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 33 -49/1 0 33 -48/1 -48/1 1 33 -47/1 0 33 -46/1 -46/1 1 33 -45/1 0 33 -44/1 -44/1 1 33 -43/1 0 33 -42/1 -42/1 1 33 -41/1 0 33 -40/1 -40/1 1 33 -39/1 0 33 -38/1 -38/1 1 33 -37/1 0 33 -36/1 -36/1 1 33 -35/1 0 33 -34/1 -34/1 1 33 -33/1 0 33 -32/1 -32/1 1 33 -31/1 0 33 -30/1 -30/1 1 33 -29/1 0 33 -28/1 -28/1 1 33 -27/1 0 33 -26/1 -26/1 1 33 -25/1 0 33 -24/1 -24/1 1 33 -23/1 0 33 -22/1 -22/1 1 33 -21/1 0 33 -20/1 -20/1 1 33 -19/1 0 33 -18/1 -18/1 1 33 -17/1 0 33 -16/1 -16/1 1 33 -15/1 0 33 -14/1 -14/1 1 33 -13/1 0 33 -12/1 -12/1 1 33 -11/1 0 33 -10/1 -10/1 1 33 -9/1 0 33 -8/1 -8/1 1 33 -7/1 0 33 -6/1 -6/1 1 33 -5/1 0 33 -4/1 -4/1 1 33 -3/1 0 33 -2/1 -2/1 1 33 -1/1 0 33 0/1 0/1 1 33 1/1 0 33 2/1 2/1 1 33 3/1 0 33 4/1 4/1 1 33 5/1 0 33 6/1 6/1 1 33 7/1 0 33 8/1 8/1 1 33 9/1 0 33 10/1 10/1 1 33 11/1 0 33 12/1 12/1 1 33 13/1 0 33 14/1 14/1 1 33 15/1 0 33 16/1 16/1 1 33 17/1 0 33 18/1 18/1 1 33 19/1 0 33 20/1 20/1 1 33 21/1 0 33 22/1 22/1 1 33 23/1 0 33 24/1 24/1 1 33 25/1 0 33 26/1 26/1 1 33 27/1 0 33 28/1 28/1 1 33 29/1 0 33 30/1 30/1 1 33 31/1 0 33 32/1 32/1 1 33 33/1 0 33 34/1 34/1 1 33 35/1 0 33 36/1 36/1 1 33 37/1 0 33 38/1 38/1 1 33 39/1 0 33 40/1 40/1 1 33 41/1 0 33 42/1 42/1 1 33 43/1 0 33 44/1 44/1 1 33 45/1 0 33 46/1 46/1 1 33 47/1 0 33 48/1 48/1 1 33 49/1 0 33 50/1 50/1 1 33 -49/2 0 33 -47/2 0 33 -45/2 0 33 -43/2 0 33 -41/2 0 33 -39/2 0 33 -37/2 0 33 -35/2 0 33 -33/2 0 33 -31/2 0 33 -29/2 0 33 -27/2 0 33 -25/2 0 33 -23/2 0 33 -21/2 0 33 -19/2 0 33 -17/2 0 33 -15/2 0 33 -13/2 0 33 -11/2 0 33 -9/2 0 33 -7/2 0 33 -5/2 0 33 -3/2 0 33 -1/2 0 33 1/2 0 33 3/2 0 33 5/2 0 33 7/2 0 33 9/2 0 33 11/2 0 33 13/2 0 33 15/2 0 33 17/2 0 33 19/2 0 33 21/2 0 33 23/2 0 33 25/2 0 33 27/2 0 33 29/2 0 33 31/2 0 33 33/2 0 33 35/2 0 33 37/2 0 33 39/2 0 33 41/2 0 33 43/2 0 33 45/2 0 33 47/2 0 33 49/2 0 33 -50/3 -17/1 1 11 0.060012 In 0.059891 0.060134 -49/3 0 11 -47/3 0 11 -46/3 -15/1 1 11 0.065203 In 0.065059 0.065347 -44/3 -15/1 1 11 0.068198 In 0.068041 0.068355 -43/3 0 11 -41/3 0 11 -40/3 -13/1 1 11 0.074981 In 0.074791 0.075172 -38/3 -13/1 1 11 0.078969 In 0.078758 0.079180 -37/3 0 11 -35/3 0 11 -34/3 -11/1 1 11 0.088210 In 0.087946 0.088473 -32/3 -11/1 1 11 0.093781 In 0.093483 0.094078 -31/3 0 11 -29/3 0 11 -28/3 -9/1 1 11 0.107105 In 0.106717 0.107493 -26/3 -9/1 1 11 0.115432 In 0.114981 0.115883 -25/3 0 11 -23/3 0 11 -22/3 -7/1 1 11 0.136303 In 0.135675 0.136932 -20/3 -7/1 1 11 0.150080 In 0.149318 0.150843 -19/3 0 11 -17/3 0 11 -16/3 -5/1 1 11 0.187388 In 0.186200 0.188576 -14/3 -5/1 1 11 0.214453 In 0.212897 0.216010 -13/3 0 11 -11/3 0 11 -10/3 -3/1 1 11 0.299725 In 0.296685 0.302765 -8/3 -3/1 1 11 0.375540 In 0.370767 0.380312 -7/3 0 11 -5/3 0 11 -4/3 -1/1 1 11 0.748571 In 0.729619 0.767524 -2/3 -1/1 1 11 1.511628 In 1.434497 1.588759 -1/3 0 11 1/3 0 11 2/3 1/1 1 11 -1.511628 In -1.588759 -1.434497 4/3 1/1 1 11 -0.748571 In -0.767524 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0.206596 0.210229 -23/5 0 33 -22/5 -4/1 1 33 0.227250 In 0.226530 0.227970 -21/5 0 33 -19/5 0 33 -18/5 -4/1 1 33 0.277819 In 0.276743 0.278896 -17/5 0 33 -16/5 -2/1 1 33 0.312411 In 0.308329 0.316493 -14/5 -4/1 1 33 0.357409 In 0.352066 0.362751 -13/5 0 33 -12/5 -2/1 1 33 0.416596 In 0.414177 0.419016 -11/5 0 33 -9/5 0 33 -8/5 -2/1 1 33 0.625237 In 0.619787 0.630687 -7/5 0 33 -6/5 0/1 1 33 0.833333 In 0.804320 0.862346 -4/5 -2/1 1 33 1.255725 In 1.189948 1.321503 -3/5 0 33 -2/5 0/1 1 33 2.500000 In 2.412961 2.587039 -1/5 0 33 1/5 0 33 2/5 0/1 1 33 -2.500000 In -2.587039 -2.412961 3/5 0 33 4/5 2/1 1 33 -1.255725 In -1.321503 -1.189948 6/5 0/1 1 33 -0.833333 In -0.862346 -0.804320 7/5 0 33 8/5 2/1 1 33 -0.625237 In -0.630687 -0.619787 9/5 0 33 11/5 0 33 12/5 2/1 1 33 -0.416596 In -0.419016 -0.414177 13/5 0 33 14/5 4/1 1 33 -0.357409 In -0.362751 -0.352066 16/5 2/1 1 33 -0.312411 In -0.316493 -0.308329 17/5 0 33 18/5 4/1 1 33 -0.277819 In -0.278896 -0.276743 19/5 0 33 21/5 0 33 22/5 4/1 1 33 -0.227250 In -0.227970 -0.226530 23/5 0 33 24/5 6/1 1 33 -0.208412 In -0.210229 -0.206596 26/5 4/1 1 33 -0.192266 In -0.193812 -0.190720 27/5 0 33 28/5 6/1 1 33 -0.178588 In -0.179033 -0.178143 29/5 0 33 31/5 0 33 32/5 6/1 1 33 -0.156239 In -0.156579 -0.155899 33/5 0 33 34/5 8/1 1 33 -0.147096 In -0.148001 -0.146191 36/5 6/1 1 33 -0.138865 In -0.139672 -0.138059 37/5 0 33 38/5 8/1 1 33 -0.131588 In -0.131829 -0.131346 39/5 0 33 41/5 0 33 42/5 8/1 1 33 -0.119041 In -0.119239 -0.118843 43/5 0 33 44/5 10/1 1 33 -0.113658 In -0.114198 -0.113117 46/5 8/1 1 33 -0.108681 In -0.109175 -0.108187 47/5 0 33 48/5 10/1 1 33 -0.104172 In -0.104323 -0.104021 49/5 0 33 -49/6 -17/2 1 11 0.122502 In 0.121994 0.123010 -47/6 -15/2 1 11 0.127607 In 0.127055 0.128158 -43/6 1/0 1 11 0.139542 In 0.138563 0.140520 -41/6 1/0 1 11 0.146349 In 0.145273 0.147426 -37/6 -13/2 1 11 0.162257 In 0.161366 0.163148 -35/6 -11/2 1 11 0.171334 In 0.170341 0.172328 -31/6 1/0 1 11 0.193567 In 0.191684 0.195449 -29/6 1/0 1 11 0.206919 In 0.204768 0.209070 -25/6 -9/2 1 11 0.240212 