How can I plot a 3D plane knowing its center point coordinates and its Normal

How can I plot a 3D plane knowing its center point coordinates and its Normal ?

Answer 1

[Roger Stafford]

Using Dr. Siva’s notation with the point at (x1,y1,z1) and normal vector v = [a,b,c], (v should be a row vector,) you can plot a surface version of the plane with this:

   w = null(v); % Find two orthonormal vectors which are orthogonal to v
   [P,Q] = meshgrid(-50:50); % Provide a gridwork (you choose the size)
   X = x1+w(1,1)*P+w(1,2)*Q; % Compute the corresponding cartesian coordinates
   Y = y1+w(2,1)*P+w(2,2)*Q; %   using the two vectors in w
   Z = z1+w(3,1)*P+w(3,2)*Q;
   surf(X,Y,Z)

[Abeer Heikal]

Thanks Roger a lot. I tried it and it works perfectly. I have a small wonder though. For this normal and the center point there can be infinite number of 3D planes. I do have a Dip and Dip Direction info for my planes. Can you kindly advise how can I implement this extra info into your suggested Matlbab script to generate a unique 3D plane?

[Roger Stafford]

If I understand you correctly Abeer, I have to disagree with your statement that "there can be infinite number of 3D planes". For a 3D plane to have a given normal direction and to contain a given point makes that plane absolutely unique - no other such plane is possible. Remember, we are speaking of mathematically perfectly flat planes, not curved ones.

Answer 2

[KSSV]

You know a point (x1,y1,z1) and normal vector (a,b,c). Then equation of plane should be:

a(x-x1)+b(y-y1)+c(z-z1) = 0 ;

[Abeer Heikal]

Thanks Dr. Siva

I know this, but I don't know how to write it in Matlab since I m new to Matlab. I appreciate it if you can help me by any way.

Answer 3

[Nitin Phadkule]

% ax+by+cz+d plane
        % 3x+2y+6z+2 plane
          y =linspace(-4,4,51);
        a=3;b=2;c=6;d=2;
          x =linspace(-4,4,51);
          [y2,x2]=meshgrid(y ,x );
            z2=(1/c).*(d+(a.*x2)+(b.*y2));% ax+by+cz+d plane
            surf( x2,y2,z2 );