SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 1/0 2 1 -50/1 -100/1 1 8 0.030000 In 0.015858 0.044142 -49/1 -98/1 1 8 0.030612 In 0.016181 0.045043 -48/1 -96/1 1 8 0.031250 In 0.016519 0.045981 -47/1 -94/1 1 8 0.031915 In 0.016870 0.046960 -46/1 -92/1 1 8 0.032609 In 0.017237 0.047981 -45/1 -90/1 1 8 0.033333 In 0.017620 0.049047 -44/1 -88/1 1 8 0.034091 In 0.018020 0.050162 -43/1 -86/1 1 8 0.034884 In 0.018439 0.051328 -42/1 -84/1 1 8 0.035714 In 0.018878 0.052550 -41/1 -82/1 1 8 0.036585 In 0.019339 0.053832 -40/1 -80/1 1 8 0.037500 In 0.019822 0.055178 -39/1 -78/1 1 8 0.038462 In 0.020331 0.056592 -38/1 -76/1 1 8 0.039474 In 0.020866 0.058082 -37/1 -74/1 1 8 0.040541 In 0.021430 0.059652 -36/1 -72/1 1 8 0.041667 In 0.022025 0.061309 -35/1 -70/1 1 8 0.042857 In 0.022654 0.063060 -34/1 -68/1 1 8 0.044118 In 0.023320 0.064915 -33/1 -66/1 1 8 0.045455 In 0.024027 0.066882 -32/1 -64/1 1 8 0.046875 In 0.024778 0.068972 -31/1 -62/1 1 8 0.048387 In 0.025577 0.071197 -30/1 -60/1 1 8 0.050000 In 0.026430 0.073570 -29/1 -58/1 1 8 0.051724 In 0.027341 0.076107 -28/1 -56/1 1 8 0.053571 In 0.028318 0.078825 -27/1 -54/1 1 8 0.055556 In 0.029366 0.081745 -26/1 -52/1 1 8 0.057692 In 0.030496 0.084889 -25/1 -50/1 1 8 0.060000 In 0.031716 0.088284 -24/1 -48/1 1 8 0.062500 In 0.033037 0.091963 -23/1 -46/1 1 8 0.065217 In 0.034474 0.095961 -22/1 -44/1 1 8 0.068182 In 0.036041 0.100323 -21/1 -42/1 1 8 0.071429 In 0.037757 0.105100 -20/1 -40/1 1 8 0.075000 In 0.039645 0.110355 -19/1 -38/1 1 8 0.078947 In 0.041731 0.116164 -18/1 -36/1 1 8 0.083333 In 0.044050 0.122617 -17/1 -34/1 1 8 0.088235 In 0.046641 0.129830 -16/1 -32/1 1 8 0.093750 In 0.049556 0.137944 -15/1 -30/1 1 8 0.100000 In 0.052860 0.147140 -14/1 -28/1 1 8 0.107143 In 0.056635 0.157650 -13/1 -26/1 1 8 0.115385 In 0.060992 0.169777 -12/1 -24/1 1 8 0.125000 In 0.066074 0.183926 -11/1 -22/1 1 8 0.136364 In 0.072081 0.200646 -10/1 -20/1 1 8 0.150000 In 0.079289 0.220711 -9/1 -18/1 1 8 0.166667 In 0.088099 0.245234 -8/1 -16/1 1 8 0.187500 In 0.099112 0.275888 -7/1 -14/1 1 8 0.214286 In 0.113270 0.315301 -6/1 -12/1 1 8 0.250000 In 0.132149 0.367851 -5/1 -10/1 1 8 0.300000 In 0.158579 0.441421 -4/1 -8/1 1 8 0.375000 In 0.198223 0.551777 -3/1 -6/1 1 8 0.500000 In 0.264298 0.735702 -2/1 -4/1 1 8 0.750000 In 0.396447 1.103553 -1/1 -2/1 1 8 1.500000 In 0.792893 2.207107 0/1 0/1 1 8 1/1 2/1 1 8 -1.500000 In -2.207107 -0.792893 2/1 4/1 1 8 -0.750000 In -1.103553 -0.396447 3/1 6/1 1 8 -0.500000 In -0.735702 -0.264298 4/1 8/1 1 8 -0.375000 In -0.551777 -0.198223 5/1 10/1 1 8 -0.300000 In -0.441421 -0.158579 6/1 12/1 1 8 -0.250000 In -0.367851 -0.132149 7/1 14/1 1 8 -0.214286 In -0.315301 -0.113270 8/1 16/1 1 8 -0.187500 In -0.275888 -0.099112 9/1 18/1 1 8 -0.166667 In -0.245234 -0.088099 10/1 20/1 1 8 -0.150000 