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 8 -49/1 -49/1 1 8 -48/1 -48/1 1 8 -47/1 -47/1 1 8 -46/1 -46/1 1 8 -45/1 -45/1 1 8 -44/1 -44/1 1 8 -43/1 -43/1 1 8 -42/1 -42/1 1 8 -41/1 -41/1 1 8 -40/1 -40/1 1 8 -39/1 -39/1 1 8 -38/1 -38/1 1 8 -37/1 -37/1 1 8 -36/1 -36/1 1 8 -35/1 -35/1 1 8 -34/1 -34/1 1 8 -33/1 -33/1 1 8 -32/1 -32/1 1 8 -31/1 -31/1 1 8 -30/1 -30/1 1 8 -29/1 -29/1 1 8 -28/1 -28/1 1 8 -27/1 -27/1 1 8 -26/1 -26/1 1 8 -25/1 -25/1 1 8 -24/1 -24/1 1 8 -23/1 -23/1 1 8 -22/1 -22/1 1 8 -21/1 -21/1 1 8 -20/1 -20/1 1 8 -19/1 -19/1 1 8 -18/1 -18/1 1 8 -17/1 -17/1 1 8 -16/1 -16/1 1 8 -15/1 -15/1 1 8 -14/1 -14/1 1 8 -13/1 -13/1 1 8 -12/1 -12/1 1 8 -11/1 -11/1 1 8 -10/1 -10/1 1 8 -9/1 -9/1 1 8 -8/1 -8/1 1 8 -7/1 -7/1 1 8 -6/1 -6/1 1 8 -5/1 -5/1 1 8 -4/1 -4/1 1 8 -3/1 -3/1 1 8 -2/1 -2/1 1 8 -1/1 -1/1 1 8 0/1 0/1 1 8 1/1 1/1 1 8 2/1 2/1 1 8 3/1 3/1 1 8 4/1 4/1 1 8 5/1 5/1 1 8 6/1 6/1 1 8 7/1 7/1 1 8 8/1 8/1 1 8 9/1 9/1 1 8 10/1 10/1 1 8 11/1 11/1 1 8 12/1 12/1 1 8 13/1 13/1 1 8 14/1 14/1 1 8 15/1 15/1 1 8 16/1 16/1 1 8 17/1 17/1 1 8 18/1 18/1 1 8 19/1 19/1 1 8 20/1 20/1 1 8 21/1 21/1 1 8 22/1 22/1 1 8 23/1 23/1 1 8 24/1 24/1 1 8 25/1 25/1 1 8 26/1 26/1 1 8 27/1 27/1 1 8 28/1 28/1 1 8 29/1 29/1 1 8 30/1 30/1 1 8 31/1 31/1 1 8 32/1 32/1 1 8 33/1 33/1 1 8 34/1 34/1 1 8 35/1 35/1 1 8 36/1 36/1 1 8 37/1 37/1 1 8 38/1 38/1 1 8 39/1 39/1 1 8 40/1 40/1 1 8 41/1 41/1 1 8 42/1 42/1 1 8 43/1 43/1 1 8 44/1 44/1 1 8 45/1 45/1 1 8 46/1 46/1 1 8 47/1 47/1 1 8 48/1 48/1 1 8 49/1 49/1 1 8 50/1 50/1 1 8 -49/2 0 4 -47/2 0 4 -45/2 0 4 -43/2 0 4 -41/2 0 4 -39/2 0 4 -37/2 0 4 -35/2 0 4 -33/2 0 4 -31/2 0 4 -29/2 0 4 -27/2 0 4 -25/2 0 4 -23/2 0 4 -21/2 0 4 -19/2 0 4 -17/2 0 4 -15/2 0 4 -13/2 0 4 -11/2 0 4 -9/2 0 4 -7/2 0 4 -5/2 0 4 -3/2 0 4 -1/2 0 4 1/2 0 4 3/2 0 4 5/2 0 4 7/2 0 4 9/2 0 4 11/2 0 4 13/2 0 4 15/2 0 4 17/2 0 4 19/2 0 4 21/2 0 4 23/2 0 4 25/2 0 4 27/2 0 4 29/2 0 4 31/2 0 4 33/2 0 4 35/2 0 4 37/2 0 4 39/2 0 4 41/2 0 4 43/2 0 4 45/2 0 4 47/2 0 4 49/2 0 4 -50/3 -16/1 1 8 0.059968 In 0.059681 0.060254 -49/3 -17/1 1 8 0.061261 In 0.060962 0.061560 -47/3 -15/1 1 8 0.063793 In 0.063469 0.064117 -46/3 -16/1 1 8 0.065259 In 0.064920 0.065598 -44/3 -14/1 1 8 0.068140 In 0.067770 0.068510 -43/3 -15/1 1 8 0.069815 In 0.069427 0.070204 -41/3 -13/1 1 8 0.073123 In 0.072697 0.073549 -40/3 -14/1 1 8 0.075056 In 0.074607 0.075504 -38/3 -12/1 1 8 0.078892 In 0.078396 0.079388 -37/3 -13/1 1 8 0.081146 In 0.080622 0.081671 -35/3 -11/1 1 8 0.085649 In 0.085065 0.086234 -34/3 -12/1 1 8 0.088313 In 0.087691 0.088934 -32/3 -10/1 1 8 0.093673 In 0.092974 0.094372 -31/3 -11/1 1 8 0.096868 In 0.096120 0.097616 -29/3 -9/1 1 8 0.103355 In 0.102504 0.104206 -28/3 -10/1 1 8 0.107259 In 0.106342 0.108175 -26/3 -8/1 1 8 0.115269 In 0.114211 0.116328 -25/3 -9/1 1 8 0.120146 In 0.118996 0.121296 -23/3 -7/1 1 8 0.130289 In 0.128937 0.131642 -22/3 -8/1 1 8 0.136555 In 0.135069 0.138040 -20/3 -6/1 1 8 0.149810 In 0.148022 0.151598 -19/3 -7/1 1 8 0.158154 In 0.156162 0.160147 -17/3 -5/1 1 8 0.176213 In 0.173740 0.178687 -16/3 -6/1 1 8 0.187873 In 0.185061 0.190684 -14/3 -4/1 1 8 0.213918 In 0.210273 0.217562 -13/3 -5/1 1 8 0.231349 In 0.227086 0.235612 -11/3 -3/1 1 8 0.272158 In 0.266260 0.278057 -10/3 -4/1 1 8 0.301020 In 0.293805 0.308236 -8/3 -2/1 1 8 0.374016 In 0.362880 0.385151 -7/3 -3/1 1 8 0.430809 In 0.416040 0.445579 -5/3 -1/1 1 8 0.597990 In 0.569564 0.626416 -4/3 -2/1 1 8 0.758065 In 0.712445 0.803684 -2/3 0/1 1 8 1.500000 In 1.323223 1.676777 -1/3 -1/1 1 8 3.285714 In 2.477592 4.093836 1/3 1/1 1 8 -3.285714 In -4.093836 -2.477592 2/3 0/1 1 8 -1.500000 In -1.676777 -1.323223 4/3 2/1 1 8 -0.758065 In -0.803684 -0.712445 5/3 1/1 1 8 -0.597990 In -0.626416 -0.569564 7/3 3/1 1 8 -0.430809 In -0.445579 -0.416040 8/3 2/1 1 8 -0.374016 In -0.385151 -0.362880 10/3 4/1 1 8 -0.301020 In -0.308236 -0.293805 11/3 3/1 1 8 -0.272158 In -0.278057 -0.266260 13/3 5/1 1 8 -0.231349 In -0.235612 -0.227086 14/3 4/1 1 8 -0.213918 In -0.217562 -0.210273 16/3 6/1 1 8 -0.187873 In -0.190684 -0.185061 17/3 5/1 1 8 -0.176213 In -0.178687 -0.173740 19/3 7/1 1 8 -0.158154 In -0.160147 -0.156162 20/3 6/1 1 8 -0.149810 In -0.151598 -0.148022 22/3 8/1 1 8 -0.136555 In -0.138040 -0.135069 23/3 7/1 1 8 -0.130289 In -0.131642 -0.128937 25/3 9/1 1 8 -0.120146 In -0.121296 -0.118996 26/3 8/1 1 8 -0.115269 In -0.116328 -0.114211 28/3 10/1 1 8 -0.107259 In -0.108175 -0.106342 29/3 9/1 1 8 -0.103355 In -0.104206 -0.102504 31/3 11/1 1 8 -0.096868 In -0.097616 -0.096120 32/3 10/1 1 8 -0.093673 In -0.094372 -0.092974 34/3 12/1 1 8 -0.088313 In -0.088934 -0.087691 35/3 11/1 1 8 -0.085649 In -0.086234 -0.085065 37/3 13/1 1 8 -0.081146 In -0.081671 -0.080622 38/3 12/1 1 8 -0.078892 In -0.079388 -0.078396 40/3 14/1 1 8 -0.075056 In -0.075504 -0.074607 41/3 13/1 1 8 -0.073123 In -0.073549 -0.072697 43/3 15/1 1 8 -0.069815 In -0.070204 -0.069427 44/3 14/1 1 8 -0.068140 In -0.068510 -0.067770 46/3 16/1 1 8 -0.065259 In -0.065598 -0.064920 47/3 15/1 1 8 -0.063793 In -0.064117 -0.063469 49/3 17/1 1 8 -0.061261 In -0.061560 -0.060962 50/3 16/1 1 8 -0.059968 In -0.060254 -0.059681 -49/4 0 2 -47/4 0 2 -45/4 0 2 -43/4 0 2 -41/4 0 2 -39/4 0 2 -37/4 0 2 -35/4 0 2 -33/4 0 2 -31/4 0 2 -29/4 0 2 -27/4 0 2 -25/4 0 2 -23/4 0 2 -21/4 0 2 -19/4 0 2 -17/4 0 2 -15/4 0 2 -13/4 0 2 -11/4 0 2 -9/4 0 2 -7/4 0 2 -5/4 0 2 -3/4 0 2 -1/4 0 2 1/4 0 2 3/4 0 2 5/4 0 2 7/4 0 2 9/4 0 2 11/4 0 2 13/4 0 2 15/4 0 2 17/4 0 2 19/4 0 2 21/4 0 2 23/4 0 2 25/4 0 2 27/4 0 2 29/4 0 2 31/4 0 2 33/4 0 2 35/4 0 2 37/4 0 2 39/4 0 2 41/4 0 2 43/4 0 2 45/4 0 2 47/4 0 2 49/4 0 2 -49/5 -9/1 1 8 0.102002 In 0.101411 0.102594 -48/5 -8/1 1 8 0.104094 In 0.102862 0.105326 -47/5 -11/1 1 8 0.106490 In 0.105200 0.107779 -46/5 -10/1 1 8 0.108747 In 0.108075 0.109420 -44/5 -8/1 1 8 0.113589 In 0.112856 0.114323 -43/5 -7/1 1 8 0.116191 In 0.114656 0.117726 -42/5 -10/1 1 8 0.119184 In 0.117569 0.120798 -41/5 -9/1 1 8 0.122017 In 0.121171 0.122863 -39/5 -7/1 1 8 0.128146 In 0.127212 0.129079 -38/5 -6/1 1 8 0.131469 In 0.129504 0.133434 -37/5 -9/1 1 8 0.135314 In 0.133233 0.137396 -36/5 -8/1 1 8 0.138975 In 0.137877 0.140073 -34/5 -6/1 1 8 0.146982 In 0.145754 0.148210 -33/5 -5/1 1 8 0.151376 In 0.148771 0.153980 -32/5 -8/1 1 8 0.156496 In 0.153712 0.159280 -31/5 -7/1 1 8 0.161409 In 0.159928 0.162890 -29/5 -5/1 1 8 0.172311 In 0.170623 0.173999 -28/5 -4/1 1 8 0.178389 In 0.174772 0.182006 -27/5 -7/1 1 8 0.185544 In 0.181631 0.189457 -26/5 -6/1 1 8 0.192480 In 0.190373 0.194586 -24/5 -4/1 1 8 0.208188 In 0.205724 0.210652 -23/5 -3/1 1 8 0.217144 In 0.211786 0.222502 -22/5 -6/1 1 8 0.227842 In 0.221943 0.233740 -21/5 -5/1 1 8 0.238367 In 0.235137 0.241597 -19/5 -3/1 1 8 0.262939 In 0.259009 0.266868 -18/5 -2/1 1 8 0.277434 In 0.268691 0.286178 -17/5 -5/1 1 8 0.295146 In 0.285253 0.305040 -16/5 -4/1 1 8 0.312992 In 0.307424 0.318560 -14/5 -2/1 1 8 0.356777 In 0.349544 0.364011 -13/5 -1/1 1 8 0.384160 In 0.367411 0.400909 -12/5 -4/1 1 8 0.419014 In 0.399096 0.438933 -11/5 -3/1 1 8 0.455683 In 0.443886 0.467480 -9/5 -1/1 1 8 0.554869 In 0.537382 0.572355 -8/5 0/1 1 8 0.625000 In 0.580806 0.669194 -7/5 -3/1 1 8 0.723238 In 0.664158 0.782317 -6/5 -2/1 1 8 0.838028 In 0.798191 0.877865 -4/5 0/1 1 