SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 0 2 -50/1 0/1 1 8 0.020000 In 0.012929 0.027071 -49/1 1/1 1 8 0.020461 In 0.013098 0.027824 -48/1 0/1 1 8 0.020833 In 0.013468 0.028199 -47/1 1/1 1 8 0.021334 In 0.013651 0.029017 -46/1 0/1 1 8 0.021739 In 0.014053 0.029425 -45/1 1/1 1 8 0.022285 In 0.014253 0.030317 -44/1 0/1 1 8 0.022727 In 0.014692 0.030763 -43/1 1/1 1 8 0.023325 In 0.014911 0.031739 -42/1 0/1 1 8 0.023810 In 0.015392 0.032227 -41/1 1/1 1 8 0.024466 In 0.015632 0.033301 -40/1 0/1 1 8 0.025000 In 0.016161 0.033839 -39/1 1/1 1 8 0.025725 In 0.016427 0.035024 -38/1 0/1 1 8 0.026316 In 0.017012 0.035620 -37/1 1/1 1 8 0.027121 In 0.017306 0.036935 -36/1 0/1 1 8 0.027778 In 0.017957 0.037599 -35/1 1/1 1 8 0.028676 In 0.018285 0.039068 -34/1 0/1 1 8 0.029412 In 0.019013 0.039810 -33/1 1/1 1 8 0.030421 In 0.019382 0.041461 -32/1 0/1 1 8 0.031250 In 0.020201 0.042299 -31/1 1/1 1 8 0.032392 In 0.020618 0.044167 -30/1 0/1 1 8 0.033333 In 0.021548 0.045118 -29/1 1/1 1 8 0.034637 In 0.022023 0.047250 -28/1 0/1 1 8 0.035714 In 0.023087 0.048341 -27/1 1/1 1 8 0.037215 In 0.023633 0.050797 -26/1 0/1 1 8 0.038462 In 0.024863 0.052060 -25/1 1/1 1 8 0.040208 In 0.025497 0.054919 -24/1 0/1 1 8 0.041667 In 0.026935 0.056398 -23/1 1/1 1 8 0.043725 In 0.027681 0.059769 -22/1 0/1 1 8 0.045455 In 0.029384 0.061525 -21/1 1/1 1 8 0.047916 In 0.030273 0.065559 -20/1 0/1 1 8 0.050000 In 0.032322 0.067678 -19/1 1/1 1 8 0.052996 In 0.033402 0.072590 -18/1 0/1 1 8 0.055556 In 0.035914 0.075197 -17/1 1/1 1 8 0.059282 In 0.037252 0.081312 -16/1 0/1 1 8 0.062500 In 0.040403 0.084597 -15/1 1/1 1 8 0.067260 In 0.042104 0.092415 -14/1 0/1 1 8 0.071429 In 0.046175 0.096682 -13/1 1/1 1 8 0.077720 In 0.048410 0.107030 -12/1 0/1 1 8 0.083333 In 0.053871 0.112796 -11/1 1/1 1 8 0.092037 In 0.056938 0.127137 -10/1 0/1 1 8 0.100000 In 0.064645 0.135355 -9/1 1/1 1 8 0.112828 In 0.069112 0.156544 -8/1 0/1 1 8 0.125000 In 0.080806 0.169194 -7/1 1/1 1 8 0.145780 In 0.087909 0.203651 -6/1 0/1 1 8 0.166667 In 0.107741 0.225592 -5/1 1/1 1 8 0.206030 In 0.120751 0.291309 -4/1 0/1 1 8 0.250000 In 0.161612 0.338388 -3/1 1/1 1 8 0.352113 In 0.192765 0.511461 -2/1 0/1 1 8 0.500000 In 0.323223 0.676777 -1/1 1/1 1 8 1.285714 In 0.477592 2.093836 0/1 0/1 1 8 1/1 1/1 1 8 2/1 0/1 1 8 -0.500000 In -0.676777 -0.323223 3/1 1/1 1 8 -0.323944 In -0.403618 -0.244270 4/1 0/1 1 8 -0.250000 In -0.338388 -0.161612 5/1 1/1 1 8 -0.195980 In -0.252833 -0.139127 6/1 0/1 1 8 -0.166667 In -0.225592 -0.107741 7/1 1/1 1 8 -0.140665 In -0.184068 -0.097262 8/1 0/1 1 8 -0.125000 In -0.169194 -0.080806 9/1 1/1 1 8 -0.109737 In -0.144710 -0.074764 10/1 0/1 1 8 -0.100000 In -0.135355 -0.064645 11/1 1/1 1 8 -0.089969 In -0.119218 -0.060719 12/1 0/1 1 8 -0.083333 In -0.112796 -0.053871 13/1 1/1 1 8 -0.076240 In -0.101363 -0.051117 14/1 0/1 1 8 -0.071429 In -0.096682 -0.046175 15/1 1/1 1 8 -0.066148 In -0.088159 -0.044137 16/1 0/1 1 8 -0.062500 In -0.084597 -0.040403 17/1 1/1 1 8 -0.058416 In -0.077999 -0.038834 18/1 0/1 1 8 -0.055556 In -0.075197 -0.035914 19/1 1/1 1 8 -0.052303 In -0.069938 -0.034669 20/1 0/1 1 8 -0.050000 In -0.067678 -0.032322 21/1 1/1 1 8 -0.047349 In -0.063388 -0.031310 22/1 0/1 1 8 -0.045455 In -0.061525 -0.029384 23/1 1/1 1 8 -0.043252 In -0.057959 -0.028545 24/1 0/1 1 8 -0.041667 In -0.056398 -0.026935 25/1 1/1 1 8 -0.039808 In -0.053387 -0.026229 26/1 0/1 1 8 -0.038462 In -0.052060 -0.024863 27/1 1/1 1 8 -0.036872 In -0.049484 -0.024260 28/1 0/1 1 8 -0.035714 In -0.048341 -0.023087 29/1 1/1 1 8 -0.034339 In -0.046112 -0.022566 30/1 0/1 1 8 -0.033333 In -0.045118 -0.021548 31/1 1/1 1 8 -0.032132 In -0.043171 -0.021094 32/1 0/1 1 8 -0.031250 In -0.042299 -0.020201 33/1 1/1 1 8 -0.030192 In -0.040582 -0.019801 34/1 0/1 1 8 -0.029412 In -0.039810 -0.019013 35/1 1/1 1 8 -0.028472 In -0.038286 -0.018658 36/1 0/1 1 8 -0.027778 In -0.037599 -0.017957 37/1 1/1 1 8 -0.026938 In -0.036236 -0.017640 38/1 0/1 1 8 -0.026316 In -0.035620 -0.017012 39/1 1/1 1 8 -0.025561 In -0.034395 -0.016727 40/1 0/1 1 8 -0.025000 In -0.033839 -0.016161 41/1 1/1 1 8 -0.024318 In -0.032731 -0.015904 42/1 0/1 1 8 -0.023810 In -0.032227 -0.015392 43/1 1/1 1 8 -0.023190 In -0.031221 -0.015158 44/1 0/1 1 8 -0.022727 In -0.030763 -0.014692 45/1 1/1 1 8 -0.022162 In -0.029844 -0.014479 46/1 0/1 1 8 -0.021739 In -0.029425 -0.014053 47/1 1/1 1 8 -0.021221 In -0.028584 -0.013858 48/1 0/1 1 8 -0.020833 In -0.028199 -0.013468 49/1 1/1 1 8 -0.020357 In -0.027426 -0.013289 50/1 0/1 1 8 -0.020000 In -0.027071 -0.012929 -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 0/1 1 8 0.060000 In 0.052929 0.067071 -49/3 1/1 1 8 0.061280 In 0.053622 0.068937 -47/3 1/1 1 8 0.063890 In 0.055887 0.071893 -46/3 0/1 1 8 0.065217 In 0.057531 0.072903 -44/3 0/1 1 8 0.068182 In 0.060147 0.076217 -43/3 1/1 1 8 0.069840 In 0.061043 0.078636 -41/3 1/1 1 8 0.073251 In 0.063996 0.082505 -40/3 0/1 1 8 0.075000 In 0.066161 0.083839 -38/3 0/1 1 8 0.078947 In 0.069643 0.088251 -37/3 1/1 1 8 0.081180 In 0.070849 0.091511 -35/3 1/1 1 8 0.085825 In 0.074857 0.096794 -34/3 0/1 1 8 0.088235 In 0.077837 0.098634 -32/3 0/1 1 8 0.093750 In 0.082701 0.104799 -31/3 1/1 1 8 0.096917 In 0.084407 0.109427 -29/3 1/1 1 8 0.103612 In 0.090158 0.117067 -28/3 0/1 1 8 0.107143 In 0.094516 0.119770 -26/3 0/1 1 8 0.115385 In 0.101786 0.128983 -25/3 1/1 1 8 0.120224 In 0.104382 0.136066 -23/3 1/1 1 8 0.130702 In 0.113321 0.148083 -22/3 0/1 1 8 0.136364 In 0.120293 0.152434 -20/3 0/1 1 8 0.150000 In 0.132322 0.167678 -19/3 1/1 1 8 0.158296 In 0.136742 