In 0.238259 0.242165 -23/6 -7/2 1 11 0.260659 In 0.258359 0.262958 -19/6 1/0 1 11 0.315869 In 0.310856 0.320882 -17/6 1/0 1 11 0.353052 In 0.346791 0.359314 -13/6 -5/2 1 11 0.462377 In 0.455144 0.469611 -11/6 -3/2 1 11 0.544629 In 0.534594 0.554665 -7/6 1/0 1 11 0.858736 In 0.821748 0.895724 -5/6 1/0 1 11 1.204380 In 1.131753 1.277006 -1/6 -1/2 1 11 6.400000 In 5.073350 7.726650 1/6 1/2 1 11 -6.400000 In -7.726650 -5.073350 5/6 1/0 1 11 -1.204380 In -1.277006 -1.131753 7/6 1/0 1 11 -0.858736 In -0.895724 -0.821748 11/6 3/2 1 11 -0.544629 In -0.554665 -0.534594 13/6 5/2 1 11 -0.462377 In -0.469611 -0.455144 17/6 1/0 1 11 -0.353052 In -0.359314 -0.346791 19/6 1/0 1 11 -0.315869 In -0.320882 -0.310856 23/6 7/2 1 11 -0.260659 In -0.262958 -0.258359 25/6 9/2 1 11 -0.240212 In -0.242165 -0.238259 29/6 1/0 1 11 -0.206919 In -0.209070 -0.204768 31/6 1/0 1 11 -0.193567 In -0.195449 -0.191684 35/6 11/2 1 11 -0.171334 In -0.172328 -0.170341 37/6 13/2 1 11 -0.162257 In -0.163148 -0.161366 41/6 1/0 1 11 -0.146349 In -0.147426 -0.145273 43/6 1/0 1 11 -0.139542 In -0.140520 -0.138563 47/6 15/2 1 11 -0.127607 In -0.128158 -0.127055 49/6 17/2 1 11 -0.122502 In -0.123010 -0.121994 -50/7 -8/1 1 33 0.140012 In 0.139594 0.140430 -48/7 -6/1 1 33 0.145823 In 0.145370 0.146277 -47/7 0 33 -46/7 -20/3 1 33 0.152186 In 0.152021 0.152352 -45/7 0 33 -44/7 -32/5 1 33 0.159137 In 0.158772 0.159503 -43/7 0 33 -41/7 0 33 -40/7 -28/5 1 33 0.174946 In 0.174504 0.175388 -39/7 0 33 -38/7 -16/3 1 33 0.184193 In 0.183950 0.184435 -37/7 0 33 -36/7 -6/1 1 33 0.194468 In 0.193661 0.195274 -34/7 -4/1 1 33 0.205864 In 0.204960 0.206768 -33/7 0 33 -32/7 -14/3 1 33 0.218776 In 0.218434 0.219118 -31/7 0 33 -30/7 -22/5 1 33 0.233434 In 0.232647 0.234220 -29/7 0 33 -27/7 0 33 -26/7 -18/5 1 33 0.269105 In 0.268060 0.270150 -25/7 0 33 -24/7 -10/3 1 33 0.291623 In 0.291015 0.292230 -23/7 0 33 -22/7 -4/1 1 33 0.318250 In 0.316090 0.320410 -20/7 -2/1 1 33 0.349955 In 0.347343 0.352566 -19/7 0 33 -18/7 -8/3 1 33 0.388973 In 0.387892 0.390054 -17/7 0 33 -16/7 -12/5 1 33 0.437861 In 0.435094 0.440628 -15/7 0 33 -13/7 0 33 -12/7 -8/5 1 33 0.582765 In 0.577863 0.587666 -11/7 0 33 -10/7 -4/3 1 33 0.699756 In 0.696258 0.703255 -9/7 0 33 -8/7 -2/1 1 33 0.875712 In 0.859361 0.892062 -6/7 0/1 1 33 1.166667 In 1.137654 1.195680 -5/7 0 33 -4/7 -2/3 1 33 1.751908 In 1.729983 1.773834 -3/7 0 33 -2/7 -2/5 1 33 3.531250 In 3.351732 3.710768 -1/7 0 33 1/7 0 33 2/7 2/5 1 33 -3.531250 In -3.710768 -3.351732 3/7 0 33 4/7 2/3 1 33 -1.751908 In -1.773834 -1.729983 5/7 0 33 6/7 0/1 1 33 -1.166667 In -1.195680 -1.137654 8/7 2/1 1 33 -0.875712 In -0.892062 -0.859361 9/7 0 33 10/7 4/3 1 33 -0.699756 In -0.703255 -0.696258 11/7 0 33 12/7 8/5 1 33 -0.582765 In -0.587666 -0.577863 13/7 0 33 15/7 0 33 16/7 12/5 1 33 -0.437861 In -0.440628 -0.435094 17/7 0 33 18/7 8/3 1 33 -0.388973 In -0.390054 -0.387892 19/7 0 33 20/7 2/1 1 33 -0.349955 In -0.352566 -0.347343 22/7 4/1 1 33 -0.318250 In -0.320410 -0.316090 23/7 0 33 24/7 10/3 1 33 -0.291623 In -0.292230 -0.291015 25/7 0 33 26/7 18/5 1 33 -0.269105 In -0.270150 -0.268060 27/7 0 33 29/7 0 33 30/7 22/5 1 33 -0.233434 In -0.234220 -0.232647 31/7 0 33 32/7 14/3 1 33 -0.218776 In -0.219118 -0.218434 33/7 0 33 34/7 4/1 1 33 -0.205864 In -0.206768 -0.204960 36/7 6/1 1 33 -0.194468 In -0.195274 -0.193661 37/7 0 33 38/7 16/3 1 33 -0.184193 In -0.184435 -0.183950 39/7 0 33 40/7 28/5 1 33 -0.174946 In -0.175388 -0.174504 41/7 0 33 43/7 0 33 44/7 32/5 1 33 -0.159137 In -0.159503 -0.158772 45/7 0 33 46/7 20/3 1 33 -0.152186 In -0.152352 -0.152021 47/7 0 33 48/7 6/1 1 33 -0.145823 In -0.146277 -0.145370 50/7 8/1 1 33 -0.140012 In -0.140430 -0.139594 -49/8 0 33 -47/8 0 33 -45/8 0 33 -43/8 0 33 -41/8 0 33 -39/8 0 33 -37/8 0 33 -35/8 0 33 -33/8 0 33 -31/8 0 33 -29/8 0 33 -27/8 0 33 -25/8 0 33 -23/8 0 33 -21/8 0 33 -19/8 0 33 -17/8 0 33 -15/8 0 33 -13/8 0 33 -11/8 0 33 -9/8 0 33 -7/8 0 33 -5/8 0 33 -3/8 0 33 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-11/9 0 11 -10/9 -1/1 1 11 0.899909 In 0.896891 0.902927 -8/9 -1/1 1 11 1.125178 In 1.120460 1.129896 -7/9 0 11 -5/9 0 11 -4/9 -1/1 1 11 2.257143 In 2.162382 2.351904 -2/9 -1/3 1 11 4.534884 In 4.303491 4.766276 -1/9 0 11 1/9 0 11 2/9 1/3 1 11 -4.534884 In -4.766276 -4.303491 4/9 1/1 1 11 -2.257143 In -2.351904 -2.162382 5/9 0 11 7/9 0 11 8/9 1/1 1 11 -1.125178 In -1.129896 -1.120460 10/9 1/1 1 11 -0.899909 In -0.902927 -0.896891 11/9 0 11 13/9 0 11 14/9 1/1 1 11 -0.642691 In -0.650387 -0.634996 16/9 5/3 1 11 -0.562164 In -0.565729 -0.558599 17/9 0 11 19/9 0 11 20/9 7/3 1 11 -0.450241 In -0.452528 -0.447955 22/9 3/1 1 11 -0.409219 In -0.412339 -0.406099 23/9 0 11 25/9 0 11 26/9 3/1 1 11 -0.346169 In -0.346616 -0.345723 28/9 3/1 1 11 -0.321416 In -0.321801 -0.321031 29/9 0 11 31/9 0 11 32/9 3/1 1 11 -0.281208 In -0.282682 -0.279735 34/9 11/3 1 11 -0.264629 In -0.265419 -0.263839 35/9 0 11 37/9 0 11 38/9 13/3 1 11 -0.236907 In -0.237541 -0.236274 40/9 5/1 1 11 -0.225036 In -0.225979 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