8 1.250000 In 1.161612 1.338388 -3/5 1/1 1 8 1.704225 In 1.385529 2.022921 -2/5 -2/1 1 8 2.785714 In 1.977592 3.593836 -1/5 -1/1 1 8 5.571429 In 3.955185 7.187673 1/5 1/1 1 8 -5.571429 In -7.187673 -3.955185 2/5 2/1 1 8 -2.785714 In -3.593836 -1.977592 3/5 -1/1 1 8 -1.704225 In -2.022921 -1.385529 4/5 0/1 1 8 -1.250000 In -1.338388 -1.161612 6/5 2/1 1 8 -0.838028 In -0.877865 -0.798191 7/5 3/1 1 8 -0.723238 In -0.782317 -0.664158 8/5 0/1 1 8 -0.625000 In -0.669194 -0.580806 9/5 1/1 1 8 -0.554869 In -0.572355 -0.537382 11/5 3/1 1 8 -0.455683 In -0.467480 -0.443886 12/5 4/1 1 8 -0.419014 In -0.438933 -0.399096 13/5 1/1 1 8 -0.384160 In -0.400909 -0.367411 14/5 2/1 1 8 -0.356777 In -0.364011 -0.349544 16/5 4/1 1 8 -0.312992 In -0.318560 -0.307424 17/5 5/1 1 8 -0.295146 In -0.305040 -0.285253 18/5 2/1 1 8 -0.277434 In -0.286178 -0.268691 19/5 3/1 1 8 -0.262939 In -0.266868 -0.259009 21/5 5/1 1 8 -0.238367 In -0.241597 -0.235137 22/5 6/1 1 8 -0.227842 In -0.233740 -0.221943 23/5 3/1 1 8 -0.217144 In -0.222502 -0.211786 24/5 4/1 1 8 -0.208188 In -0.210652 -0.205724 26/5 6/1 1 8 -0.192480 In -0.194586 -0.190373 27/5 7/1 1 8 -0.185544 In -0.189457 -0.181631 28/5 4/1 1 8 -0.178389 In -0.182006 -0.174772 29/5 5/1 1 8 -0.172311 In -0.173999 -0.170623 31/5 7/1 1 8 -0.161409 In -0.162890 -0.159928 32/5 8/1 1 8 -0.156496 In -0.159280 -0.153712 33/5 5/1 1 8 -0.151376 In -0.153980 -0.148771 34/5 6/1 1 8 -0.146982 In -0.148210 -0.145754 36/5 8/1 1 8 -0.138975 In -0.140073 -0.137877 37/5 9/1 1 8 -0.135314 In -0.137396 -0.133233 38/5 6/1 1 8 -0.131469 In -0.133434 -0.129504 39/5 7/1 1 8 -0.128146 In -0.129079 -0.127212 41/5 9/1 1 8 -0.122017 In -0.122863 -0.121171 42/5 10/1 1 8 -0.119184 In -0.120798 -0.117569 43/5 7/1 1 8 -0.116191 In -0.117726 -0.114656 44/5 8/1 1 8 -0.113589 In -0.114323 -0.112856 46/5 10/1 1 8 -0.108747 In -0.109420 -0.108075 47/5 11/1 1 8 -0.106490 In -0.107779 -0.105200 48/5 8/1 1 8 -0.104094 In -0.105326 -0.102862 49/5 9/1 1 8 -0.102002 In -0.102594 -0.101411 -49/6 0 4 -47/6 0 4 -43/6 0 4 -41/6 0 4 -37/6 0 4 -35/6 0 4 -31/6 0 4 -29/6 0 4 -25/6 0 4 -23/6 0 4 -19/6 0 4 -17/6 0 4 -13/6 0 4 -11/6 0 4 -7/6 0 4 -5/6 0 4 -1/6 0 4 1/6 0 4 5/6 0 4 7/6 0 4 11/6 0 4 13/6 0 4 17/6 0 4 19/6 0 4 23/6 0 4 25/6 0 4 29/6 0 4 31/6 0 4 35/6 0 4 37/6 0 4 41/6 0 4 43/6 0 4 47/6 0 4 49/6 0 4 -50/7 -36/5 1 8 0.140077 In 0.139775 0.140379 -48/7 -34/5 1 8 0.145751 In 0.145424 