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

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Abeer Heikal 2016-6-22

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回答： Nitin Phadkule 2021-9-18

采纳的回答： Roger Stafford

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

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Answer 1

Roger Stafford 2016-6-23

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编辑：Roger Stafford 2016-6-23

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)

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Abeer Heikal 2016-6-26

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 2016-6-27

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.

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