 9 -11/4 0 9 -9/4 -7/1 1 9 0.466176 In 0.382353 0.550000 -7/4 0 9 -5/4 0 9 -3/4 -1/1 1 9 1.337500 In 1.300000 1.375000 -1/4 0 9 1/4 0 9 3/4 1/1 1 9 -1.337500 In -1.375000 -1.300000 5/4 0 9 7/4 0 9 9/4 7/1 1 9 -0.466176 In -0.550000 -0.382353 11/4 0 9 13/4 0 9 15/4 7/1 1 9 -0.269737 In -0.289474 -0.250000 17/4 0 9 19/4 0 9 21/4 13/1 1 9 -0.195526 In -0.220000 -0.171053 23/4 0 9 25/4 0 9 27/4 15/1 1 9 -0.151042 In -0.166667 -0.135417 29/4 0 9 31/4 0 9 33/4 21/1 1 9 -0.124679 In -0.141026 -0.108333 35/4 0 9 37/4 0 9 39/4 21/1 1 9 -0.104393 In -0.114583 -0.094203 41/4 0 9 43/4 0 9 45/4 27/1 1 9 -0.091049 In -0.101852 -0.080247 47/4 0 9 49/4 0 9 -49/5 0 9 -48/5 -24/1 1 9 0.105952 In 0.095238 0.116667 -47/5 0 9 -46/5 0 9 -44/5 0 9 -43/5 0 9 -42/5 -18/1 1 9 0.120370 In 0.111111 0.129630 -41/5 0 9 -39/5 -37/2 1 9 0.136445 In 0.110390 0.162500 -38/5 0 9 -37/5 0 9 -36/5 -16/1 1 9 0.140603 In 0.129032 0.152174 -34/5 0 9 -33/5 1/0 1 9 0.151531 In 0.150000 0.153061 -32/5 0 9 -31/5 0 9 -29/5 0 9 -28/5 0 9 -27/5 1/0 1 9 0.185213 In 0.182927 0.187500 -26/5 0 9 -24/5 -12/1 1 9 0.211905 In 0.190476 0.233333 -23/5 0 9 -22/5 0 9 -21/5 -19/2 1 9 0.251386 In 0.207317 0.295455 -19/5 0 9 -18/5 -10/1 1 9 0.284091 In 0.250000 0.318182 -17/5 0 9 -16/5 0 9 -14/5 0 9 -13/5 0 9 -12/5 -4/1 1 9 0.418750 In 0.400000 0.437500 -11/5 0 9 -9/5 -9/2 1 9 0.597222 In 0.472222 0.722222 -8/5 0 9 -7/5 0 9 -6/5 -2/1 1 9 0.837500 In 0.800000 0.875000 -4/5 0 9 -3/5 1/0 1 9 1.687500 In 1.500000 1.875000 -2/5 0 9 -1/5 0 9 1/5 0 9 2/5 0 9 3/5 1/0 1 9 -1.687500 In -1.875000 -1.500000 4/5 0 9 6/5 2/1 1 9 -0.837500 In -0.875000 -0.800000 7/5 0 9 8/5 0 9 9/5 9/2 1 9 -0.597222 In -0.722222 -0.472222 11/5 0 9 12/5 4/1 1 9 -0.418750 In -0.437500 -0.400000 13/5 0 9 14/5 0 9 16/5 0 9 17/5 0 9 18/5 10/1 1 9 -0.284091 In -0.318182 -0.250000 19/5 0 9 21/5 19/2 1 9 -0.251386 In -0.295455 -0.207317 22/5 0 9 23/5 0 9 24/5 12/1 1 9 -0.211905 In -0.233333 -0.190476 26/5 0 9 27/5 1/0 1 9 -0.185213 In -0.187500 -0.182927 28/5 0 9 29/5 0 9 31/5 0 9 32/5 0 9 33/5 1/0 1 9 -0.151531 In -0.153061 -0.150000 34/5 0 9 36/5 16/1 1 9 -0.140603 In -0.152174 -0.129032 37/5 0 9 38/5 0 9 39/5 37/2 1 9 -0.136445 In -0.162500 -0.110390 41/5 0 9 42/5 18/1 1 9 -0.120370 In -0.129630 -0.111111 43/5 0 9 44/5 0 9 46/5 0 9 47/5 0 9 48/5 24/1 1 9 -0.105952 In -0.116667 -0.095238 49/5 0 9 -49/6 -20/1 2 3 0.131501 In 0.104340 0.158662 -47/6 -19/1 2 3 0.136833 In 0.109041 0.164626 -43/6 -17/1 2 3 0.148923 In 0.119839 0.178008 -41/6 -16/1 2 3 0.155815 In 0.126082 0.185549 -37/6 -15/1 3 3 0.180944 In 0.134615 0.227273 -35/6 -13/1 3 3 0.186553 In 0.145833 0.227273 -31/6 -12/1 2 3 0.205780 In 0.167079 0.244481 -29/6 -11/1 2 3 0.219202 In 0.179469 0.258935 -25/6 -9/1 2 3 0.252189 In 0.210721 0.293657 -23/6 -8/1 2 3 0.272790 In 0.230818 0.314762 -19/6 -7/1 3 3 0.342949 In 0.269231 0.416667 -17/6 -7/1 3 3 0.395833 In 0.291667 0.500000 -13/6 -6/1 2 3 0.510345 In 0.380832 0.639858 -11/6 -5/1 2 3 0.600639 In 0.451948 0.749330 -7/6 -3/1 2 3 0.930233 In 0.721361 1.139104 -5/6 -2/1 2 3 1.283582 In 