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 23 -49/1 -49/1 1 23 -48/1 -48/1 1 23 -47/1 -47/1 1 23 -46/1 -46/1 1 23 -45/1 -45/1 1 23 -44/1 -44/1 1 23 -43/1 -43/1 1 23 -42/1 -42/1 1 23 -41/1 -41/1 1 23 -40/1 -40/1 1 23 -39/1 -39/1 1 23 -38/1 -38/1 1 23 -37/1 -37/1 1 23 -36/1 -36/1 1 23 -35/1 -35/1 1 23 -34/1 -34/1 1 23 -33/1 -33/1 1 23 -32/1 -32/1 1 23 -31/1 -31/1 1 23 -30/1 -30/1 1 23 -29/1 -29/1 1 23 -28/1 -28/1 1 23 -27/1 -27/1 1 23 -26/1 -26/1 1 23 -25/1 -25/1 1 23 -24/1 -24/1 1 23 -23/1 -23/1 1 23 -22/1 -22/1 1 23 -21/1 -21/1 1 23 -20/1 -20/1 1 23 -19/1 -19/1 1 23 -18/1 -18/1 1 23 -17/1 -17/1 1 23 -16/1 -16/1 1 23 -15/1 -15/1 1 23 -14/1 -14/1 1 23 -13/1 -13/1 1 23 -12/1 -12/1 1 23 -11/1 -11/1 1 23 -10/1 -10/1 1 23 -9/1 -9/1 1 23 -8/1 -8/1 1 23 -7/1 -7/1 1 23 -6/1 -6/1 1 23 -5/1 -5/1 1 23 -4/1 -4/1 1 23 -3/1 -3/1 1 23 -2/1 -2/1 1 23 -1/1 -1/1 1 23 0/1 0/1 1 23 1/1 1/1 1 23 2/1 2/1 1 23 3/1 3/1 1 23 4/1 4/1 1 23 5/1 5/1 1 23 6/1 6/1 1 23 7/1 7/1 1 23 8/1 8/1 1 23 9/1 9/1 1 23 10/1 10/1 1 23 11/1 11/1 1 23 12/1 12/1 1 23 13/1 13/1 1 23 14/1 14/1 1 23 15/1 15/1 1 23 16/1 16/1 1 23 17/1 17/1 1 23 18/1 18/1 1 23 19/1 19/1 1 23 20/1 20/1 1 23 21/1 21/1 1 23 22/1 22/1 1 23 23/1 23/1 1 23 24/1 24/1 1 23 25/1 25/1 1 23 26/1 26/1 1 23 27/1 27/1 1 23 28/1 28/1 1 23 29/1 29/1 1 23 30/1 30/1 1 23 31/1 31/1 1 23 32/1 32/1 1 23 33/1 33/1 1 23 34/1 34/1 1 23 35/1 35/1 1 23 36/1 36/1 1 23 37/1 37/1 1 23 38/1 38/1 1 23 39/1 39/1 1 23 40/1 40/1 1 23 41/1 41/1 1 23 42/1 42/1 1 23 43/1 43/1 1 23 44/1 44/1 1 23 45/1 45/1 1 23 46/1 46/1 1 23 47/1 47/1 1 23 48/1 48/1 1 23 49/1 49/1 1 23 50/1 50/1 1 23 -49/2 -49/2 1 23 -47/2 -47/2 1 23 -45/2 -45/2 1 23 -43/2 -43/2 1 23 -41/2 -41/2 1 23 -39/2 -39/2 1 23 -37/2 -37/2 1 23 -35/2 -35/2 1 23 -33/2 -33/2 1 23 -31/2 -31/2 1 23 -29/2 -29/2 1 23 -27/2 -27/2 1 23 -25/2 -25/2 1 23 -23/2 -23/2 1 23 -21/2 -21/2 1 23 -19/2 -19/2 1 23 -17/2 -17/2 1 23 -15/2 -15/2 1 23 -13/2 -13/2 1 23 -11/2 -11/2 1 23 -9/2 -9/2 1 23 -7/2 -7/2 1 23 -5/2 -5/2 1 23 -3/2 -3/2 1 23 -1/2 -1/2 1 23 1/2 1/2 1 23 3/2 3/2 1 23 5/2 5/2 1 23 7/2 7/2 1 23 9/2 9/2 1 23 11/2 11/2 1 23 13/2 13/2 1 23 15/2 15/2 1 23 17/2 17/2 1 23 19/2 19/2 1 23 21/2 21/2 1 23 23/2 23/2 1 23 25/2 25/2 1 23 27/2 27/2 1 23 29/2 29/2 1 23 31/2 31/2 1 23 33/2 33/2 1 23 35/2 35/2 1 23 37/2 37/2 1 23 39/2 39/2 1 23 41/2 41/2 1 23 43/2 43/2 1 23 45/2 45/2 1 23 47/2 47/2 1 23 49/2 49/2 1 