From vertices to Equations of the Plane

Hi!

I was wondering whether there is a Matlab function which can calculate the equation of a plane from the vertices. Let's say that I have the following three vertices:

(0,0,0), (2,3,6) and (3,1,5)

Then I would like to have a function that gets these vertices as input and gives me the equation of a plane as output, which is 9x+8y-7z+0=0. In fact, I found such a tool online: http://keisan.casio.com/exec/system/1223596129

but I would like to have the same function in Matlab (preferably the one which also can handle more dimensions).

Does such a function exist?

Thanks!

Alex

[sixwwwwww]

Do you like this function to be written? or you need some pre-defined function in MATLAB for this purpose?

Answer 1

[Cedric]

Hint: you can start with the following and implement the few additional computations required (realizing that a 4th parameter must be computed)..

 >> v1 = [0,0,0] ; v2 = [2,3,6] ; v3 = [3,1,5] ;
 >> n = cross(v2-v1, v3-v1)
 n =
     9     8    -7

Answer 2

[Matt J]

There is also vert2lcon in this FEX submission. http://www.mathworks.com/matlabcentral/fileexchange/30892-representing-polyhedral-convex-hulls-by-vertices-or-inequalities

The equality constraints give the equation for the plane. You can ignore the inequality constraints.

It will also handle N-dimensions, for N not too large.

[Matt J]

So, using your example data

    >> [~,~,Aeq,beq]=vert2lcon([0 0 0; 2 3 6; 3 1 5]);

    >> s=9/Aeq(1); Aeq=s*Aeq, beq=s*beq

    Aeq =

        9.0000    8.0000   -7.0000

    beq =

         0