SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 0 1 -50/1 0/1 1 3 0.020000 In 0.008453 0.031547 -49/1 1/0 1 3 0.020411 In 0.020171 0.020651 -48/1 0/1 1 3 0.020833 In 0.008805 0.032861 -47/1 1/0 1 3 0.021280 In 0.021018 0.021541 -46/1 0/1 1 3 0.021739 In 0.009188 0.034290 -45/1 1/0 1 3 0.022226 In 0.021941 0.022511 -44/1 0/1 1 3 0.022727 In 0.009606 0.035849 -43/1 1/0 1 3 0.023260 In 0.022948 0.023572 -42/1 0/1 1 3 0.023810 In 0.010063 0.037556 -41/1 1/0 1 3 0.024395 In 0.024052 0.024739 -40/1 0/1 1 3 0.025000 In 0.010566 0.039434 -39/1 1/0 1 3 0.025647 In 0.025267 0.026026 -38/1 0/1 1 3 0.026316 In 0.011122 0.041509 -37/1 1/0 1 3 0.027034 In 0.026612 0.027455 -36/1 0/1 1 3 0.027778 In 0.011740 0.043815 -35/1 1/0 1 3 0.028579 In 0.028108 0.029051 -34/1 0/1 1 3 0.029412 In 0.012431 0.046393 -33/1 1/0 1 3 0.030312 In 0.029782 0.030843 -32/1 0/1 1 3 0.031250 In 0.013208 0.049292 -31/1 1/0 1 3 0.032269 In 0.031668 0.032870 -30/1 0/1 1 3 0.033333 In 0.014088 0.052578 -29/1 1/0 1 3 0.034496 In 0.033810 0.035183 -28/1 0/1 1 3 0.035714 In 0.015095 0.056334 -27/1 1/0 1 3 0.037054 In 0.036262 0.037846 -26/1 0/1 1 3 0.038462 In 0.016256 0.060667 -25/1 1/0 1 3 0.040021 In 0.039097 0.040946 -24/1 0/1 1 3 0.041667 In 0.017610 0.065723 -23/1 1/0 1 3 0.043506 In 0.042414 0.044598 -22/1 0/1 1 3 0.045455 In 0.019211 0.071698 -21/1 1/0 1 3 0.047655 In 0.046345 0.048965 -20/1 0/1 1 3 0.050000 In 0.021132 0.078868 -19/1 1/0 1 3 0.052680 In 0.051079 0.054281 -18/1 0/1 1 3 0.055556 In 0.023481 0.087631 -17/1 1/0 1 3 0.058891 In 0.056891 0.060892 -16/1 0/1 1 3 0.062500 In 0.026416 0.098584 -15/1 1/0 1 3 0.066766 In 0.064196 0.069335 -14/1 0/1 1 3 0.071429 In 0.030189 0.112668 -13/1 1/0 1 3 0.077075 In 0.073652 0.080498 -12/1 0/1 1 3 0.083333 In 0.035221 0.131446 -11/1 1/0 1 3 0.091160 In 0.086376 0.095945 -10/1 0/1 1 3 0.100000 In 0.042265 0.157735 -9/1 1/0 1 3 0.111570 In 0.104413 0.118727 -8/1 0/1 1 3 0.125000 In 0.052831 0.197169 -7/1 1/0 1 3 0.143836 In 0.131972 0.155699 -6/1 0/1 1 3 0.166667 In 0.070442 0.262892 -5/1 1/0 1 3 0.202703 In 0.179297 0.226109 -4/1 0/1 1 3 0.250000 In 0.105662 0.394338 -3/1 1/0 1 3 0.346154 In 0.279537 0.412771 -2/1 0/1 1 3 0.500000 In 0.211325 0.788675 -1/1 1/0 1 3 1.500000 In 0.633975 2.366025 0/1 0/1 1 3 1/1 1/0 1 3 -1.500000 In -2.366025 -0.633975 2/1 0/1 1 3 -0.500000 In -0.788675 -0.211325 3/1 1/0 1 3 -0.346154 