23 -50/3 -18/1 1 23 0.060025 In 0.059690 0.060361 -49/3 -15/1 1 23 0.061202 In 0.060853 0.061551 -47/3 -17/1 1 23 0.063858 In 0.063479 0.064238 -46/3 -14/1 1 23 0.065192 In 0.064797 0.065588 -44/3 -16/1 1 23 0.068215 In 0.067781 0.068648 -43/3 -13/1 1 23 0.069739 In 0.069286 0.070192 -41/3 -15/1 1 23 0.073209 In 0.072710 0.073708 -40/3 -12/1 1 23 0.074967 In 0.074444 0.075491 -38/3 -14/1 1 23 0.078992 In 0.078411 0.079573 -37/3 -11/1 1 23 0.081043 In 0.080432 0.081655 -35/3 -13/1 1 23 0.085767 In 0.085082 0.086452 -34/3 -10/1 1 23 0.088191 In 0.087467 0.088915 -32/3 -12/1 1 23 0.093814 In 0.092995 0.094634 -31/3 -9/1 1 23 0.096721 In 0.095850 0.097593 -29/3 -11/1 1 23 0.103527 In 0.102529 0.104525 -28/3 -8/1 1 23 0.107079 In 0.106012 0.108147 -26/3 -10/1 1 23 0.115484 In 0.114242 0.116726 -25/3 -7/1 1 23 0.119922 In 0.118583 0.121261 -23/3 -9/1 1 23 0.130564 In 0.128977 0.132152 -22/3 -6/1 1 23 0.136265 In 0.134536 0.137994 -20/3 -8/1 1 23 0.150175 In 0.148075 0.152275 -19/3 -5/1 1 23 0.157768 In 0.155450 0.160085 -17/3 -7/1 1 23 0.176720 In 0.173813 0.179628 -16/3 -4/1 1 23 0.187330 In 0.184063 0.190597 -14/3 -6/1 1 23 0.214669 In 0.210379 0.218959 -13/3 -3/1 1 23 0.230531 In 0.225584 0.235478 -11/3 -5/1 1 23 0.273387 In 0.266431 0.280342 -10/3 -2/1 1 23 0.299652 In 0.291296 0.308007 -8/3 -4/1 1 23 0.376374 In 0.363198 0.389549 -7/3 -1/1 1 23 0.428064 In 0.411027 0.445101 -5/3 -3/1 1 23 0.604240 In 0.570347 0.638133 -4/3 0/1 1 23 0.750000 In 0.697871 0.802129 -2/3 -2/1 1 23 1.545455 In 1.327462 1.763447 -1/3 1/1 1 23 3.181818 In 2.309849 4.053788 1/3 -1/1 1 23 -3.181818 In -4.053788 -2.309849 2/3 2/1 1 23 -1.545455 In -1.763447 -1.327462 4/3 0/1 1 23 -0.750000 In -0.802129 -0.697871 5/3 3/1 1 23 -0.604240 In -0.638133 -0.570347 7/3 1/1 1 23 -0.428064 In -0.445101 -0.411027 8/3 4/1 1 23 -0.376374 In -0.389549 -0.363198 10/3 2/1 1 23 -0.299652 In -0.308007 -0.291296 11/3 5/1 1 23 -0.273387 In -0.280342 -0.266431 13/3 3/1 1 23 -0.230531 In -0.235478 -0.225584 14/3 6/1 1 23 -0.214669 In -0.218959 -0.210379 16/3 4/1 1 23 -0.187330 In -0.190597 -0.184063 17/3 7/1 1 23 -0.176720 In -0.179628 -0.173813 19/3 5/1 1 23 -0.157768 In -0.160085 -0.155450 20/3 8/1 1 23 -0.150175 In -0.152275 -0.148075 22/3 6/1 1 23 -0.136265 In -0.137994 -0.134536 23/3 9/1 1 23 -0.130564 In -0.132152 -0.128977 25/3 7/1 1 23 -0.119922 In -0.121261 -0.118583 26/3 10/1 1 23 -0.115484 