In -0.220711 -0.079289 11/1 22/1 1 8 -0.136364 In -0.200646 -0.072081 12/1 24/1 1 8 -0.125000 In -0.183926 -0.066074 13/1 26/1 1 8 -0.115385 In -0.169777 -0.060992 14/1 28/1 1 8 -0.107143 In -0.157650 -0.056635 15/1 30/1 1 8 -0.100000 In -0.147140 -0.052860 16/1 32/1 1 8 -0.093750 In -0.137944 -0.049556 17/1 34/1 1 8 -0.088235 In -0.129830 -0.046641 18/1 36/1 1 8 -0.083333 In -0.122617 -0.044050 19/1 38/1 1 8 -0.078947 In -0.116164 -0.041731 20/1 40/1 1 8 -0.075000 In -0.110355 -0.039645 21/1 42/1 1 8 -0.071429 In -0.105100 -0.037757 22/1 44/1 1 8 -0.068182 In -0.100323 -0.036041 23/1 46/1 1 8 -0.065217 In -0.095961 -0.034474 24/1 48/1 1 8 -0.062500 In -0.091963 -0.033037 25/1 50/1 1 8 -0.060000 In -0.088284 -0.031716 26/1 52/1 1 8 -0.057692 In -0.084889 -0.030496 27/1 54/1 1 8 -0.055556 In -0.081745 -0.029366 28/1 56/1 1 8 -0.053571 In -0.078825 -0.028318 29/1 58/1 1 8 -0.051724 In -0.076107 -0.027341 30/1 60/1 1 8 -0.050000 In -0.073570 -0.026430 31/1 62/1 1 8 -0.048387 In -0.071197 -0.025577 32/1 64/1 1 8 -0.046875 In -0.068972 -0.024778 33/1 66/1 1 8 -0.045455 In -0.066882 -0.024027 34/1 68/1 1 8 -0.044118 In -0.064915 -0.023320 35/1 70/1 1 8 -0.042857 In -0.063060 -0.022654 36/1 72/1 1 8 -0.041667 In -0.061309 -0.022025 37/1 74/1 1 8 -0.040541 In -0.059652 -0.021430 38/1 76/1 1 8 -0.039474 In -0.058082 -0.020866 39/1 78/1 1 8 -0.038462 In -0.056592 -0.020331 40/1 80/1 1 8 -0.037500 In -0.055178 -0.019822 41/1 82/1 1 8 -0.036585 In -0.053832 -0.019339 42/1 84/1 1 8 -0.035714 In -0.052550 -0.018878 43/1 86/1 1 8 -0.034884 In -0.051328 -0.018439 44/1 88/1 1 8 -0.034091 In -0.050162 -0.018020 45/1 90/1 1 8 -0.033333 In -0.049047 -0.017620 46/1 92/1 1 8 -0.032609 In -0.047981 -0.017237 47/1 94/1 1 8 -0.031915 In -0.046960 -0.016870 48/1 96/1 1 8 -0.031250 In -0.045981 -0.016519 49/1 98/1 1 8 -0.030612 In -0.045043 -0.016181 50/1 100/1 1 8 -0.030000 In -0.044142 -0.015858 -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 -32/1 1 8 0.061551 In 0.054695 0.068408 -49/3 -34/1 1 8 0.063262 In 0.054958 0.071566 -47/3 -30/1 1 8 0.065466 In 0.058215 0.072718 -46/3 -32/1 1 8 0.067404 In 0.058512 0.076297 -44/3 -28/1 1 8 0.069913 In 0.062219 0.077607 -43/3 -30/1 1 8 0.072128 In 0.062559 0.081697 -41/3 -26/1 1 8 0.075008 In 0.066814 0.083202 -40/3 -28/1 1 8 0.077563 In 0.067206 0.087920 -38/3 -24/1 1 8 0.080904 In 0.072142 0.089665 -37/3 -26/1 1 8 0.083885 In 0.072600 0.095170 -35/3 -22/1 1 8 0.087806 In 0.078394 0.097218 -34/3 -24/1 1 8 0.091328 In 0.078934 0.103722 -32/3 -20/1 1 8 0.095996 In 0.085832 0.106160 -31/3 -22/1 1 8 0.100222 In 0.086480 0.113964 -29/3 -18/1 1 8 0.105871 In 0.094830 0.116913 -28/3 -20/1 1 8 0.111035 In 0.095622 0.126449 -26/3 -16/1 1 8 0.118012 In 0.105935 0.130090 -25/3 -18/1 1 8 0.124465 In 0.106924 0.142007 -23/3 -14/1 1 8 0.133300 In 0.119985 0.146615 -22/3 -16/1 1 8 0.141593 In 0.121256 0.161930 -20/3 -12/1 1 8 0.153141 In 0.138333 0.167950 -19/3 -14/1 1 8 0.164190 In 0.140025 0.188356 -17/3 -10/1 1 8 0.179928 In 0.163305 0.196550 -16/3 -12/1 1 8 0.195378 In 0.165668 0.225089 -14/3 -8/1 1 8 0.218085 In 0.199279 0.236891 -13/3 -10/1 1 8 0.241214 In 0.202809 0.279619 -11/3 -6/1 1 8 0.276824 In 0.255580 0.298068 -10/3 -8/1 1 8 0.315217 In 0.261416 0.369019 -8/3 -4/1 1 8 0.379032 In 0.356222 0.401842 -7/3 -6/1 1 8 0.455056 In 0.367661 0.542451 -5/3 -2/1 1 8 0.602041 In 0.587610 0.616472 -4/3 -4/1 1 8 0.821429 In 0.619398 1.023459 -2/3 0/1 1 8 1.500000 In 1.323223 1.676777 -1/3 -2/1 1 8 5.500000 In 1.964466 9.035534 1/3 2/1 1 8 -5.500000 In -9.035534 -1.964466 2/3 0/1 1 8 -1.500000 In -1.676777 -1.323223 4/3 4/1 1 8 -0.821429 In -1.023459 -0.619398 5/3 2/1 1 8 -0.602041 In -0.616472 -0.587610 7/3 6/1 1 8 -0.455056 In -0.542451 -0.367661 8/3 4/1 1 8 -0.379032 In -0.401842 -0.356222 10/3 8/1 1 8 -0.315217 In -0.369019 -0.261416 11/3 6/1 1 8 -0.276824 In -0.298068 -0.255580 13/3 10/1 1 8 -0.241214 In -0.279619 -0.202809 14/3 8/1 1 8 -0.218085 In -0.236891 -0.199279 16/3 12/1 1 8 -0.195378 In -0.225089 -0.165668 17/3 10/1 1 8 -0.179928 In -0.196550 -0.163305 19/3 14/1 1 8 -0.164190 In -0.188356 -0.140025 20/3 12/1 1 8 -0.153141 In -0.167950 -0.138333 22/3 16/1 1 8 -0.141593 In -0.161930 -0.121256 23/3 14/1 1 8 -0.133300 In -0.146615 -0.119985 25/3 18/1 1 8 -0.124465 In -0.142007 -0.106924 26/3 16/1 1 8 -0.118012 In -0.130090 -0.105935 28/3 20/1 1 8 -0.111035 In -0.126449 -0.095622 29/3 18/1 1 8 -0.105871 In -0.116913 -0.094830 31/3 22/1 1 8 -0.100222 In -0.113964 -0.086480 32/3 20/1 1 8 -0.095996 In -0.106160 -0.085832 34/3 24/1 1 8 -0.091328 In -0.103722 -0.078934 35/3 22/1 1 8 -0.087806 In -0.097218 -0.078394 37/3 26/1 1 8 -0.083885 In -0.095170 -0.072600 38/3 24/1 1 8 -0.080904 In -0.089665 -0.072142 40/3 28/1 1 8 -0.077563 In -0.087920 -0.067206 41/3 26/1 1 8 -0.075008 In -0.083202 -0.066814 43/3 30/1 1 8 -0.072128 In -0.081697 -0.062559 44/3 28/1 1 8 -0.069913 In -0.077607 -0.062219 46/3 32/1 1 8 -0.067404 In -0.076297 -0.058512 47/3 30/1 1 8 -0.065466 In -0.072718 -0.058215 49/3 34/1 1 8 -0.063262 In -0.071566 -0.054958 50/3 32/1 1 8 -0.061551 In -0.068408 -0.054695 -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 -18/1 1 8 0.102838 In 0.096697 0.108979 -48/5 -20/1 1 8 0.105368 In 0.097212 0.113525 -47/5 -18/1 1 8 0.107332 In 0.100322 0.114343 -46/5 -20/1 1 8 0.110116 In 0.100875 0.119357 -44/5 -16/1 1 8 0.114496 In 0.107811 0.121181 -43/5 -18/1 1 8 0.117639 In 0.108451 0.126827 -42/5 -16/1 1 8 0.120092 In 0.112335 0.127849 -41/5 -18/1 1 8 0.123590 In 0.113030 0.134151 -39/5 -14/1 1 8 0.129135 In 0.121811 0.136459 -38/5 -16/1 1 8 0.133144 In 0.122628 