In -0.412771 -0.279537 4/1 0/1 1 3 -0.250000 In -0.394338 -0.105662 5/1 1/0 1 3 -0.202703 In -0.226109 -0.179297 6/1 0/1 1 3 -0.166667 In -0.262892 -0.070442 7/1 1/0 1 3 -0.143836 In -0.155699 -0.131972 8/1 0/1 1 3 -0.125000 In -0.197169 -0.052831 9/1 1/0 1 3 -0.111570 In -0.118727 -0.104413 10/1 0/1 1 3 -0.100000 In -0.157735 -0.042265 11/1 1/0 1 3 -0.091160 In -0.095945 -0.086376 12/1 0/1 1 3 -0.083333 In -0.131446 -0.035221 13/1 1/0 1 3 -0.077075 In -0.080498 -0.073652 14/1 0/1 1 3 -0.071429 In -0.112668 -0.030189 15/1 1/0 1 3 -0.066766 In -0.069335 -0.064196 16/1 0/1 1 3 -0.062500 In -0.098584 -0.026416 17/1 1/0 1 3 -0.058891 In -0.060892 -0.056891 18/1 0/1 1 3 -0.055556 In -0.087631 -0.023481 19/1 1/0 1 3 -0.052680 In -0.054281 -0.051079 20/1 0/1 1 3 -0.050000 In -0.078868 -0.021132 21/1 1/0 1 3 -0.047655 In -0.048965 -0.046345 22/1 0/1 1 3 -0.045455 In -0.071698 -0.019211 23/1 1/0 1 3 -0.043506 In -0.044598 -0.042414 24/1 0/1 1 3 -0.041667 In -0.065723 -0.017610 25/1 1/0 1 3 -0.040021 In -0.040946 -0.039097 26/1 0/1 1 3 -0.038462 In -0.060667 -0.016256 27/1 1/0 1 3 -0.037054 In -0.037846 -0.036262 28/1 0/1 1 3 -0.035714 In -0.056334 -0.015095 29/1 1/0 1 3 -0.034496 In -0.035183 -0.033810 30/1 0/1 1 3 -0.033333 In -0.052578 -0.014088 31/1 1/0 1 3 -0.032269 In -0.032870 -0.031668 32/1 0/1 1 3 -0.031250 In -0.049292 -0.013208 33/1 1/0 1 3 -0.030312 In -0.030843 -0.029782 34/1 0/1 1 3 -0.029412 In -0.046393 -0.012431 35/1 1/0 1 3 -0.028579 In -0.029051 -0.028108 36/1 0/1 1 3 -0.027778 In -0.043815 -0.011740 37/1 1/0 1 3 -0.027034 In -0.027455 -0.026612 38/1 0/1 1 3 -0.026316 In -0.041509 -0.011122 39/1 1/0 1 3 -0.025647 In -0.026026 -0.025267 40/1 0/1 1 3 -0.025000 In -0.039434 -0.010566 41/1 1/0 1 3 -0.024395 In -0.024739 -0.024052 42/1 0/1 1 3 -0.023810 In -0.037556 -0.010063 43/1 1/0 1 3 -0.023260 In -0.023572 -0.022948 44/1 0/1 1 3 -0.022727 In -0.035849 -0.009606 45/1 1/0 1 3 -0.022226 In -0.022511 -0.021941 46/1 0/1 1 3 -0.021739 In -0.034290 -0.009188 47/1 1/0 1 3 -0.021280 In -0.021541 -0.021018 48/1 0/1 1 3 -0.020833 In -0.032861 -0.008805 49/1 1/0 1 3 -0.020411 In -0.020651 -0.020171 50/1 0/1 1 3 -0.020000 In -0.031547 -0.008453 -49/2 -1/1 1 3 0.040683 In 0.029380 0.051986 -47/2 1/1 1 3 0.042711 In 0.029902 0.055519 -45/2 -1/1 1 3 0.044287 In 0.032025 0.056549 -43/2 1/1 1 3 0.046700 In 0.032647 0.060754 -41/2 -1/1 