0.179849 -17/3 1/1 1 8 0.176980 In 0.152502 0.201458 -16/3 0/1 1 8 0.187500 In 0.165403 0.209597 -14/3 0/1 1 8 0.214286 In 0.189032 0.239540 -13/3 1/1 1 8 0.231680 In 0.198183 0.265178 -11/3 1/1 1 8 0.274043 In 0.233094 0.314993 -10/3 0/1 1 8 0.300000 In 0.264645 0.335355 -8/3 0/1 1 8 0.375000 In 0.330806 0.419194 -7/3 1/1 1 8 0.432225 In 0.359887 0.504563 -5/3 1/1 1 8 0.608040 In 0.494335 0.721746 -4/3 0/1 1 8 0.750000 In 0.661612 0.838388 -2/3 0/1 1 8 1.500000 In 1.323223 1.676777 -1/3 1/1 1 8 3.571429 In 1.955185 5.187673 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 0/1 1 8 -0.750000 In -0.838388 -0.661612 5/3 1/1 1 8 -0.597990 In -0.626416 -0.569564 7/3 1/1 1 8 -0.427110 In -0.456045 -0.398175 8/3 0/1 1 8 -0.375000 In -0.419194 -0.330806 10/3 0/1 1 8 -0.300000 In -0.335355 -0.264645 11/3 1/1 1 8 -0.271975 In -0.295375 -0.248576 13/3 1/1 1 8 -0.230200 In -0.251136 -0.209264 14/3 0/1 1 8 -0.214286 In -0.239540 -0.189032 16/3 0/1 1 8 -0.187500 In -0.209597 -0.165403 17/3 1/1 1 8 -0.176114 In -0.193249 -0.158980 19/3 1/1 1 8 -0.157603 In -0.173278 -0.141928 20/3 0/1 1 8 -0.150000 In -0.167678 -0.132322 22/3 0/1 1 8 -0.136364 In -0.152434 -0.120293 23/3 1/1 1 8 -0.130229 In -0.143599 -0.116859 25/3 1/1 1 8 -0.119824 In -0.132272 -0.107376 26/3 0/1 1 8 -0.115385 In -0.128983 -0.101786 28/3 0/1 1 8 -0.107143 In -0.119770 -0.094516 29/3 1/1 1 8 -0.103315 In -0.114247 -0.092383 31/3 1/1 1 8 -0.096657 In -0.106959 -0.086354 32/3 0/1 1 8 -0.093750 In -0.104799 -0.082701 34/3 0/1 1 8 -0.088235 In -0.098634 -0.077837 35/3 1/1 1 8 -0.085621 In -0.094858 -0.076384 37/3 1/1 1 8 -0.080997 In -0.089779 -0.072216 38/3 0/1 1 8 -0.078947 In -0.088251 -0.069643 40/3 0/1 1 8 -0.075000 In -0.083839 -0.066161 41/3 1/1 1 8 -0.073102 In -0.081095 -0.065109 43/3 1/1 1 8 -0.069705 In -0.077354 -0.062056 44/3 0/1 1 8 -0.068182 In -0.076217 -0.060147 46/3 0/1 1 8 -0.065217 In -0.072903 -0.057531 47/3 1/1 1 8 -0.063777 In -0.070819 -0.056734 49/3 1/1 1 8 -0.061176 In -0.067950 -0.054402 50/3 0/1 1 8 -0.060000 In -0.067071 -0.052929 -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 1/1 1 8 0.102098 In 0.094146 0.110050 -48/5 0/1 1 8 0.104167 In 0.096801 0.111532 -47/5 1/1 1 8 0.106446 In 0.098122 0.114769 -46/5 0/1 1 8 0.108696 In 0.101010 0.116382 -44/5 0/1 1 8 0.113636 In 0.105601 0.121672 -43/5 1/1 1 8 0.116355 In 0.107176 0.125533 -42/5 0/1 1 8 0.119048 In 0.110630 0.127466 -41/5 1/1 1 8 0.122035 In 0.112359 0.131710 -39/5 1/1 1 8 0.128298 In 0.118069 0.138526 -38/5 0/1 1 8 0.131579 In 0.122275 0.140883 -37/5 1/1 1 8 0.135239 In 0.124391 0.146087 -36/5 0/1 1 8 0.138889 In 0.129068 0.148710 -34/5 0/1 1 8 0.147059 In 0.136660 0.157457 -33/5 1/1 1 8 0.151647 In 0.139309 0.163986 -32/5 0/1 1 8 0.156250 In 0.145201 0.167299 -31/5 1/1 1 8 0.161441 In 0.148195 0.174688 -29/5 1/1 1 8 0.172588 In 0.158292 0.186884 -28/5 0/1 1 8 0.178571 In 0.165945 0.191198 -27/5 1/1 1 8 0.185388 In 0.169866 0.200911 -26/5 0/1 1 8 0.192308 In 0.178709 0.205906 -24/5 0/1 1 8 0.208333 In 0.193602 0.223065 -23/5 1/1 1 8 0.217679 In 0.198961 0.236397 -22/5 0/1 1 8 0.227273 In 0.211202 0.243343 -21/5 1/1 1 8 0.238446 In 0.217596 0.259297 -19/5 1/1 1 8 0.263595 In 0.240082 0.287109 -18/5 0/1 1 8 0.277778 In 0.258136 0.297420 -17/5 1/1 1 8 0.294678 In 0.267752 0.321603 -16/5 0/1 1 8 0.312500 In 0.290403 0.334597 -14/5 0/1 1 8 0.357143 In 0.331889 0.382397 -13/5 1/1 1 8 0.385640 In 0.347956 0.423325 -12/5 0/1 1 8 0.416667 In 0.387204 0.446129 -11/5 1/1 1 8 0.456050 In 0.409250 0.502849 -9/5 1/1 1 8 0.557960 In 0.496757 0.619162 -8/5 0/1 1 8 0.625000 In 0.580806 0.669194 -7/5 1/1 1 8 0.718670 In 0.631864 0.805476 -6/5 0/1 1 8 0.833333 In 0.774408 0.892259 -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 0/1 1 8 2.500000 In 2.323223 2.676777 -1/5 1/1 1 8 5.857143 In 3.432777 8.281509 1/5 1/1 1 8 -5.571429 In -7.187673 -3.955185 2/5 0/1 1 8 -2.500000 In -2.676777 -2.323223 3/5 1/1 1 8 -1.676056 In -1.755730 -1.596382 4/5 0/1 1 8 -1.250000 In -1.338388 -1.161612 6/5 0/1 1 8 -0.833333 In -0.892259 -0.774408 7/5 1/1 1 8 -0.713555 In -0.728023 -0.699087 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 1/1 1 8 -0.453981 In -0.471531 -0.436432 12/5 0/1 1 8 -0.416667 In -0.446129 -0.387204 13/5 1/1 1 8 -0.384160 In -0.400909 -0.367411 14/5 0/1 1 8 -0.357143 In -0.382397 -0.331889 16/5 0/1 1 8 -0.312500 In -0.334597 -0.290403 17/5 1/1 1 8 -0.293812 In -0.308499 -0.279125 18/5 0/1 1 8 -0.277778 In -0.297420 -0.258136 19/5 1/1 1 8 -0.262903 In -0.276619 -0.249187 21/5 1/1 1 8 -0.237879 In -0.250710 -0.225048 22/5 0/1 1 8 -0.227273 In -0.243343 -0.211202 23/5 1/1 1 8 -0.217206 In -0.229239 -0.205173 24/5 0/1 1 8 -0.208333 In -0.223065 -0.193602 26/5 0/1 1 8 -0.192308 In -0.205906 -0.178709 27/5 1/1 1 8 -0.185045 In -0.195717 -0.174374 28/5 0/1 1 8 -0.178571 In -0.191198 -0.165945 29/5 1/1 1 8 -0.172291 In -0.182382 -0.162200 31/5 1/1 1 8 -0.161181 In -0.170748 -0.151615 32/5 0/1 1 8 -0.156250 In -0.167299 -0.145201 33/5 1/1 1 8 -0.151418 In -0.160509 -0.142326 34/5 0/1 1 8 -0.147059 In -0.157457 -0.136660 36/5 0/1 1 8 -0.138889 In -0.148710 -0.129068 37/5 1/1 1 8 -0.135056 In -0.143321 -0.126791 38/5 0/1 1 8 -0.131579 In -0.140883 -0.122275 39/5 1/1 1 8 -0.128133 In -0.136037 -0.120230 41/5 1/1 1 8 -0.121886 In -0.129458 -0.114314 42/5 0/1 1 8 -0.119048 In -0.127466 -0.110630 43/5 1/1 1 8 -0.116219 In -0.123486 -0.108953 44/5 0/1 1 8 -0.113636 In -0.121672 -0.105601 46/5 0/1 1 8 -0.108696 In -0.116382 -0.101010 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