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 3 -49/1 1/0 1 3 0.020411 In 0.020171 0.020651 -48/1 -48/1 1 3 -47/1 1/0 1 3 0.021280 In 0.021018 0.021541 -46/1 -46/1 1 3 -45/1 1/0 1 3 0.022226 In 0.021941 0.022511 -44/1 -44/1 1 3 -43/1 1/0 1 3 0.023260 In 0.022948 0.023572 -42/1 -42/1 1 3 -41/1 1/0 1 3 0.024395 In 0.024052 0.024739 -40/1 -40/1 1 3 -39/1 1/0 1 3 0.025647 In 0.025267 0.026026 -38/1 -38/1 1 3 -37/1 1/0 1 3 0.027034 In 0.026612 0.027455 -36/1 -36/1 1 3 -35/1 1/0 1 3 0.028579 In 0.028108 0.029051 -34/1 -34/1 1 3 -33/1 1/0 1 3 0.030312 In 0.029782 0.030843 -32/1 -32/1 1 3 -31/1 1/0 1 3 0.032269 In 0.031668 0.032870 -30/1 -30/1 1 3 -29/1 1/0 1 3 0.034496 In 0.033810 0.035183 -28/1 -28/1 1 3 -27/1 1/0 1 3 0.037054 In 0.036262 0.037846 -26/1 -26/1 1 3 -25/1 1/0 1 3 0.040021 In 0.039097 0.040946 -24/1 -24/1 1 3 -23/1 1/0 1 3 0.043506 In 0.042414 0.044598 -22/1 -22/1 1 3 -21/1 1/0 1 3 0.047655 In 0.046345 0.048965 -20/1 -20/1 1 3 -19/1 1/0 1 3 0.052680 In 0.051079 0.054281 -18/1 -18/1 1 3 -17/1 1/0 1 3 0.058891 In 0.056891 0.060892 -16/1 -16/1 1 3 -15/1 1/0 1 3 0.066766 In 0.064196 0.069335 -14/1 -14/1 1 3 -13/1 1/0 1 3 0.077075 In 0.073652 0.080498 -12/1 -12/1 1 3 -11/1 1/0 1 3 0.091160 In 0.086376 0.095945 -10/1 -10/1 1 3 -9/1 1/0 1 3 0.111570 In 0.104413 0.118727 -8/1 -8/1 1 3 -7/1 1/0 1 3 0.143836 In 0.131972 0.155699 -6/1 -6/1 1 3 -5/1 1/0 1 3 0.202703 In 0.179297 0.226109 -4/1 -4/1 1 3 -3/1 1/0 1 3 0.346154 In 0.279537 0.412771 -2/1 -2/1 1 3 -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 2/1 1 3 3/1 1/0 1 3 -0.346154 In -0.412771 -0.279537 4/1 4/1 1 3 5/1 1/0 1 3 -0.202703 In -0.226109 -0.179297 6/1 6/1 1 3 7/1 1/0 1 3 -0.143836 In -0.155699 -0.131972 8/1 8/1 1 3 9/1 1/0 1 3 -0.111570 In -0.118727 -0.104413 10/1 10/1 1 3 11/1 1/0 1 3 -0.091160 In -0.095945 -0.086376 12/1 12/1 1 3 13/1 1/0 1 3 -0.077075 In -0.080498 -0.073652 14/1 14/1 1 3 15/1 1/0 1 3 -0.066766 In -0.069335 -0.064196 16/1 16/1 1 3 17/1 1/0 1 3 -0.058891 In -0.060892 -0.056891 18/1 18/1 1 3 19/1 1/0 1 3 -0.052680 In -0.054281 -0.051079 20/1 20/1 1 3 21/1 1/0 1 3 -0.047655 In -0.048965 -0.046345 22/1 22/1 1 3 23/1 1/0 1 3 -0.043506 In -0.044598 -0.042414 24/1 24/1 1 3 25/1 1/0 1 3 -0.040021 In -0.040946 -0.039097 26/1 26/1 1 3 27/1 1/0 1 3 -0.037054 In -0.037846 -0.036262 28/1 28/1 1 3 29/1 1/0 1 3 -0.034496 In -0.035183 -0.033810 30/1 30/1 1 3 31/1 1/0 1 3 -0.032269 In -0.032870 -0.031668 32/1 32/1 1 3 33/1 1/0 1 3 -0.030312 In -0.030843 -0.029782 34/1 34/1 1 3 35/1 1/0 1 3 -0.028579 In -0.029051 -0.028108 36/1 36/1 1 3 37/1 1/0 1 3 -0.027034 In -0.027455 -0.026612 38/1 38/1 1 3 39/1 1/0 1 3 -0.025647 In -0.026026 -0.025267 40/1 40/1 1 3 41/1 1/0 1 3 -0.024395 In -0.024739 -0.024052 42/1 