1.027665 1.539499 -1/6 -1/1 3 3 3.500000 Right 1/6 1/1 3 3 -3.500000 Left 5/6 2/1 2 3 -1.283582 In -1.539499 -1.027665 7/6 3/1 2 3 -0.930233 In -1.139104 -0.721361 11/6 5/1 2 3 -0.600639 In -0.749330 -0.451948 13/6 6/1 2 3 -0.510345 In -0.639858 -0.380832 17/6 7/1 3 3 -0.395833 In -0.500000 -0.291667 19/6 7/1 3 3 -0.342949 In -0.416667 -0.269231 23/6 8/1 2 3 -0.272790 In -0.314762 -0.230818 25/6 9/1 2 3 -0.252189 In -0.293657 -0.210721 29/6 11/1 2 3 -0.219202 In -0.258935 -0.179469 31/6 12/1 2 3 -0.205780 In -0.244481 -0.167079 35/6 13/1 3 3 -0.186553 In -0.227273 -0.145833 37/6 15/1 3 3 -0.180944 In -0.227273 -0.134615 41/6 16/1 2 3 -0.155815 In -0.185549 -0.126082 43/6 17/1 2 3 -0.148923 In -0.178008 -0.119839 47/6 19/1 2 3 -0.136833 In -0.164626 -0.109041 49/6 20/1 2 3 -0.131501 In -0.158662 -0.104340 -50/7 0 9 -48/7 -16/1 1 9 0.146875 In 0.137500 0.156250 -47/7 0 9 -46/7 0 9 -45/7 1/0 1 9 0.155564 In 0.154412 0.156716 -44/7 0 9 -43/7 0 9 -41/7 0 9 -40/7 0 9 -39/7 1/0 1 9 0.179500 In 0.177966 0.181034 -38/7 0 9 -37/7 0 9 -36/7 -12/1 1 9 0.195833 In 0.183333 0.208333 -34/7 0 9 -33/7 1/0 1 9 0.212143 In 0.210000 0.214286 -32/7 0 9 -31/7 0 9 -30/7 -10/1 1 9 0.235000 In 0.220000 0.250000 -29/7 0 9 -27/7 -17/2 1 9 0.265784 In 0.234694 0.296875 -26/7 0 9 -25/7 0 9 -24/7 -8/1 1 9 0.293750 In 0.275000 0.312500 -23/7 0 9 -22/7 0 9 -20/7 0 9 -19/7 0 9 -18/7 -6/1 1 9 0.391667 In 0.366667 0.416667 -17/7 0 9 -16/7 0 9 -15/7 -11/2 1 9 0.484769 In 0.410714 0.558824 -13/7 0 9 -12/7 -4/1 1 9 0.587500 In 0.550000 0.625000 -11/7 0 9 -10/7 0 9 -9/7 1/0 1 9 0.778846 In 0.750000 0.807692 -8/7 0 9 -6/7 -2/1 1 9 1.175000 In 1.100000 1.250000 -5/7 0 9 -4/7 0 9 -3/7 1/0 1 9 2.362500 In 2.100000 2.625000 -2/7 0 9 -1/7 0 9 1/7 0 9 2/7 0 9 3/7 1/0 1 9 -2.362500 In -2.625000 -2.100000 4/7 0 9 5/7 0 9 6/7 2/1 1 9 -1.175000 In -1.250000 -1.100000 8/7 0 9 9/7 1/0 1 9 -0.778846 In -0.807692 -0.750000 10/7 0 9 11/7 0 9 12/7 4/1 1 9 -0.587500 In -0.625000 -0.550000 13/7 0 9 15/7 11/2 1 9 -0.484769 In -0.558824 -0.410714 16/7 0 9 17/7 0 9 18/7 6/1 1 9 -0.391667 In -0.416667 -0.366667 19/7 0 9 20/7 0 9 22/7 0 9 23/7 0 9 24/7 8/1 1 9 -0.293750 In -0.312500 -0.275000 25/7 0 9 26/7 0 9 27/7 17/2 1 9 -0.265784 In -0.296875 -0.234694 29/7 0 9 30/7 10/1 1 9 -0.235000 In -0.250000 -0.220000 31/7 0 9 32/7 0 9 33/7 1/0 1 9 -0.212143 In -0.214286 -0.210000 34/7 0 9 36/7 12/1 1 9 -0.195833 In -0.208333 -0.183333 37/7 0 9 38/7 0 9 39/7 1/0 1 9 -0.179500 In -0.181034 -0.177966 40/7 0 9 41/7 0 9 43/7 0 9 44/7 0 9 45/7 1/0 1 9 -0.155564 In -0.156716 -0.154412 46/7 0 9 47/7 0 9 48/7 16/1 1 9 -0.146875 In -0.156250 -0.137500 50/7 0 9 -49/8 0 9 -47/8 0 9 -45/8 -15/1 1 9 0.179167 In 0.166667 0.191667 -43/8 0 9 -41/8 0 9 -39/8 -35/3 1 9 0.216865 In 0.177632 0.256098 -37/8 0 9 -35/8 0 9 -33/8 -9/1 1 9 0.243519 In 0.231481 0.255556 -31/8 0 9 -29/8 0 9 -27/8 -9/1 1 9 0.298611 In 0.277778 0.319444 -25/8 0 9 -23/8 0 9 -21/8 -5/1 1 9 0.382099 In 0.367647 0.396552 -19/8 0 9 -17/8 0 9 -15/8 -5/1 1 9 0.537500 In 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