gin_spirit's blog

[help]- two lines.
By gin_spirit, history, 17 months ago, In English

Given two lines L1 and L2, How can I determine whether they are parallel or not? Here L1 contains (x1,y1)(x2,y2) and L2 contains (X3,y3)(x4,y4)

  • Vote: I like it
  • +6
  • Vote: I do not like it

Comments Comments (1)
| Write comment?
»
17 months ago, # |
  Vote: I like it +20 Vote: I do not like it

I find the nicest way is to use cross product. This avoids any potential division by zero.

Let $$$L_1$$$ be defined by points $$$P_1$$$ and $$$P_2$$$ and $$$L_2$$$ be defined by points $$$P_3$$$ and $$$P_4$$$. Then $$$(P_2 - P_1) \times (P_4 - P_3) = 0$$$ if and only if $$$L_1$$$ and $$$L_2$$$ are parallel. Of course, when using floating points you would rather check if the absolute value of the cross product is less than some very small number, probably something like $$$\epsilon = 10^{-9}$$$.

→ Reply