Изменения

<tex> v = (b - a) \times (c - a) </tex> <tex> \tilde{v} = (b_x - a_x) \times (c_y - a_y) - (b_y - a_y) \times (c_x - a_x) = </tex><tex> = [ (b_x - a_x) (c_y - a_y) (1 + \delta_1) (1 + \delta_2) (1 + \delta_3) - </tex><tex> - (b_y - a_y) (c_x - a_x) (1 + \delta_4) (1 + \delta_5) (1 + \delta_6) ] (1 + \delta_7), |\delta_i| \leq \varepsilon_m </tex> <tex> v \approx \tilde{v} </tex> <tex> e = (|(b_x - a_x) (c_y - a_y)| + |(b_y - a_y) (c_x - a_x)|) </tex> <tex> \epsilon = |v - \tilde{v}| \leq e \times (4 \varepsilon_m + 6 \varepsilon_m^2 + 4 \varepsilon_m^3 + \varepsilon_m^4) </tex> <tex> e (1 - \varepsilon)^4 \leq |(b_x - a_x) \times (c_y - a_y) - (b_y - a_y) \times (c_x - a_x)| </tex> <tex> e \leq \tilde{e} \frac{1}{(1 - \varepsilon_m)^4} = \tilde{e} (1 + 4 \varepsilon_m + 10 \varepsilon_m^2 + 20 \varepsilon_m^3 + \cdots) </tex> <tex> \epsilon \leq \tilde{\epsilon} \leq \tilde{\epsilon} (1 + 4 \varepsilon_m + 10 \varepsilon_m^2 + 20 \varepsilon_m^3 + \cdots) (4 \varepsilon_m + 6 \varepsilon_m^2 + 4 \varepsilon_m^3 + \varepsilon_m^4) </tex> <tex> \tilde{\epsilon} < 8 \varepsilon_m \tilde{\epsilon} </tex>