How to find a point lies inside the plane in 3d

Question

I have a plane with 3D coordinates of vertices in world coordinate system and also plane equation.

Coordinates                             
x   y   z       
19.1320421  72.9177745  0   P1      
19.1320426  72.9178202  0   P2  
19.1320426  72.9178202  12.04   P3  
19.1320421  72.9177745  12.04   P4  

Plane eqn:

-0.999945876x+0.010404061y+0z-18.37241258 =0

Point:19.13208745   72.91761882 2.35762E-06

Can anyone describe or provide a link for how to find a point lies within or not in the plane that will help me understand and implement them?

Answer 1

If you plug in the values into the equation, then if the equality holds, the point lies in the plane. This means all you have to do is plug in x, y and z into the equation and check if it is equal to 0.

It's important to consider that you are using decimals here, so to make sure a rounding error does not throw you off you can simply check if its within a threshold.

Answer 2

A plane equation is the equation that will give a 0 for any points inside that plane. You already have the plane equation, so all you need to do is to enter the new x, y, z in the equation. If you get 0 then the point is in that plane.

Answer 3

Substituting the coordinates in the plane equation you should get zero if the point lies within the plane.