I am going through one of the most basic line drawing algorithms and stuck with the following mathematical explanations. The implicit function of line equation is:
f(x,y) = ax + by + c
The Book(Computer Graphics , Principles and practice) mentions that
f(x,y) = 0 , when any point m is on line f(x,y) < 0, when any point m is above the line, and f(x,y) > 0, when any point m is below the line.
It would be great to have some explanation of the claim above. I tried to figure out the first one with the following example:
3x + 2y = 1 => 3x + 2y -1 = 0, where a = 3, b = 2 and c = -1
All I figure out that I need to plug in a (x,y) coordinate so that 3x + 2y - 1 = 0. I am not sure how to choose this coordinate value .
And I am clueless about the next two cases. An example demonstrating all the three cases would be fantastic !