Twist

Twist is the rational equivlant of $$\tan^2\theta$$ from traditional trigonometry. Twist is defined for non-perpendicular non-null lines $$l_1 \equiv \langle a_1:b_1:c_1\rangle $$ and $$l_2 \equiv \langle a_2:b_2:c_2 \rangle$$ by is the number:

$$ c(l_1,l_2)\equiv \frac{(a_1 b_2 - a_2 b_1)^2}{(a_1 a_2 + b_1 b_2)^2} $$

twist is related to spread and cross by:

$$ t(l_1,l_2) = \frac{s(l_1,l_2)}{c(l_1,l_2)} $$