In -0.116726 -0.114242 28/3 8/1 1 23 -0.107079 In -0.108147 -0.106012 29/3 11/1 1 23 -0.103527 In -0.104525 -0.102529 31/3 9/1 1 23 -0.096721 In -0.097593 -0.095850 32/3 12/1 1 23 -0.093814 In -0.094634 -0.092995 34/3 10/1 1 23 -0.088191 In -0.088915 -0.087467 35/3 13/1 1 23 -0.085767 In -0.086452 -0.085082 37/3 11/1 1 23 -0.081043 In -0.081655 -0.080432 38/3 14/1 1 23 -0.078992 In -0.079573 -0.078411 40/3 12/1 1 23 -0.074967 In -0.075491 -0.074444 41/3 15/1 1 23 -0.073209 In -0.073708 -0.072710 43/3 13/1 1 23 -0.069739 In -0.070192 -0.069286 44/3 16/1 1 23 -0.068215 In -0.068648 -0.067781 46/3 14/1 1 23 -0.065192 In -0.065588 -0.064797 47/3 17/1 1 23 -0.063858 In -0.064238 -0.063479 49/3 15/1 1 23 -0.061202 In -0.061551 -0.060853 50/3 18/1 1 23 -0.060025 In -0.060361 -0.059690 -49/4 1/0 1 23 0.081634 In 0.081287 0.081982 -47/4 1/0 1 23 0.085108 In 0.084730 0.085486 -45/4 1/0 1 23 0.088891 In 0.088479 0.089303 -43/4 1/0 1 23 0.093025 In 0.092574 0.093477 -41/4 1/0 1 23 0.097563 In 0.097067 0.098060 -39/4 1/0 1 23 0.102567 In 0.102019 0.103115 -37/4 1/0 1 23 0.108112 In 0.107502 0.108721 -35/4 1/0 1 23 0.114290 In 0.113609 0.114971 -33/4 1/0 1 23 0.121217 In 0.120451 0.121983 -31/4 1/0 1 23 0.129038 In 0.128170 0.129906 -29/4 1/0 1 23 0.137938 In 0.136946 0.138930 -27/4 1/0 1 23 0.148157 In 0.147013 0.149301 -25/4 1/0 1 23 0.160011 In 0.158677 0.161346 -23/4 1/0 1 23 0.173927 In 0.172351 0.175504 -21/4 1/0 1 23 0.190495 In 0.188603 0.192386 -19/4 1/0 1 23 0.210552 In 0.208241 0.212862 -17/4 1/0 1 23 0.235330 In 0.232443 0.238216 -15/4 1/0 1 23 0.266718 In 0.263011 0.270426 -13/4 1/0 1 23 0.307771 In 0.302835 0.312708 -11/4 1/0 1 23 0.363767 In 0.356872 0.370663 -9/4 1/0 1 23 0.444683 In 0.434381 0.454986 -7/4 1/0 1 23 0.571936 In 0.554899 0.588973 -5/4 1/0 1 23 0.801394 In 0.767973 0.834814 -3/4 1/0 1 23 1.339806 In 1.246683 1.432929 -1/4 1/0 1 23 4.181818 In 3.309849 5.053788 1/4 1/0 1 23 -4.181818 In -5.053788 -3.309849 3/4 1/0 1 23 -1.339806 In -1.432929 -1.246683 5/4 1/0 1 23 -0.801394 In -0.834814 -0.767973 7/4 1/0 1 23 -0.571936 In -0.588973 -0.554899 9/4 1/0 1 23 -0.444683 In -0.454986 -0.434381 11/4 1/0 1 23 -0.363767 In -0.370663 -0.356872 13/4 1/0 1 23 -0.307771 In -0.312708 -0.302835 15/4 1/0 1 23 -0.266718 In -0.270426 -0.263011 17/4 1/0 1 23 -0.235330 In -0.238216 -0.232443 19/4 1/0 1 23 -0.210552 In -0.212862 -0.208241 21/4 1/0 1 23 -0.190495 