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r=HardMix(b,a)=\left\{ \begin{aligned}&1&b+a\geq 1\\&0&else \end{aligned}\right.
r=HardMix(b,a)={10b+a≥1else
但是如果填充介入表达式,则结果将合线性光类似
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r=HardMix_{fill}(b,a)=\left\{ \begin{aligned}&0& \frac{fill\times a+b-fill}{(1-fill)}<0\\ &\\ &\frac{fill\times a+b-fill}{(1-fill)}&0\leq \frac{fill\times a+b-fill}{(1-fill)}\leq 1\\&\\ &1& \frac{fill\times a+b-fill}{(1-fill)}>1 \end{aligned}\right.
r=HardMixfill(b,a)=⎩⎨⎧0(1−fill)fill×a+b−fill1(1−fill)fill×a+b−fill<00≤(1−fill)fill×a+b−fill≤1(1−fill)fill×a+b−fill>1
如果fill的取值是
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\begin{aligned}r=HardMix_{fill}(b,a)=&\left\{ \begin{aligned}&0& \frac{0.5\times a+b-0.5}{(1-0.5)}<0\\ &\\ &\frac{0.5\times a+b-0.5}{(1-0.5)}&0\leq \frac{0.5\times a+b-0.5}{(1-0.5)}\leq 1\\ &\\&1& \frac{0.5\times a+b-0.5}{(1-0.5)}>1 \end{aligned}\right.\\&\\&=\left\{ \begin{aligned}&0& a+2b-1<0\\ &\\ &a+2b-1&0\leq a+2b-1\leq 1\\&\\ &1& a+2b-1>1 \end{aligned}\right.\end{aligned}
r=HardMixfill(b,a)=⎩⎨⎧0(1−0.5)0.5×a+b−0.51(1−0.5)0.5×a+b−0.5<00≤(1−0.5)0.5×a+b−0.5≤1(1−0.5)0.5×a+b−0.5>1=⎩⎨⎧0a+2b−11a+2b−1<00≤a+2b−1≤1a+2b−1>1