42/1 1 3 43/1 1/0 1 3 -0.023260 In -0.023572 -0.022948 44/1 44/1 1 3 45/1 1/0 1 3 -0.022226 In -0.022511 -0.021941 46/1 46/1 1 3 47/1 1/0 1 3 -0.021280 In -0.021541 -0.021018 48/1 48/1 1 3 49/1 1/0 1 3 -0.020411 In -0.020651 -0.020171 50/1 50/1 1 3 -49/2 -25/1 1 3 0.040894 In 0.040631 0.041157 -47/2 -23/1 1 3 0.042473 In 0.042189 0.042757 -45/2 -23/1 1 3 0.044537 In 0.044224 0.044849 -43/2 -21/1 1 3 0.046416 In 0.046077 0.046755 -41/2 -21/1 1 3 0.048892 In 0.048515 0.049268 -39/2 -19/1 1 3 0.051166 In 0.050754 0.051578 -37/2 -19/1 1 3 0.054191 In 0.053729 0.054654 -35/2 -17/1 1 3 0.056999 In 0.056488 0.057511 -33/2 -17/1 1 3 0.060779 In 0.060197 0.061361 -31/2 -15/1 1 3 0.064334 In 0.063682 0.064986 -29/2 -15/1 1 3 0.069191 In 0.068437 0.069944 -27/2 -13/1 1 3 0.073835 In 0.072977 0.074694 -25/2 -13/1 1 3 0.080305 In 0.079290 0.081320 -23/2 -11/1 1 3 0.086630 In 0.085449 0.087812 -21/2 -11/1 1 3 0.095674 In 0.094233 0.097115 -19/2 -9/1 1 3 0.104790 In 0.103062 0.106519 -17/2 -9/1 1 3 0.118321 In 0.116117 0.120524 -15/2 -7/1 1 3 0.132588 In 0.129821 0.135355 -13/2 -7/1 1 3 0.155022 In 0.151240 0.158804 -11/2 -5/1 1 3 0.180473 In 0.175349 0.185598 -9/2 -5/1 1 3 0.224771 In 0.216825 0.232716 -7/2 -3/1 1 3 0.282609 In 0.270058 0.295160 -5/2 -3/1 1 3 0.409091 In 0.382848 0.435334 -3/2 -1/1 1 3 0.653846 In 0.587229 0.720463 -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 -0.653846 In -0.720463 -0.587229 5/2 3/1 1 3 -0.409091 In -0.435334 -0.382848 7/2 3/1 1 3 -0.282609 In -0.295160 -0.270058 9/2 5/1 1 3 -0.224771 In -0.232716 -0.216825 11/2 5/1 1 3 -0.180473 In -0.185598 -0.175349 13/2 7/1 1 3 -0.155022 In -0.158804 -0.151240 15/2 7/1 1 3 -0.132588 In -0.135355 -0.129821 17/2 9/1 1 3 -0.118321 In -0.120524 -0.116117 19/2 9/1 1 3 -0.104790 In -0.106519 -0.103062 21/2 11/1 1 3 -0.095674 In -0.097115 -0.094233 23/2 11/1 1 3 -0.086630 In -0.087812 -0.085449 25/2 13/1 1 3 -0.080305 In -0.081320 -0.079290 27/2 13/1 1 3 -0.073835 In -0.074694 -0.072977 29/2 15/1 1 3 -0.069191 In -0.069944 -0.068437 31/2 15/1 1 3 -0.064334 In -0.064986 -0.063682 33/2 17/1 1 3 -0.060779 In -0.061361 -0.060197 35/2 17/1 1 3 -0.056999 In -0.057511 -0.056488 37/2 19/1 1 3 -0.054191 In -0.054654 -0.053729 39/2 19/1 1 3 -0.051166 In -0.051578 -0.050754 41/2 21/1 1 3 -0.048892 In -0.049268 -0.048515 43/2 21/1 1 3 -0.046416 In -0.046755 -0.046077 45/2 23/1 1 3 -0.044537 In -0.044849 -0.044224 47/2 23/1 1 3 -0.042473 In -0.042757 -0.042189 49/2 25/1 1 3 -0.040894 In -0.041157 -0.040631 -50/3 -18/1 1 1 0.060662 In 0.058824 0.062500 -49/3 -17/1 1 1 0.061553 In 0.060606 0.062500 -47/3 -15/1 1 1 0.063508 In 0.062500 0.064516 -46/3 -14/1 1 1 0.064583 In 0.062500 0.066667 -44/3 -16/1 1 1 0.069048 In 0.066667 0.071429 -43/3 -15/1 1 1 0.070197 In 0.068966 0.071429 -41/3 -13/1 1 1 0.072751 In 0.071429 0.074074 -40/3 -12/1 1 1 0.074176 In 0.071429 0.076923 -38/3 -14/1 1 1 0.080128 In 0.076923 0.083333 -37/3 -13/1 1 1 0.081667 In 0.080000 0.083333 -35/3 -11/1 1 1 0.085145 In 0.083333 0.086957 -34/3 -10/1 1 1 0.087121 In 0.083333 0.090909 -32/3 -12/1 1 1 0.095455 In 0.090909 0.100000 -31/3 -11/1 1 1 0.097619 In 0.095238 0.100000 -29/3 -9/1 1 1 0.102632 In 0.100000 0.105263 -28/3 -8/1 1 1 0.105556 In 0.100000 0.111111 -26/3 -10/1 1 1 0.118056 In 0.111111 0.125000 -25/3 -9/1 1 1 0.121324 In 0.117647 0.125000 -23/3 -7/1 1 1 0.129167 In 0.125000 0.133333 -22/3 -6/1 1 1 0.133929 In 0.125000 0.142857 -20/3 -8/1 1 1 0.154762 In 0.142857 0.166667 -19/3 -7/1 1 1 0.160256 In 0.153846 0.166667 -17/3 -5/1 1 1 0.174242 In 0.166667 0.181818 -16/3 -4/1 1 1 0.183333 In 0.166667 0.200000 -14/3 -6/1 1 1 0.225000 In 0.200000 0.250000 -13/3 -5/1 1 1 0.236111 In 0.222222 0.250000 -11/3 -3/1 1 1 0.267857 In 0.250000 0.285714 -10/3 -2/1 1 1 0.291667 In 0.250000 0.333333 -8/3 -4/1 1 1 0.416667 In 0.333333 0.500000 -7/3 -3/1 1 1 0.450000 In 0.400000 0.500000 -5/3 -1/1 1 1 0.583333 In 0.500000 0.666667 -4/3 0/1 1 1 0.750000 In 0.500000 1.000000 -2/3 -2/1 1 1 1.000000 Right -1/3 -1/1 1 1 2.000000 Right 1/3 1/1 1 1 -2.000000 Left 2/3 2/1 1 1 -1.000000 Left 4/3 0/1 1 1 -0.750000 In -1.000000 -0.500000 5/3 1/1 1 1 -0.583333 In -0.666667 -0.500000 7/3 3/1 1 1 -0.450000 In -0.500000 -0.400000 8/3 4/1 1 1 -0.416667 In -0.500000 -0.333333 10/3 2/1 1 1 -0.291667 In -0.333333 -0.250000 11/3 3/1 1 1 -0.267857 In -0.285714 -0.250000 13/3 5/1 1 1 -0.236111 In -0.250000 -0.222222 14/3 6/1 1 1 -0.225000 In -0.250000 -0.200000 16/3 4/1 1 1 -0.183333 In -0.200000 -0.166667 17/3 5/1 1 1 -0.174242 In -0.181818 -0.166667 19/3 7/1 1 1 -0.160256 In -0.166667 -0.153846 20/3 8/1 1 1 -0.154762 In -0.166667 -0.142857 22/3 6/1 1 1 -0.133929 In -0.142857 -0.125000 23/3 7/1 1 1 -0.129167 In -0.133333 -0.125000 25/3 9/1 1 1 -0.121324 In -0.125000 -0.117647 26/3 10/1 1 1 -0.118056 In -0.125000 -0.111111 28/3 8/1 1 1 -0.105556 In -0.111111 -0.100000 29/3 9/1 1 1 -0.102632 In -0.105263 -0.100000 31/3 11/1 1 1 -0.097619 In -0.100000 -0.095238 32/3 12/1 1 1 -0.095455 In -0.100000 -0.090909 34/3 10/1 1 1 -0.087121 In -0.090909 -0.083333 35/3 11/1 1 1 -0.085145 In -0.086957 -0.083333 37/3 13/1 1 1 -0.081667 In -0.083333 -0.080000 38/3 14/1 1 1 -0.080128 In -0.083333 -0.076923 40/3 12/1 1 1 -0.074176 In -0.076923 -0.071429 41/3 13/1 1 1 -0.072751 In -0.074074 -0.071429 43/3 15/1 1 1 -0.070197 In -0.071429 -0.068966 44/3 16/1 1 1 -0.069048 In -0.071429 -0.066667 46/3 14/1 1 1 -0.064583 In -0.066667 -0.062500 47/3 15/1 1 1 -0.063508 In -0.064516 -0.062500 49/3 17/1 