See if two points are on same side of a line in point normal form?

[originalfamousjohnsmith]

I already have the means to check if two points are on the same side of a plane defined as three points. That is almost always the case that comes up, but in one place all I ever have is a point and a normal to define the plane. I tried to convert the point normal form plane to a triangle, but this method doesn't quite work right. It's not numerically robust. I can see why but fixing it would be iffy and since it's a hacked together means I was hoping to find someone who knows how to do this in the 'right' way.

However, I can't seem to think of a way to check if two points are on the same side or not in that form. I also can't seem to figure out a robust way to put it into 3 point form without going way more elaborate than the problem probably calls for.

So, if someone knows an easy way to accomplish either of these objectives that would be awesome.

[originalfamousjohnsmith]

Nevermind. I found it was easier and much faster to just convert it to hessian normal form.