In -0.192386 -0.188603 23/4 1/0 1 23 -0.173927 In -0.175504 -0.172351 25/4 1/0 1 23 -0.160011 In -0.161346 -0.158677 27/4 1/0 1 23 -0.148157 In -0.149301 -0.147013 29/4 1/0 1 23 -0.137938 In -0.138930 -0.136946 31/4 1/0 1 23 -0.129038 In -0.129906 -0.128170 33/4 1/0 1 23 -0.121217 In -0.121983 -0.120451 35/4 1/0 1 23 -0.114290 In -0.114971 -0.113609 37/4 1/0 1 23 -0.108112 In -0.108721 -0.107502 39/4 1/0 1 23 -0.102567 In -0.103115 -0.102019 41/4 1/0 1 23 -0.097563 In -0.098060 -0.097067 43/4 1/0 1 23 -0.093025 In -0.093477 -0.092574 45/4 1/0 1 23 -0.088891 In -0.089303 -0.088479 47/4 1/0 1 23 -0.085108 In -0.085486 -0.084730 49/4 1/0 1 23 -0.081634 In -0.081982 -0.081287 -49/5 -9/1 1 23 0.102027 In 0.101680 0.102375 -48/5 -10/1 1 23 0.104175 In 0.103993 0.104356 -47/5 -9/1 1 23 0.106375 In 0.106186 0.106565 -46/5 -10/1 1 23 0.108714 In 0.108319 0.109109 -44/5 -8/1 1 23 0.113620 In 0.113189 0.114051 -43/5 -9/1 1 23 0.116289 In 0.116063 0.116515 -42/5 -8/1 1 23 0.119038 In 0.118801 0.119275 -41/5 -9/1 1 23 0.121974 In 0.121477 0.122471 -39/5 -7/1 1 23 0.128185 In 0.127635 0.128734 -38/5 -8/1 1 23 0.131592 In 0.131302 0.131881 -37/5 -7/1 1 23 0.135123 In 0.134818 0.135428 -36/5 -8/1 1 23 0.138919 In 0.138274 0.139564 -34/5 -6/1 1 23 0.147032 In 0.146310 0.147755 -33/5 -7/1 1 23 0.151532 In 0.151148 0.151916 -32/5 -6/1 1 23 0.156234 In 0.155826 0.156642 -31/5 -7/1 1 23 0.161331 In 0.160461 0.162201 -29/5 -5/1 1 23 0.172378 In 0.171385 0.173371 -28/5 -6/1 1 23 0.178595 In 0.178062 0.179128 -27/5 -5/1 1 23 0.185163 In 0.184590 0.185736 -26/5 -6/1 1 23 0.192367 In 0.191131 0.193604 -24/5 -4/1 1 23 0.208283 In 0.206833 0.209733 -23/5 -5/1 1 23 0.217427 In 0.216637 0.218217 -22/5 -4/1 1 23 0.227240 In 0.226377 0.228103 -21/5 -5/1 1 23 0.238189 In 0.236293 0.240085 -19/5 -3/1 1 23 0.263082 In 0.260769 0.265395 -18/5 -4/1 1 23 0.277838 In 0.276548 0.279127 -17/5 -3/1 1 23 0.294064 In 0.292620 0.295509 -16/5 -4/1 1 23 0.312670 In 0.309403 0.315937 -14/5 -2/1 1 23 0.357016 In 0.352757 0.361275 -13/5 -3/1 1 23 0.384734 In 0.382261 0.387208 -12/5 -2/1 1 23 0.416566 In 0.413666 0.419465 -11/5 -3/1 1 23 0.454939 In 0.448023 0.461854 -9/5 -1/1 1 23 0.555317 In 0.545014 0.565619 -8/5 -2/1 1 23 0.625341 In 0.618807 0.631874 -7/5 -1/1 1 23 0.714032 In 0.705514 0.722550 -6/5 -2/1 1 23 0.834951 In 0.811671 0.858232 -4/5 0/1 1 23 1.250000 In 1.197871 1.302129 -3/5 -1/1 1 