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calculation the angle betwen X-axis created due coordinate system rotation - after projection the coordinate system on the plane

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UWM
UWM on 13 Jan 2020
Answered: darova on 13 Jan 2020
CCF_000030.jpg
I have a coordinate system XYZ (black on figure) which can be rotated around
Z axis (Zrot angle) or around Y axis (Yrot angle) or around both axisies (around Z first and then around rotated (in first rotation around Z axis) Y axis).
E.g. after rotation only around Z axis we get X'Y'Z coordinate system (see fig).
I have also the direction (point P) defined by azimuth and evation (e.g. AZ, EL) in XYZ coordinate system (blue on figure).
Rotation code are below:
% geodetic elevation and azimuth in deg(El, AZ)
Esvo = 50;
Asvo = 30;
% MatLab elevation and azimuth
Esv = Esvo;
Asv = Asvo;
if Asvo < 180; Asv=-Asvo;
else Asv = 360-Asvo;
end
r=1
dtr = pi/180;
Es=Esv*dtr % deg to rad conversion
As=Asv*dtr % deg to rad conversion
% initial position in MatLab
[x0,y0,z0] = sph2cart(As,Es,r)
poz0 = [x0 y0 z0]
% coordinate system rotation angles in deg (Zrot=Aro1; Yrot=Ero1)
Ero1 = 10;
Aro1 = 40;
% AZ change after Zrot rotation (geodetic)
Asvn = Asvo-Aro1
% chenged AZ in MatLab
if Asvn < 180; Asvn=-Asvn;
else Asvn = 360-Asvn;
end
Esv=Esv*dtr % deg to rad conversion
Asvn=Asvn*dtr % deg to rad conversion
% position after rotation around Z-axis
[x1,y1,z1] = sph2cart(Asvn,Esv,r)
poz1 = [x1 y1 z1]
% rotation around Y-axis
ROTY = [ cosd(Ero1) 0 sind(Ero1);
0 1 0;
-sind(Ero1) 0 cosd(Ero1)];
% position after two rotation (in MatLab)
poz2 = poz1*ROTY;
x2 = poz2(1);
y2 = poz2(2);
z2 = poz2(3);
I would like to create a PLANE (red on figure) which is perpendicular to direction P (direction P will be normal to PLANE) and then calculate angle B
which is the difference betwen X and X' axisies orthogonally projected on PLANE (red on fig).
Any suggestions how can be it done?

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Answers (1)

darova
darova on 13 Jan 2020
Here is an idea of how to project axis onto plane:
  • Unit vector (normal) of a plane:
  • Distance to plane:
  • Axis projected onto plane:
123.png
Having both projected axes:

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