1 3 0.048592 In 0.035194 0.061989 -39/2 1/1 1 3 0.051512 In 0.035946 0.067079 -37/2 -1/1 1 3 0.053824 In 0.039059 0.068588 -35/2 1/1 1 3 0.057431 In 0.039988 0.074874 -33/2 -1/1 1 3 0.060318 In 0.043878 0.076759 -31/2 1/1 1 3 0.064885 In 0.045053 0.084718 -29/2 -1/1 1 3 0.068596 In 0.050053 0.087139 -27/2 1/1 1 3 0.074565 In 0.051588 0.097543 -25/2 -1/1 1 3 0.079509 In 0.058251 0.100767 -23/2 1/1 1 3 0.087642 In 0.060340 0.114944 -21/2 -1/1 1 3 0.094554 In 0.069660 0.119447 -19/2 1/1 1 3 0.106285 In 0.072668 0.139901 -17/2 -1/1 1 3 0.116628 In 0.086627 0.146629 -15/2 1/1 1 3 0.135015 In 0.091328 0.178702 -13/2 -1/1 1 3 0.152174 In 0.114521 0.189827 -11/2 1/1 1 3 0.185083 In 0.122882 0.247284 -9/2 -1/1 1 3 0.219008 In 0.168908 0.269109 -7/2 1/1 1 3 0.294521 In 0.187750 0.401291 -5/2 -1/1 1 3 0.391892 In 0.321674 0.462110 -3/2 1/1 1 3 0.730769 In 0.397683 1.063856 -1/2 -1/1 1 3 2.500000 In 1.633975 3.366025 1/2 1/1 1 3 -2.500000 In -3.366025 -1.633975 3/2 -1/1 1 3 -0.730769 In -1.063856 -0.397683 5/2 1/1 1 3 -0.391892 In -0.462110 -0.321674 7/2 -1/1 1 3 -0.294521 In -0.401291 -0.187750 9/2 1/1 1 3 -0.219008 In -0.269109 -0.168908 11/2 -1/1 1 3 -0.185083 In -0.247284 -0.122882 13/2 1/1 1 3 -0.152174 In -0.189827 -0.114521 15/2 -1/1 1 3 -0.135015 In -0.178702 -0.091328 17/2 1/1 1 3 -0.116628 In -0.146629 -0.086627 19/2 -1/1 1 3 -0.106285 In -0.139901 -0.072668 21/2 1/1 1 3 -0.094554 In -0.119447 -0.069660 23/2 -1/1 1 3 -0.087642 In -0.114944 -0.060340 25/2 1/1 1 3 -0.079509 In -0.100767 -0.058251 27/2 -1/1 1 3 -0.074565 In -0.097543 -0.051588 29/2 1/1 1 3 -0.068596 In -0.087139 -0.050053 31/2 -1/1 1 3 -0.064885 In -0.084718 -0.045053 33/2 1/1 1 3 -0.060318 In -0.076759 -0.043878 35/2 -1/1 1 3 -0.057431 In -0.074874 -0.039988 37/2 1/1 1 3 -0.053824 In -0.068588 -0.039059 39/2 -1/1 1 3 -0.051512 In -0.067079 -0.035946 41/2 1/1 1 3 -0.048592 In -0.061989 -0.035194 43/2 -1/1 1 3 -0.046700 In -0.060754 -0.032647 45/2 1/1 1 3 -0.044287 In -0.056549 -0.032025 47/2 -1/1 1 3 -0.042711 In -0.055519 -0.029902 49/2 1/1 1 3 -0.040683 In -0.051986 -0.029380 -50/3 0 1 -49/3 0 1 -47/3 0 1 -46/3 0 1 -44/3 0 1 -43/3 0 1 -41/3 0 1 -40/3 0 1 -38/3 0 1 -37/3 0 1 -35/3 0 1 -34/3 0 1 -32/3 0 1 -31/3 0 1 -29/3 0 1 -28/3 0 1 -26/3 0 1 -25/3 0 1 -23/3 0 1 -22/3 0 1 -20/3 0 1 -19/3 0 1 -17/3 0 1 -16/3 0 1 -14/3 0 1 -13/3 0 1 -11/3 0 1 -10/3 0 1 -8/3 0 1 -7/3 