Perpendicular distance between point and plane

I have been working on fitting a plane to 3d points and then calculating the perpendicular distance between each point and the plane using Matlab. So far I can find the plane equation in Ax+By+Cz+D=0 form and calculate the distance using (Ax0+By0+Cz0+D)/sqrt(A^2+B^2+C^2). However, in some Matlab codes plane is defined as Ax+By+C=z which seems quite different from the above plane equation. Even though I did some research about difference of these equations, I could not find any satisfactory answer. Could you please explain me the difference between these two plane definitions and could you please inform me about the distance between any point and plane Ax+By+C=z ? I am looking forward to hearing from you. Thanks in advance

Answer 1

[Image Analyst]

It's the same equation, just the coefficients are different. "A" of the simple equation is just A/(C*sqrt(A^2+B^2+C^2)) of the more complicated equation, and so on for the other coefficients. Remember from algebra, you can multiply of divide both sides of an equation by the same number and it's still the same equation. I mean, isn't y=20*x the same equation as 5*y = 100*x? It's the same thing with your equations.