0.143661 -37/5 -14/1 1 8 0.136296 In 0.127618 0.144974 -36/5 -16/1 1 8 0.140823 In 0.128516 0.153130 -34/5 -12/1 1 8 0.148067 In 0.139989 0.156144 -33/5 -14/1 1 8 0.153358 In 0.141070 0.165647 -32/5 -12/1 1 8 0.157555 In 0.147714 0.167395 -31/5 -14/1 1 8 0.163641 In 0.148918 0.178365 -29/5 -10/1 1 8 0.173506 In 0.164545 0.182468 -28/5 -12/1 1 8 0.180809 In 0.166040 0.195579 -27/5 -10/1 1 8 0.186671 In 0.175322 0.198021 -26/5 -12/1 1 8 0.195289 In 0.177020 0.213557 -24/5 -8/1 1 8 0.209507 In 0.199548 0.219466 -23/5 -10/1 1 8 0.220232 In 0.201750 0.238714 -22/5 -8/1 1 8 0.228992 In 0.215622 0.242361 -21/5 -10/1 1 8 0.242124 In 0.218196 0.266051 -19/5 -6/1 1 8 0.264376 In 0.253467 0.275285 -18/5 -8/1 1 8 0.281646 In 0.257031 0.306260 -17/5 -6/1 1 8 0.296134 In 0.279978 0.312289 -16/5 -8/1 1 8 0.318548 In 0.284334 0.352763 -14/5 -4/1 1 8 0.358247 In 0.347313 0.369182 -13/5 -6/1 1 8 0.390578 In 0.354040 0.427115 -12/5 -4/1 1 8 0.419014 In 0.399096 0.438933 -11/5 -6/1 1 8 0.465665 In 0.408004 0.523326 -9/5 -2/1 1 8 0.555901 In 0.551509 0.560293 -8/5 -4/1 1 8 0.637097 In 0.568667 0.705526 -7/5 -2/1 1 8 0.716495 In 0.694626 0.738364 -6/5 -4/1 1 8 0.867647 In 0.722066 1.013228 -4/5 0/1 1 8 1.250000 In 1.161612 1.338388 -3/5 -2/1 1 8 1.735294 In 1.444133 2.026456 -2/5 0/1 1 8 2.500000 In 2.323223 2.676777 -1/5 -2/1 1 8 9.500000 In 3.136039 15.863961 1/5 2/1 1 8 -9.500000 In -15.863961 -3.136039 2/5 0/1 1 8 -2.500000 In -2.676777 -2.323223 3/5 2/1 1 8 -1.735294 In -2.026456 -1.444133 4/5 0/1 1 8 -1.250000 In -1.338388 -1.161612 6/5 4/1 1 8 -0.867647 In -1.013228 -0.722066 7/5 2/1 1 8 -0.716495 In -0.738364 -0.694626 8/5 4/1 1 8 -0.637097 In -0.705526 -0.568667 9/5 2/1 1 8 -0.555901 In -0.560293 -0.551509 11/5 6/1 1 8 -0.465665 In -0.523326 -0.408004 12/5 4/1 1 8 -0.419014 In -0.438933 -0.399096 13/5 6/1 1 8 -0.390578 In -0.427115 -0.354040 14/5 4/1 1 8 -0.358247 In -0.369182 -0.347313 16/5 8/1 1 8 -0.318548 In -0.352763 -0.284334 17/5 6/1 1 8 -0.296134 In -0.312289 -0.279978 18/5 8/1 1 8 -0.281646 In -0.306260 -0.257031 19/5 6/1 1 8 -0.264376 In -0.275285 -0.253467 21/5 10/1 1 8 -0.242124 In -0.266051 -0.218196 22/5 8/1 1 8 -0.228992 In -0.242361 -0.215622 23/5 10/1 1 8 -0.220232 In -0.238714 -0.201750 24/5 8/1 1 8 -0.209507 In -0.219466 -0.199548 26/5 12/1 1 8 -0.195289 In -0.213557 -0.177020 27/5 10/1 1 8 -0.186671 In -0.198021 -0.175322 28/5 12/1 1 8 -0.180809 In -0.195579 -0.166040 29/5 10/1 1 8 -0.173506 In -0.182468 -0.164545 31/5 14/1 1 8 -0.163641 In -0.178365 -0.148918 32/5 12/1 1 8 -0.157555 In -0.167395 -0.147714 33/5 14/1 1 8 -0.153358 In -0.165647 -0.141070 34/5 12/1 1 8 -0.148067 In -0.156144 -0.139989 36/5 16/1 1 8 -0.140823 In -0.153130 -0.128516 37/5 14/1 1 8 -0.136296 In -0.144974 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