0 1 -5/3 0 1 -4/3 0 1 -2/3 0 1 -1/3 0 1 1/3 0 1 2/3 0 1 4/3 0 1 5/3 0 1 7/3 0 1 8/3 0 1 10/3 0 1 11/3 0 1 13/3 0 1 14/3 0 1 16/3 0 1 17/3 0 1 19/3 0 1 20/3 0 1 22/3 0 1 23/3 0 1 25/3 0 1 26/3 0 1 28/3 0 1 29/3 0 1 31/3 0 1 32/3 0 1 34/3 0 1 35/3 0 1 37/3 0 1 38/3 0 1 40/3 0 1 41/3 0 1 43/3 0 1 44/3 0 1 46/3 0 1 47/3 0 1 49/3 0 1 50/3 0 1 -49/4 -1/1 1 3 0.081505 In 0.070683 0.092327 -47/4 1/1 1 3 0.085270 In 0.071939 0.098602 -45/4 1/1 1 3 0.089068 In 0.075095 0.103041 -43/4 -1/1 1 3 0.092860 In 0.080680 0.105040 -41/4 -1/1 1 3 0.097382 In 0.084672 0.110092 -39/4 1/1 1 3 0.102806 In 0.086480 0.119132 -37/4 1/1 1 3 0.108378 In 0.091083 0.125673 -35/4 -1/1 1 3 0.114045 In 0.099430 0.128659 -33/4 -1/1 1 3 0.120943 In 0.105564 0.136323 -31/4 1/1 1 3 0.129424 In 0.108389 0.150459 -29/4 1/1 1 3 0.138382 In 0.115719 0.161046 -27/4 -1/1 1 3 0.147758 In 0.129535 0.165982 -25/4 -1/1 1 3 0.159552 In 0.140142 0.178961 -23/4 1/1 1 3 0.174653 In 0.145167 0.204140 -21/4 1/1 1 3 0.191377 In 0.158622 0.224131 -19/4 -1/1 1 3 0.209797 In 0.185785 0.233808 -17/4 -1/1 1 3 0.234411 In 0.208410 0.260412 -15/4 1/1 1 3 0.268546 In 0.219720 0.317372 -13/4 1/1 1 3 0.310277 In 0.252085 0.368468 -11/4 -1/1 1 3 0.361878 In 0.328386 0.395371 -9/4 -1/1 1 3 0.442149 In 0.406363 0.477935 -7/4 1/1 1 3 0.582192 In 0.451695 0.712689 -5/4 1/1 1 3 0.824324 In 0.613669 1.034979 -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 -0.824324 In -1.034979 -0.613669 7/4 -1/1 1 3 -0.582192 In -0.712689 -0.451695 9/4 1/1 1 3 -0.442149 In -0.477935 -0.406363 11/4 1/1 1 3 -0.361878 In -0.395371 -0.328386 13/4 -1/1 1 3 -0.310277 In -0.368468 -0.252085 15/4 -1/1 1 3 -0.268546 In -0.317372 -0.219720 17/4 1/1 1 3 -0.234411 In -0.260412 -0.208410 19/4 1/1 1 3 -0.209797 In -0.233808 -0.185785 21/4 -1/1 1 3 -0.191377 In -0.224131 -0.158622 23/4 -1/1 1 3 -0.174653 In -0.204140 -0.145167 25/4 1/1 1 3 -0.159552 In -0.178961 -0.140142 27/4 1/1 1 3 -0.147758 In -0.165982 -0.129535 29/4 -1/1 1 3 -0.138382 In -0.161046 -0.115719 31/4 -1/1 1 3 -0.129424 In -0.150459 -0.108389 33/4 1/1 1 3 -0.120943 In -0.136323 -0.105564 35/4 1/1 1 3 -0.114045 In -0.128659 -0.099430 37/4 -1/1 1 3 -0.108378 In -0.125673 -0.091083 39/4 -1/1 1 3 -0.102806 In -0.119132 -0.086480 41/4 1/1 1 3 -0.097382 In -0.110092 -0.084672 43/4 1/1 1 3 -0.092860 In -0.105040 -0.080680 45/4 -1/1 1 3 -0.089068 In -0.103041 -0.075095 