0.146079 -47/7 -19/3 1 8 0.148749 In 0.147442 0.150056 -46/7 -4/1 1 8 0.152081 In 0.149071 0.155092 -45/7 -9/1 1 8 0.155779 In 0.152620 0.158937 -44/7 -20/3 1 8 0.159332 In 0.157832 0.160832 -43/7 -31/5 1 8 0.162895 In 0.162486 0.163304 -41/7 -29/5 1 8 0.170619 In 0.170171 0.171068 -40/7 -16/3 1 8 0.174745 In 0.172941 0.176549 -39/7 -3/1 1 8 0.179373 In 0.175186 0.183560 -38/7 -8/1 1 8 0.184540 In 0.180109 0.188972 -37/7 -17/3 1 8 0.189534 In 0.187412 0.191656 -36/7 -26/5 1 8 0.194593 In 0.194010 0.195177 -34/7 -24/5 1 8 0.205720 In 0.205067 0.206372 -33/7 -13/3 1 8 0.211752 In 0.209104 0.214401 -32/7 -2/1 1 8 0.218613 In 0.212395 0.224830 -31/7 -7/1 1 8 0.226339 In 0.219674 0.233003 -30/7 -14/3 1 8 0.233866 In 0.230636 0.237097 -29/7 -21/5 1 8 0.241610 In 0.240710 0.242509 -27/7 -19/5 1 8 0.259002 In 0.257968 0.260036 -26/7 -10/3 1 8 0.268651 In 0.264388 0.272914 -25/7 -1/1 1 8 0.279856 In 0.269672 0.290040 -24/7 -6/1 1 8 0.292651 In 0.281515 0.303786 -23/7 -11/3 1 8 0.305279 In 0.299774 0.310783 -22/7 -16/5 1 8 0.318584 In 0.317020 0.320148 -20/7 -14/5 1 8 0.349534 In 0.347651 0.351417 -19/7 -7/3 1 8 0.367383 In 0.359413 0.375353 -18/7 0/1 1 8 0.388889 In 0.369247 0.408531 -17/7 -5/1 1 8 0.414080 In 0.391818 0.436341 -16/7 -8/3 1 8 0.439516 In 0.428111 0.450921 -15/7 -11/5 1 8 0.467540 In 0.464171 0.470909 -13/7 -9/5 1 8 0.537372 In 0.532921 0.541823 -12/7 -4/3 1 8 0.580986 In 0.561067 0.600904 -11/7 1/1 1 8 0.638056 In 0.585407 0.690705 -10/7 -4/1 1 8 0.709184 In 0.644245 0.774122 -9/7 -5/3 1 8 0.784912 In 0.748592 0.821232 -8/7 -6/5 1 8 0.878151 In 0.866267 0.890035 -6/7 -4/5 1 8 1.161765 In 1.140967 1.182562 -5/7 -1/3 1 8 1.391960 In 1.278254 1.505665 -4/7 2/1 1 8 1.822581 In 1.412003 2.233159 -3/7 -3/1 1 8 2.619048 In 1.810926 3.427170 -2/7 -2/3 1 8 3.785714 In 2.977592 4.593836 -1/7 -1/5 1 8 7.285714 In 6.477592 8.093836 1/7 1/5 1 8 -7.285714 In -8.093836 -6.477592 2/7 2/3 1 8 -3.785714 In -4.593836 -2.977592 3/7 3/1 1 8 -2.619048 In -3.427170 -1.810926 4/7 -2/1 1 8 -1.822581 In -2.233159 -1.412003 5/7 1/3 1 8 -1.391960 In -1.505665 -1.278254 6/7 4/5 1 8 -1.161765 In -1.182562 -1.140967 8/7 6/5 1 8 -0.878151 In -0.890035 -0.866267 9/7 5/3 1 8 -0.784912 In -0.821232 -0.748592 10/7 4/1 1 8 -0.709184 In -0.774122 -0.644245 11/7 -1/1 1 8 -0.638056 In -0.690705 -0.585407 12/7 4/3 1 8 -0.580986 In 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