Procedure ‐ Lines Parallel

Description

This procedure is used determine if a number of lines are parallel.

Inputs

The inputs for this procedure are:

• lines: The lines to check if they are parallel.

Outputs

The outputs of this procedure are:

• parallel: Whether or not the lines are parallel.

Procedure

The procedure for this is as follows:

For all lines in lines:

• If the line is not parallel to the first line in lines, return false.
  • This check is done the following way:
    Let $\vec{v}$ be the normal vector of the first line and $\vec{u}$ be the normal vector of the other line.
    Then if the lines are parallel if and only if $\vec{v} \times \vec{u} = \vec{0}$.
    This can also be rewriten as $\vec{v}_x \vec{u}_y = \vec{u}_x \vec{v}_y$, this way we avoid comparing to zero.