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math3dpointplane

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

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?

Solution

  • 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.