1 1 -0.061553 In -0.062500 -0.060606 50/3 18/1 1 1 -0.060662 In -0.062500 -0.058824 -49/4 -13/1 1 3 0.081746 In 0.081007 0.082485 -47/4 -11/1 1 3 0.084998 In 0.084200 0.085797 -45/4 -9/1 1 3 0.088589 In 0.085988 0.091189 -43/4 -13/1 1 3 0.093529 In 0.090631 0.096428 -41/4 -11/1 1 3 0.097725 In 0.096669 0.098780 -39/4 -9/1 1 3 0.102410 In 0.101250 0.103569 -37/4 -7/1 1 3 0.107689 In 0.103847 0.111530 -35/4 -11/1 1 3 0.115082 In 0.110695 0.119468 -33/4 -9/1 1 3 0.121469 In 0.119838 0.123100 -31/4 -7/1 1 3 0.128793 In 0.126960 0.130627 -29/4 -5/1 1 3 0.137310 In 0.131069 0.143550 -27/4 -9/1 1 3 0.149573 In 0.142171 0.156975 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3 -0.213733 In -0.228809 -0.198657 21/4 3/1 1 3 -0.189498 In -0.201361 -0.177634 23/4 5/1 1 3 -0.173496 In -0.176822 -0.170169 25/4 7/1 1 3 -0.160460 In -0.163306 -0.157614 27/4 9/1 1 3 -0.149573 In -0.156975 -0.142171 29/4 5/1 1 3 -0.137310 In -0.143550 -0.131069 31/4 7/1 1 3 -0.128793 In -0.130627 -0.126960 33/4 9/1 1 3 -0.121469 In -0.123100 -0.119838 35/4 11/1 1 3 -0.115082 In -0.119468 -0.110695 37/4 7/1 1 3 -0.107689 In -0.111530 -0.103847 39/4 9/1 1 3 -0.102410 In -0.103569 -0.101250 41/4 11/1 1 3 -0.097725 In -0.098780 -0.096669 43/4 13/1 1 3 -0.093529 In -0.096428 -0.090631 45/4 9/1 1 3 -0.088589 In -0.091189 -0.085988 47/4 11/1 1 3 -0.084998 In -0.085797 -0.084200 49/4 13/1 1 3 -0.081746 In -0.082485 -0.081007 -49/5 -19/2 1 3 0.101871 In 0.101111 0.102630 -48/5 -8/1 1 3 0.103972 In 0.101949 0.105995 -47/5 -17/2 1 3 0.105869 In 0.103410 0.108329 -46/5 -6/1 1 3 0.108365 In 0.103975 0.112756 -44/5 -12/1 1 3 0.114407 In 0.109514 0.119300 -43/5 -19/2 1 3 0.117046 In 0.114040 0.120052 -42/5 -10/1 1 3 0.119414 In 0.116746 0.122083 -41/5 -17/2 1 3 0.122213 In 0.121120 0.123306 -39/5 -15/2 1 3 0.127939 In 0.126741 0.129137 -38/5 -6/1 1 3 0.131285 In 0.128059 0.134510 -37/5 -13/2 1 3 0.134332 In 0.130374 0.138291 -36/5 -4/1 1 3 0.138430 In 0.131273 0.145587 -34/5 -10/1 1 3 0.148456 In 0.140228 0.156684 -33/5 -15/2 1 3 0.152860 In 0.147736 0.157984 -32/5 -8/1 1 3 0.156915 In 0.152308 0.161521 -31/5 -13/2 1 3 0.161754 In 0.159839 0.163668 -29/5 -11/2 1 3 0.171940 In 0.169777 0.174103 -28/5 -4/1 1 3 0.178082 In 0.172151 0.184014 -27/5 -9/2 1 3 0.183761 In 0.176359 0.191163 -26/5 -2/1 1 3 0.191700 In 0.178008 0.205392 -24/5 -8/1 1 3 0.211538 In 0.194884 0.228193 -23/5 -11/2 1 3 0.220327 In 0.209694 0.230961 -22/5 -6/1 1 3 0.228814 In 0.219028 0.238599 -21/5 -9/2 1 3 0.239130 In 0.234947 0.243314 -19/5 -7/2 1 3 0.262089 In 0.257064 0.267114 -18/5 -2/1 1 3 0.276860 In 0.262545 0.291174 -17/5 -5/2 1 3 0.290974 In 0.272460 0.309487 -16/5 0/1 1 3 0.312500 In 0.276416 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