47/4 -1/1 1 3 -0.085270 In -0.098602 -0.071939 49/4 1/1 1 3 -0.081505 In -0.092327 -0.070683 -49/5 1/2 1 3 0.102333 In 0.077562 0.127104 -48/5 0/1 1 3 0.104167 In 0.092139 0.116195 -47/5 1/0 1 3 0.106399 In 0.105092 0.107706 -46/5 2/1 1 3 0.109079 In 0.093790 0.124369 -44/5 -2/1 1 3 0.113370 In 0.103224 0.123516 -43/5 1/0 1 3 0.116300 In 0.114739 0.117862 -42/5 0/1 1 3 0.119048 In 0.105301 0.132794 -41/5 -1/2 1 3 0.121579 In 0.095127 0.148030 -39/5 1/2 1 3 0.128672 In 0.097159 0.160184 -38/5 0/1 1 3 0.131579 In 0.116386 0.146772 -37/5 1/0 1 3 0.135168 In 0.133059 0.137277 -36/5 2/1 1 3 0.139547 In 0.119033 0.160060 -34/5 -2/1 1 3 0.146651 In 0.134651 0.158652 -33/5 1/0 1 3 0.151562 In 0.148910 0.154213 -32/5 0/1 1 3 0.156250 In 0.138208 0.174292 -31/5 -1/2 1 3 0.160652 In 0.126396 0.194909 -29/5 1/2 1 3 0.173275 In 0.130008 0.216542 -28/5 0/1 1 3 0.178571 In 0.157952 0.199191 -27/5 1/0 1 3 0.185270 In 0.181308 0.189232 -26/5 2/1 1 3 0.193676 In 0.162869 0.224483 -24/5 -2/1 1 3 0.207657 In 0.193591 0.221722 -23/5 1/0 1 3 0.217528 In 0.212068 0.222989 -22/5 0/1 1 3 0.227273 In 0.201030 0.253516 -21/5 -1/2 1 3 0.236762 In 0.188286 0.285239 -19/5 1/2 1 3 0.265250 In 0.196416 0.334083 -18/5 0/1 1 3 0.277778 In 0.245703 0.309853 -17/5 1/0 1 3 0.294457 In 0.284457 0.304458 -16/5 2/1 1 3 0.316754 In 0.257810 0.375698 -14/5 -2/1 1 3 0.356164 In 0.344301 0.368028 -13/5 1/0 1 3 0.385375 In 0.368260 0.402491 -12/5 0/1 1 3 0.416667 In 0.368554 0.464779 -11/5 -1/2 1 3 0.450276 In 0.368937 0.531616 -9/5 1/2 1 3 0.566116 In 0.401499 0.730732 -8/5 0/1 1 3 0.625000 In 0.552831 0.697169 -7/5 1/0 1 3 0.719178 In 0.659861 0.778495 -6/5 2/1 1 3 0.884615 In 0.618146 1.151085 -4/5 -2/1 1 3 1.318182 In 1.081993 1.554371 -3/5 1/0 1 3 1.730769 In 1.397683 2.063856 -2/5 0/1 1 3 2.500000 In 2.211325 2.788675 -1/5 -1/2 1 3 6.500000 In 3.901924 9.098076 1/5 1/2 1 3 -6.500000 In -9.098076 -3.901924 2/5 0/1 1 3 -2.500000 In -2.788675 -2.211325 3/5 1/0 1 3 -1.730769 In -2.063856 -1.397683 4/5 2/1 1 3 -1.318182 In -1.554371 -1.081993 6/5 -2/1 1 3 -0.884615 In -1.151085 -0.618146 7/5 1/0 1 3 -0.719178 In -0.778495 -0.659861 8/5 0/1 1 3 -0.625000 In -0.697169 -0.552831 9/5 -1/2 1 3 -0.566116 In -0.730732 -0.401499 11/5 1/2 1 3 -0.450276 In -0.531616 -0.368937 12/5 0/1 1 3 -0.416667 In -0.464779 -0.368554 13/5 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