Procedure ‐ Line C Coefficient

Goal

The goal of the line c coefficient procedure is to find the $c$ coefficient of a line equation in the form of $ax + bx + c = 0$.

Inputs

The inputs for this procedure are:

• normalVector: The normal vector of the line.
• point: A point on the line.

Outputs

The outputs of this procedure are:

• cCoefficient: The $c$ coefficient of the line equation.

Procedure

The procedure for this is as follows:

$\text{let } \vec{n} \text{ be the normal vector}$
$\text{let } P \text{ be the point on the line}$
$\text{let } ax + bx + c = 0 \text{ be the equation of the line}$

$P = [P_x, P_y]$
$\vec{n} = (\vec{n}_x, \vec{n}_y)$

$\text{then}$

$a = \vec{n}_x, b = \vec{n}_y$
$a P_x + b P_y + c = 0$

$\text{from that:}$

$\vec{n}_x P_x + \vec{n}_y P_y + c = 0$
$c = -(\vec{n}_x P_x + \vec{n}_y P_y)$