MATLAB: How to measur the inclination angle of a palne

3d plotsplane direction angles

Let's say I have plane with two known points p1(x1, y1, z1) and p2(x2, y2, z2) somewhere in space. Is there any way to measure the inclination angle\angles for that plane? Which angle from the three angles (with respect to x, y or z axes) can be considered the inclination angle of that plane? Or I need calculate the three inclination angles?

Or I can say it in other way to add more details:

I have four known extrimeties points of a plane. I derived the plain equation from three known points only. Then, I measure the longest diagonal of the plane and I need to measure the inclination angle from that diagonal vector which has two known points. I attached a file that explain the problem with more details.

Can you help me please because i can't find any answer for a while.

Best Answer

Is there a way?

NO. Sorry, but absolutely not since two points do not determine a plane. There are infinitely many planes that will pass through any two points, Each of which can lie at any angle you so desire.

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MATLAB: Angle between a plane and horizontal

The angle between the two planes are the angle between the two normal vectors, so your approach is correct. I'm not sure why you need to do atand though. I think once you do the dot product, you can use acosd directily

MATLAB: Loosing quadrant data using atan2 when finding angle between 3 points (in 3D space) in MATLAB

You diagram looks like 2D and not 3D.

In 3D you can turn around and look in opposite direction. The atan2 formula assume you look from the cross vector direction and thus the angle is always > 0.

If you have a preference direction (for example vector normal and come out of your drawing plane) you need to take the dot product of the cross-vector and this normal vector and reverse the sign.

d = [0;0,1] % your preference direction
x = cross(v1,v2);
nx = norm(x);
A = atan2(nx, dot(v1,v2));
x = x / nx;
if dot(x,d) < 0
  x = -x;
  A = -A;
end
% v2 is obtained by rotating v1 about the (unit) x vector of angle A radian

Best Answer

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MATLAB: Angle between a plane and horizontal

MATLAB: Loosing quadrant data using atan2 when finding angle between 3 points (in 3D space) in MATLAB

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