23 1.669903 In 1.623341 1.716464 -2/5 0/1 1 23 2.500000 In 2.395743 2.604257 -1/5 -1/1 1 23 5.181818 In 4.309849 6.053788 1/5 1/1 1 23 -5.181818 In -6.053788 -4.309849 2/5 0/1 1 23 -2.500000 In -2.604257 -2.395743 3/5 1/1 1 23 -1.669903 In -1.716464 -1.623341 4/5 0/1 1 23 -1.250000 In -1.302129 -1.197871 6/5 2/1 1 23 -0.834951 In -0.858232 -0.811671 7/5 1/1 1 23 -0.714032 In -0.722550 -0.705514 8/5 2/1 1 23 -0.625341 In -0.631874 -0.618807 9/5 1/1 1 23 -0.555317 In -0.565619 -0.545014 11/5 3/1 1 23 -0.454939 In -0.461854 -0.448023 12/5 2/1 1 23 -0.416566 In -0.419465 -0.413666 13/5 3/1 1 23 -0.384734 In -0.387208 -0.382261 14/5 2/1 1 23 -0.357016 In -0.361275 -0.352757 16/5 4/1 1 23 -0.312670 In -0.315937 -0.309403 17/5 3/1 1 23 -0.294064 In -0.295509 -0.292620 18/5 4/1 1 23 -0.277838 In -0.279127 -0.276548 19/5 3/1 1 23 -0.263082 In -0.265395 -0.260769 21/5 5/1 1 23 -0.238189 In -0.240085 -0.236293 22/5 4/1 1 23 -0.227240 In -0.228103 -0.226377 23/5 5/1 1 23 -0.217427 In -0.218217 -0.216637 24/5 4/1 1 23 -0.208283 In -0.209733 -0.206833 26/5 6/1 1 23 -0.192367 In -0.193604 -0.191131 27/5 5/1 1 23 -0.185163 In -0.185736 -0.184590 28/5 6/1 1 23 -0.178595 In -0.179128 -0.178062 29/5 5/1 1 23 -0.172378 In -0.173371 -0.171385 31/5 7/1 1 23 -0.161331 In -0.162201 -0.160461 32/5 6/1 1 23 -0.156234 In -0.156642 -0.155826 33/5 7/1 1 23 -0.151532 In -0.151916 -0.151148 34/5 6/1 1 23 -0.147032 In -0.147755 -0.146310 36/5 8/1 1 23 -0.138919 In -0.139564 -0.138274 37/5 7/1 1 23 -0.135123 In -0.135428 -0.134818 38/5 8/1 1 23 -0.131592 In -0.131881 -0.131302 39/5 7/1 1 23 -0.128185 In -0.128734 -0.127635 41/5 9/1 1 23 -0.121974 In -0.122471 -0.121477 42/5 8/1 1 23 -0.119038 In -0.119275 -0.118801 43/5 9/1 1 23 -0.116289 In -0.116515 -0.116063 44/5 8/1 1 23 -0.113620 In -0.114051 -0.113189 46/5 10/1 1 23 -0.108714 In -0.109109 -0.108319 47/5 9/1 1 23 -0.106375 In -0.106565 -0.106186 48/5 10/1 1 23 -0.104175 In -0.104356 -0.103993 49/5 9/1 1 23 -0.102027 In -0.102375 -0.101680 -49/6 -17/2 1 23 0.122474 In 0.122125 0.122823 -47/6 -15/2 1 23 0.127634 In 0.127255 0.128014 -43/6 -15/2 1 23 0.139568 In 0.139114 0.140021 -41/6 -13/2 1 23 0.146309 In 0.145810 0.146807 -37/6 -13/2 1 23 0.162207 In 0.161595 0.162820 -35/6 -11/2 1 23 0.171384 In 0.170700 0.172068 -31/6 -11/2 1 23 0.193613 In 0.192740 0.194486 -29/6 -9/2 1 23 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